Operations Management for Environmental Sustainability: Operational Measures, Regulations and Carbon Constrained Decisions 9783031376023, 9783031376009, 3031376005

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SpringerBriefs in Operations Management Guowei Dou · Lijun Ma · Kun Wei · Qingyu Zhang

Operations Management for Environmental Sustainability Operational Measures, Regulations and Carbon Constrained Decisions

SpringerBriefs in Operations Management Series Editor Suresh P. Sethi, The University of Texas at Dallas, Texas, USA

SpringerBriefs present concise summaries of cutting-edge research and practical applications across a wide spectrum of fields. Featuring compact volumes of 50 to 125 pages, the series covers a range of content from professional to academic. Typical topics might include: • A timely report of state-of-the art analytical techniques • A bridge between new research results, as published in journal articles, and a contextual literature review • A snapshot of a hot or emerging topic • An in-depth case study or clinical example • A presentation of core concepts that students must understand in order to make independent contributions SpringerBriefs in Operations Management showcase emerging theory, empirical research, and practical application in the various areas of operations management (OM), supply chain management (SCM), germane elements of Operations Research (optimization, stochastic modeling, inventory control, etc.) and all related areas of Decision Science and Analytics as applied to the practice of OM, from a global author community. Briefs are characterized by fast, global electronic dissemination, standard publishing contracts, standardized manuscript preparation and formatting guidelines, and expedited production schedules.

Guowei Dou • Lijun Ma • Kun Wei • Qingyu Zhang

Operations Management for Environmental Sustainability Operational Measures, Regulations and Carbon Constrained Decisions

Guowei Dou College of Management and Institute of Big Data Intelligent Management and Decision Shenzhen University Shenzhen, Guangdong, China

Lijun Ma College of Management and Institute of Big Data Intelligent Management and Decision Shenzhen University Shenzhen, Guangdong, China

Kun Wei College of Management Shenzhen University Shenzhen, Guangdong, China

Qingyu Zhang College of Management Shenzhen University Shenzhen, Guangdong, China

ISSN 2365-8320 ISSN 2365-8339 (electronic) SpringerBriefs in Operations Management ISBN 978-3-031-37602-3 ISBN 978-3-031-37600-9 (eBook) https://doi.org/10.1007/978-3-031-37600-9 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Paper in this product is recyclable.

To our families and friends.

Preface

Environmental sustainability has received increasing attention from both governments and enterprises over the last few decades. Governments around the world “placed global warming and greenhouse-gas reduction as one of highest priorities” (Pelosi, 2007), and business executives put the issues related to the environment at the top of their agendas (Krass et al., 2013). For example, as the largest developing country, the Chinese government is committed to achieving “carbon neutrality” in 2060; Apple Inc. takes great responsibility for environmental protection, and effort has been devoted to realizing “carbon neutrality” for every single product by 2030. Concerning environmental sustainability, operational issues under emission regulations on both firms and supply chains have been widely studied. The research in this area mainly explores ways to control carbon emissions from both the firm’s (supply chain’s) and government’s perspectives by modeling a dynamic game between them. As the game leader, the government decides emission regulations such as carbon tax, emission permit cap, and economic incentives such as subsidy or consumer rebates, while as the follower, firms or supply chains decide the production scale, the product price, ways of collaboration, and the effort or investment for green production technologies. Although many researchers have studied challenges related to environmental sustainability and the roles that manufacturers and governments play in this domain, there are still many more opportunities to improve industry practices and governmental policies. In this book, from some novel perspectives, we develop stylized analytical models to explore optimal decisions for firms, supply chains, and the government to develop an eco-friendly economy. First, considering differentiated emission permit-buying and emission permit-selling prices, we explore the optimal emission permit cap of the government under cap-and-trade regulation. Second, based on the practice that the carbon tax may vary from time to time, we explore how to establish a two-period carbon tax scheme for firms on a two-period planning horizon. Then, under the carbon tax policy, we come to the context of supply chains, where we explore how to balance the economic and environmental performances in a closedloop supply chain, how to implement trade-in programs when employing green vii

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technology, and how to strategically use blockchain technology to improve the supply chain’s environmental performance. This book is written for students, researchers, and practitioners to better understand operation management under emission constraints and to provide directions/instructions on how to improve environmental sustainability. We wish to thank Tsan-Ming Choi, Xiaoping Xu, Wei Zhang, and Ping He, who have worked with us in the area of operation management for sustainability. Also, we would like to thank the anonymous reviewers for their valuable comments and suggestions on the improvement of this book, and we would like to express our deep gratitude to the production team for their support for the publication of this book, especially to Senior Editor Poongothai Chockalingam. This book is supported in part by the National Natural Science Foundation of China (Nos.71701135, 71871145, 72031004), Key Project of the National Social Science Foundation of China (21AGL014); Natural Science Foundation of Guangdong (2021A1515011894, 2023A1515012268); Guangdong 13th-Five-Year-Plan Philosophical and Social Science Fund (GD20CGL28); and Shenzhen Science and Technology Program (JCYJ20210324093208022, 20220804114140001). We are grateful for their financial support. Shenzhen, China December 2022

Guowei Dou Lijun Ma Kun Wei Qingyu Zhang

References Krass, D., Nedorezov, T., & Ovchinnikov, A. (2013). Environmental taxes and the choice of green technology. Production and Operations Management, 22(5), 1035–1055. Pelosi, N. (2007). Green expectations. The Economist, November 15. Available at http://www.economist.com/node/10093979

Contents

1

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Aim of This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 4 5

2

Production Planning and Cap-Setting Under Cap-and-Trade Regulation Considering Differentiated Emission Trading Prices . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Optimal Decisions of the Manufacturer . . . . . . . . . . . . . . . . . . . . 2.5 Optimal Cap of the Regulator . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7 7 8 10 12 17 20 21 26

A Two-Period Carbon Tax Regulation for Manufacturing and Remanufacturing Production Planning . . . . . . . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Modeling Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 No Remanufacturing Case . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Remanufacturing Case . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Results and Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Comparisons of the Cases With and Without Remanufacturing . . . 3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29 29 31 33 34 34 35 40 44 46 51

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A Joint Analysis of the Environmental and Economic Performances of Closed-Loop Supply Chains Under Carbon Tax Regulation . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Operational Decisions Concerning Remanufacturing . . . . . 4.2.2 Environmental Implications Concerning Remanufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Benchmark Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Remanufacturing Cases . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Environmental Impact of Remanufacturing . . . . . . . . . . . . 4.4.2 Entire Emissions Among the CLSCs . . . . . . . . . . . . . . . . . 4.4.3 Entire Profits Among the CLSCs . . . . . . . . . . . . . . . . . . . 4.5 Numerical Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Impacts of the Emission Intensities on All Emissions . . . . . 4.5.2 Government’s Subsidy and Tax Price . . . . . . . . . . . . . . . . 4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Does Implementing Trade-In and Green Technology Together Benefit the Environment? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . 5.1.2 Research Questions and Major Findings . . . . . . . . . . . . . . 5.1.3 Contribution Statements and Organization . . . . . . . . . . . . . 5.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Trade-In Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Closed-Loop Supply Chains . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 Emission Abatement Decisions . . . . . . . . . . . . . . . . . . . . . 5.2.4 Government Policies for Environmentally Sustainable Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Basic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Benchmark Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Models with GT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Comparisons and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 Pricing Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Impacts of the Carbon Tax and the Emission Abatement Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.3 Environmental Performance . . . . . . . . . . . . . . . . . . . . . . . 5.4.4 Economic Performance . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Government Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Extension: Consumers’ Environmental Awareness . . . . . . . . . . . .

53 53 55 55 56 57 57 58 64 64 65 67 69 70 71 72 73 82 85 85 85 87 88 89 89 90 91 92 92 92 95 97 98 99 100 102 103 106

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Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7.1 Concluding Remarks and Managerial Insights . . . . . . . . . . 5.7.2 Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Coordination of a Supply Chain with an Online Platform Considering Green Technology in the Blockchain Era . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . 6.1.2 Research Questions and Major Findings . . . . . . . . . . . . . . 6.1.3 Contribution Statement and Paper’s Structure . . . . . . . . . . 6.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 The Selection of Online Platform Modes . . . . . . . . . . . . . . 6.2.2 Emission Abatement Decision of a Dual-Channel Supply Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.3 Coordination of a Dual-Channel Supply Chain . . . . . . . . . 6.3 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Optimal Operational Decisions . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.1 Marketplace Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.2 Reselling Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Supply Chain Coordination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.1 The Optimal Decisions in the Centralized Supply Chain . . . 6.5.2 Supply Chain Coordination via Marketplace Mode . . . . . . 6.5.3 Supply Chain Coordination via the Reselling Mode . . . . . . 6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

123 123 123 125 126 126 126 127 128 129 130 130 132 133 133 135 136 138 139 146

Chapter 1

Overview

1.1

Introduction

Environmental sustainability has been one of the main concerns for governments, practitioners, and researchers for a long time. In particular, concerns about carbon emissions rise in most countries and regions all over the world. Currently, “carbon neutrality” has been taken as the target of environmental protection for most countries. For instance, the Chinese government announced that it will strive to peak carbon dioxide emissions by 2030 and achieve carbon neutrality by 2060,1 and Europe turns carbon neutrality goals into laws that they commit to reach climate neutrality by 2050.2 To alleviate the impact of carbon emissions, some regulations and legislations have been proposed and applied in many countries. Among these regulations and legislations, carbon emission trading (also known as “cap-and-trade,” a marketbased mechanism to curb emissions from firms) has been broadly adopted by agencies and governments (Gong & Zhou, 2013; Choi, 2013; He et al., 2017; Thompson et al., 2018; Pan et al., 2019). The European Union’s Emission Trading System (EU ETS) is the first and largest international scheme for emission permit trading. In 2010, the EU ETS covered 11,000 power stations and industrial plants in 30 countries (DG CLIMA, 2010) and involved over 50% of all emissions in the European Union (Benjaafar et al., 2013). During the “third stage” (2013–2020) of the European Union’s Emissions Trading Scheme, over which 57% of the total allowances were “auctioned,” while the remaining allowances were available for free.3 As we can observe, the settlement price of the emission allowance was 23.28

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http://www.China.org.cn/opinion/2021-02/02/content_77180870.htm http://www.chinadaily.com.cn/a/202104/22/WS6080d2b2a31024ad0bab9841.html 3 https://ec.europa.eu/clima/policies/ets/allowances_en 2

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Dou et al., Operations Management for Environmental Sustainability, SpringerBriefs in Operations Management, https://doi.org/10.1007/978-3-031-37600-9_1

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Overview

€/ton on 2 February 2020.4 In China, seven emission trading markets are established (with the first one in Shenzhen). In the Shenzhen ETS, up to 10% of the allowances may be given to enterprises without charges, and a reserve equal to 3% will be auctioned.5 Note that the average emission trading price was 5.16 RMB/ton in December 2019.6 In addition to cap-and-trade regulations, emission taxes are taken as another main regulation around the world (Yenipazarli, 2016). For instance, in January 2018, Argentina implemented a carbon tax covering most “liquid fuels” at a price of 10 USD per ton of emissions. In January 2019, the tax also became operational for other fuels such as “fuel oil, mineral coal, and petroleum coke” at 10% of the full tax rate. The tax is estimated to cover approximately 20% of the nation’s “GHG emissions.”7 In June 2018, the “Greenhouse Gas Pollution Pricing Act” was implemented in Canada, which required that all provinces in Canada launch a carbon pricing policy by 1 January 2019, and the requirements would increase each year until 2022.8 In the United Kingdom, the carbon price (tax) was introduced in 2013 at a rate of 4.94 British pounds per ton of emission. The rate is capped at 18 British pounds until 2021.9 In 2019, South Africa recently introduced an economy-wide carbon tax (the first carbon tax regulation in Africa). Additionally, in the same year, Singapore brought in a carbon tax for all “large emitters.”10 In response to these regulations, sustainable development and environmentally friendly business have been taken as critical priorities by enterprises, and incorporating emission abatement into production planning becomes indispensable concerning manufacturers’ operational planning. For instance, an increasing number of manufacturers employ green technologies in the process of manufacturing to lower the emissions generated from this process. Specifically, as outlined in the WBCSD (2009) report, carbon capture and storage (CCS) is the key technology driving significant carbon emission reduction in cement manufacturing. Carbon emissions with CCS are projected to be 0.54 tons per ton of clinker, compared with 2.34 (gas) to 4.4 (coal) tons without CCS. In the manufacturing of electronic devices, Apple focuses on making energy-efficient products with the wide use of “renewable energy” and recycled materials.11 Among the Apple products, the iPhone 13 Pro Max is the first to use 100% certified recycled gold in the plating of

4

https://www.eex.com/en/market-data/environmental-markets/spot-market/european-emissionallowances 5 http://www.cerx.cn/inventoreducation/364.htm 6 http://ggzy.sz.gov.cn/cn/jyxx/tpfq/jggg/202001/t20200106_18966929.htm 7 https://climateactiontracker.org/countries/argentina/ 8 https://canada.citizensclimatelobby.org/laser-talk-canadas-carbon-pricing-policy/ 9 https://www.ucl.ac.uk/consultants/news/2020/jan/british-carbon-tax-leads-93-drop-coal-firedelectricity 10 https://cleantechnica.com/2019/10/24/the-development-of-global-carbon-taxes-monthly update/ 11 https://www.apple.com/environment/pdf/products/iphone/iPhone_11_Pro_PER_sept2019.pdf

1.1

Introduction

3

the main logic board and 100% recycled rare earth elements in all magnets.12 Now, Apple announces that they have realized carbon neutrality for their operation until 2020, and this target will be realized for all the products of Apple in 2030. Similarly, Samsung has made a “planet-first” commitment, leading to its innovative bioplasticbased mobile phones composed of industrial corn waste and recycled plastic. Despite the advancement in technology, low-carbon operations also play a critical role in reducing the overall emissions for manufacturers. For instance, Samsung operates the “Re + program” to recover end-of-life products, whereby it collected and processed 3.12 million tons of electronic waste worldwide from 2009 to 2017,13 and the accumulated emissions reduced for the product use phase reached 301 million tons from 2009 to 2020.14 Based on the recollection program, manufacturers are able to take further measures, such as remanufacturing, to reduce carbon emissions. Due to the less material and less energy that are consumed throughout the remanufacturing process, the remanufactured products become greener. Together with the recollection, many firms also implement trade-in programs for a wide range of products, such as household appliances, mobile phones, and even electronic vehicles (e.g., Tesla and BYD). Trade-in programs encourage consumers to buy new products with rebates; more importantly, the newly released products are manufactured with more advanced technology and thus are more environmentally friendly. Therefore, trade-in programs efficiently help lower emissions. On the consumer side, evidence shows that consumers are becoming more environmentally conscious; thus, “greener” products are increasingly preferred by consumers (Ji et al., 2017). Catering with this preference, together with the use of green technologies, digital technology such as blockchain is increasingly used to enhance consumers’ trust in the greenness of products, thus promoting consumers’ purchasing behavior (Dutta et al., 2020; Cai et al., 2021). As we can observe in practice, in 2011, on TMALL.com (one of the largest e-commerce platforms in China), 0.4 billion commodities were endowed with digital identity with the use of blockchain technology, and consumers were able to obtain access to the related information. Therefore, the application of blockchain technology helps consumers ensure the authenticity of green information, which can increase the possibility for consumers to buy green products (Choi, 2019). From the perspective of operations management, the above practices lead us to the following questions: (1) under the emission regulation of the government, how should manufacturers make a series of operational decisions, such as how to make production planning for both manufacturing and remanufacturing, how to set the optimal product price, how to invest in the use of green technology and how to choose the type of green technology, how to implement the trade-in program, and

12

https://www.apple.com/environment/pdf/products/iphone/iPhone_13_Pro_Max_PER_ Sept2021.pdf 13 https://www.samsung.com/cn/aboutsamsung/sustainability/development/environment/our-com mitment/eco-management/ 14 https://www.samsung.com/au/sustainability/environment/climate-action/

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how to use digital technology, such as blockchain, to promote consumers’ environmental-concern purchasing behavior? (2) On the regulation side, how can regulatory decisions be made, such as setting the emission cap and deciding the emission tax price or the subsidy, to better enhance environmental sustainability? (3) What are the impact mechanisms of the market characteristics on the decisions for both the government and the manufacturers, or what are the boundary conditions (and the corresponding properties) for the government and the manufacturers to change their decisions? By building mathematical models, we will try to explore answers to these questions. Next, we elaborate on the specific aim of this book.

1.2

Aim of This Book

This book aims to explore the operational measures of manufacturers or supply chains that are regulated by carbon emission regulations from the government. Two widely implemented emission regulations are considered, i.e., cap-and-trade regulation and carbon tax regulation. The operational strategies of manufacturers include production planning and pricing, product collection and remanufacturing, the investment and use of green technology, trade-in programs, channel relationship selection, and the use of blockchain technology. For each optimization of the operational strategy for the manufacturer or the supply chain, we further explore the regulatory decisions for the government from a game-theoretical perspective, including how to set the emission cap and the emission tax price. Five chapters are presented to cover the content above. In Chap. 2, we explore the production planning and pricing decisions of a selfpricing manufacturer and the optimal cap setting decisions of a regulator under capand-trade regulation. The manufacturer has to incorporate the carbon emissions and the corresponding costs into his optimal decisions. Initially, the manufacturer receives an emission cap at the beginning of his planning horizon; then, he can buy some emission permits if the cap is not sufficient or sell the extra emission permits, with a lower selling price than the buying price. Then, with the objective of maximizing social welfare, we explore how to set the optimal emission cap from the perspective of the government. In Chaps. 3 and 4, we discuss the operational measures in terms of remanufacturing over two periods. In the first period, new products are manufactured and sold to the market; then, in the second period, used products are collected, remanufactured, and sold to consumers. On the basis of the manufacturer’s or the supply chain’s decisions, we explore how to set the emission tax prices over the two periods, that is, we explore the possibility and feasibility of implementing a periodic emission tax scheme. By doing so, we try to explore the relationship between the flexibility of regulation and environmental performance or social welfare. Additionally, we jointly analyze the environmental and economic performances of closed-loop supply chains under carbon tax regulation, where remanufacturing is implemented through the reverse channels of retailer collection, manufacturer collection, and third-party collection. Through both theoretical and

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5

numerical analyses, we explore the more efficient reverse channel and emission tax price, which help derive the Pareto improvement. In Chap. 5, we explore whether environmental performance can be double improved when both green technology and trade-in programs are implemented. Three scenarios are considered, i.e., the manufacturer (the retailer) collects used products without using green technology, the manufacturer (the retailer) collects used products, and the manufacturer uses green technology. Then, we explore the optimal emission tax and subsidy policy for the government, and the emission taxes and the corresponding subsidy for both consumers and manufacturers are summarized. Finally, in Chap. 6, we consider a supply chain consisting of a manufacturer and a retailer, where the manufacturer adopts green technology and blockchain technology and sells its products through the retailer and an online platform. We explore the impact of blockchain technology in promoting the greenness of products and economic gains for the manufacturer and the platform, respectively. In addition, the coordination mechanisms of the supply chain are discussed.

References Benjaafar, S., Li, Y., & Daskin, M. (2013). Carbon footprint and the management of supply chains: Insights from simple models. IEEE Transactions on Automation Science and Engineering, 10(1), 99–116. Cai, Y. J., Choi, T. M., & Zhang, J. (2021). Platform supported supply chain operations in the blockchain era: Supply contracting and moral hazards. Decision Sciences, 52(4), 866–892. Choi, T. M. (2013). Local sourcing and fashion quick response system: The impacts of carbon footprint tax. Transportation Research Part E: Logistics and Transportation Review, 55, 43–54. Choi, T. M. (2019). Blockchain-technology-supported platforms for diamond authentication and certification in luxury supply chains. Transportation Research Part E: Logistics and Transportation Review, 128, 17–29. DG CLIMA. (2010). The EU Emission Trading System (EU ETS). http://ec.europa.eu/clima/ policies/ets/index_en.htm. Dutta, P., Choi, T. M., Somani, S., & Butala, R. (2020). Blockchain technology in supply chain operations: Applications, challenges and research opportunities. Transportation Research Part e: Logistics and Transportation Review, 142, 102067. Gong, X., & Zhou, S. X. (2013). Optimal production planning with emissions trading. Operations Research, 61(4), 908–924. He, P., Dou, G., & Zhang, W. (2017). Optimal production planning and cap setting under cap-andtrade regulation. Journal of the Operational Research Society, 68(9), 1094–1105. Ji, J., Zhang, Z., & Yang, L. (2017). Carbon emission reduction decisions in the retail-/dual-channel supply chain with consumers’ preference. Journal of Cleaner Production, 141, 852–867. Pan, Y., Yang, W., Ma, N., Chen, Z., Zhou, M., & Xiong, Y. (2019). Game analysis of carbon emission verification: A case study from Shenzhen’s cap-and-trade system in China. Energy Policy, 130, 418–428. Thompson, W., Johansson, R., Meyer, S., & Whistance, J. (2018). The US biofuel mandate as a substitute for carbon cap-and-trade. Energy Policy, 113, 368–375.

6

1

Overview

World Business Council for Sustainable Development (WBCSD). (2009). Cement Technology Roadmap 2009: Carbon Emissions Reductions up to 2050. Available at http://www.wbcsd. org/DocRoot/mka1EKor6mqLVb9w903o/WBCSD-IEA_Cement Roadmap.pdf. Yenipazarli, A. (2016). Managing new and remanufactured products to mitigate environmental damage under emissions regulation. European Journal of Operational Research, 249(1), 117–130.

Chapter 2

Production Planning and Cap-Setting Under Cap-and-Trade Regulation Considering Differentiated Emission Trading Prices

2.1

Introduction

As a natural byproduct in many firms’ production processes, carbon emissions are generated as an undesirable output. To alleviate the impact of carbon emissions, some regulations and legislations have been proposed and applied in many countries. Carbon emission trading, also known as “cap-and-trade,” is a market-based mechanism to curb emissions from firms. It has been broadly adopted by agencies and governments. The European Union Emission Trading System (EU ETS) is the first and largest international scheme for the trading of emission permits. Under capand-trade regulation, firms receive an initial quantity of permits (i.e., the “cap”) on their emissions for free from regulators, and they are simultaneously authorized to purchase more permits or sell excess permits via an outside emission trading market (Yale, 2008). With this regulation, firms’ production will be affected since the cost associated with carbon emissions should be considered. In this chapter, we investigate the optimal operational decisions of a self-pricing manufacturer and the optimal cap of a regulator under cap-and-trade regulation. To derive the optimal solutions, a Stackelberg game model is proposed. The regulator is the leader, which sets the emission cap to the manufacturer to maximize social welfare. The manufacturer is the follower, which makes the optimal joint production and pricing decisions to maximize its profit with the given emission cap. In our analysis, we first derive the manufacturer’s optimal joint production and pricing decisions and the corresponding total emissions (optimal total emissions for short) under varying cases and then solve the regulator’s optimal emission cap to maximize social welfare. Moreover, some properties of both players’ optimal solutions with respect to production and regulation parameters (e.g., emission intensity, emission trading prices) are explored, and some special results are found. In particular, in this chapter, we assume that the permit purchasing price is not lower than the permit selling price, which plays a key role in deriving the optimal solutions. Although we © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Dou et al., Operations Management for Environmental Sustainability, SpringerBriefs in Operations Management, https://doi.org/10.1007/978-3-031-37600-9_2

7

8

2 Production Planning and Cap-Setting Under Cap-and-Trade. . .

call them prices, they actually represent the marginal cost and revenue of purchasing and selling one unit permit, respectively. They can be quite significant and have been studied both empirically and theoretically (Stavins, 1995; Woerdman, 2001). In practice, and the literature, the method of permit allocation can be classified into three main ways other than cap-and-trade: grandfathering, benchmark, and permit auction. Nevertheless, each method has its shortcomings. Grandfathering allocates permits to firms free of charge on the basis of historical emissions or process inputs (Subramanian et al., 2007). Therefore, it is difficult to give the accurate permit quota generally by grandfathering, and much income is lost in contrast to auction. Consequently, the opportunity cost rises to a high level. Benchmarks are a means of reallocating permits periodically according to the emission targets of firms; although they reduce costs compared to grandfathering, benchmarks are confirmed to be hard to execute (Edwards & Hutton, 2001). Auction is a biding way to acquire permits and is considered much more effective (Cramton & Kerr, 2002), but it increases the cost of firms in permit hunting compared to the first two ways. In this chapter the permit allocation from a game-theoretical perspective under cap-and-trade regulation is effective not only in allocating the accurate permit quota compared to grandfathering and benchmark but also in reducing the permit-hunting cost of firms because of the free initial cap compared to auction. To our knowledge, there is already some research studying the regulator’s problem by means of gametheoretical analysis (Krass et al. (2013), for instance).

2.2

Literature Review

In the literature, although there are already many theoretical and empirical studies focusing on carbon emission regulations (David, 2005; Wey & Yang, 2005; Hovi & Holtsmark, 2006; Yale, 2008; Mandell, 2008; Harrison & Smith, 2009; Carbone et al., 2009), little research has been done on the operational decisions under these regulations. We review some of them here. Bauer et al. (2009) incorporate environment-related costs into freight transportation planning and propose an integer program that minimizes the amount of greenhouse gas emissions from transportation activities. Kim (2014) provides a Lagrangian heuristic for mathematically determining the variable speed and bunkering port with a nonlinear program to minimize the bunker fuel, ship time costs, and carbon tax imposed on greenhouse gas emissions. Yalabik & Fairchild, (2011) examine the effects of consumer, regulatory, and competitive pressure on firm abatement investments and analyze a scenario where two firms compete for emission-sensitive customers. Hoen et al. (2011) analyze the effects of two regulation mechanisms on the transport mode selection decision. Although environmental cost or penalty is taken as the emission constraint, cap-and-trade is not included in the above studies. In contrast, some other studies are on the background of cap-and-trade. For instance, Zhang et al. (2011) address the problem of a manufacturer’s optimal production policy under stochastic demand in the cap-and-trade system. Du et al. (2011) give a

2.2

Literature Review

9

game-theoretical analysis for an emission permit supplier and an emissiondependent firm within a supply chain in a setting of cap-and-trade regulation. However, the situation of selling redundant emissions is not modeled as well as emission purchasing in both papers. Benjaafar et al. (2013) introduce a series of simple and general models to illustrate how carbon footprint considerations could be incorporated into operational decisions, where many observations and insights are obtained. Hua et al. (2011) investigate how firms react in inventory management under carbon emission regulation based on the EOQ model. They derive the optimal order quantity and examine the impacts of regulation parameters on optimal decisions, carbon emissions, and total costs. Zhang and Xu (2013) investigate the multi-item production planning problem with a carbon cap-and-trade mechanism under stochastic demand. These studies incorporate both emission purchasing and selling scenarios. Nevertheless, the prices of emission purchasing and selling are assumed to be equal, as is done in most of the existing studies. To the best of our knowledge, the only study that distinguishes permit purchasing and selling prices is Gong and Zhou (2013). They investigate the impact of emission trading on a manufacturer’s technology choice and production planning by modeling different permit purchasing and selling prices. Since a firm can either purchase permits from or sell permits to agencies through an emission trading market, the permit purchasing and selling prices could be different. Similar to Gong and Zhou (2013), we in particular assume the permit purchasing price to be no lower than the permit selling price in this chapter, which plays a key role in deriving some novel insights concerning the optimal solutions. Thus, the scenario in which the permit trading prices are equal is a special case of our exploration in this chapter. Drake et al. (2010) study a two-stage decision problem of a firm under two regulations (cap-and-trade and carbon tax). In the first stage, the firm chooses production capacities in a “dirty” and a “clean” technology. Given the technology choice, the firm in the second stage chooses production quantities to maximize its profit. Letmathe and Balakrishnan (2005) study the production mix and production quantities of a firm under several different types of environmental constraints, including threshold values, penalties and taxes, and/or emission trading. Subramanian et al. (2007) model a three-stage game in which firms first invest in emission abatement, then participate in a share auction for permits, and produce output. Apart from operational issues that are analyzed in the above studies, we also study the regulator’s problem concerning the optimal cap-setting strategy. To the best of our knowledge, the only two works analyzing the regulator’s problem are Krass et al. (2013) and Du et al. (2012). The latter research focuses on a so-called emission-dependent supply chain in the cap-and-trade system. They analyze the effect of emission regulation on the decision-making of the supply chain as well as distribution fairness in social welfare. However, the authority problem is investigated from the perspective of maximizing the total utility of the supply chain. In comparison, Krass et al. (2013) study several important aspects of using environmental taxes as well as the role of fixed cost subsidies and consumer rebates to motivate the choice of innovative and “green” emission-reducing technologies. In

10

2 Production Planning and Cap-Setting Under Cap-and-Trade. . .

addition, they analyze the problem of the regulator that anticipates the firm’s reaction to the environmental policy and thus sets the levels of taxes, subsidies, and rebates strategically from a social welfare maximizing perspective. In their analysis, social welfare equals the sum of consumers and the manufacturer’s surplus mining the environmental damage measured by multiplying the emission by a certain coefficient. We model the regulator’s problem in a similar way to later research, but considering that much more serious damage would be caused by an increasing unit of emissions, we define social welfare loss caused by emissions with quadratic environmental damage to be more consistent with practice. Such a social welfare loss definition, together with the distinct permit purchasing and selling prices, constitutes the two critical aspects that enable this work to differentiate itself from the existing research. The remainder of this chapter is organized as follows: In Sect. 2.3, we formulate the profit-maximizing problem of the manufacturer and the social welfare model of the regulator under cap-and-trade regulation. In Sect. 2.4, we derive the manufacturer’s optimal production quantities (correspondingly the optimal total emissions) with a given emission intensity and cap-and-trade regulation under different circumstances. In Sect. 2.5, we explore the regulator’s optimal cap to maximize the social welfare of the whole system. In addition, the properties of the optimal solutions with respect to some parameters are also explored. Finally, in Sect. 2.6, we summarize the paper and give some suggestions on topics for future research.

2.3

Problem Formulation

This chapter considers the optimal solutions of a self-pricing manufacturer and the optimal cap of a regulator under cap-and-trade regulation. We model them as a Stackelberg game model, where the regulator acts as the leader and the manufacturer acts as the follower. During the analysis, we first derive the manufacturer’s optimal joint production and pricing decisions and the corresponding total emissions and then solve the regulator’s optimal emission cap. The objective of the manufacturer is to make production and pricing decisions to maximize its profit (including the emission trading cost). Covered by the cap-andtrade regulation, the manufacturer initially receives a free quantity of permits on its emission from a regulator, i.e., cap C (C ≥ 0), and is allowed to purchase or sell the (emission) permits through an outside permit market. The purchasing and selling prices per unit permit are b and s (s ≤ b), respectively. The self-pricing manufacturer produces a product to meet its deterministic demand from a product market. Denote by p and q the price and production quantity of the product, respectively. It is clear that the production quantity equals the deterministic demand. Assume that

2.3

Problem Formulation

11

Regulator

C Permit market

b s

Manufacturer

p, q

Product market

E Emission

Fig. 2.1 Illustration of the considered system

p = α - βq,

ð2:1Þ

where α (α > 0) is the maximal potential revenue of the product and β is the sensitivity of the price with respect to production quantity. The unit production cost is c, which is assumed to be a constant. Assume that α > c to ensure that the manufacturer produces products to meet the demands from the customer; thus, we exclude the trivial situation that the manufacturer never produces owing to the quite expensive cost. Let q and e be the production quantity and the emission intensity, respectively. Then, the total emissions associated with production are E = eq. If the resulting total emission is larger than the granted cap (i.e., E > C), then the manufacturer needs to purchase more emission permits through the permit market at the purchasing price b to avoid a huge penalty. In contrast, if the resulting total emission is less than the granted cap (E < C), the manufacturer can sell excess emission permits to the permit market at selling price s. The considered system in this chapter is illustrated in Fig. 2.1. The optimal profit Π can be found by solving the following model: Π = max q ≥ 0 ðα - βq - cÞq þ sðC - eqÞþ - bðeq - C Þþ ,

ð2:2Þ

where (α - βq - c)q is the profit of the manufacturer through producing and selling products and s(C - eq)+ - b(eq - C)+ is the net income from emission trading through the permit market under any given cap C. It is clear that the optimal profit decreases in the permit purchasing price, while it increases in the permit selling price. In addition, it can also be found that the optimal profit decreases in the gap between the emission purchasing and selling prices by fixing one of them. Let q be the optimal production quantity that maximizes profit. Then, the corresponding optimal total emission is E = eq. Note that the optimal price p can also be found based on the optimal production quantity q and Eq. (2.1). When the manufacturer satisfies the demand from customers, the generated emissions cause social damage to the environment. Since much more significant environmental damage will be caused by an increasing unit of emission, we use a quadratic function V(E) to measure the social damage to the environment, i.e.,

12

Production Planning and Cap-Setting Under Cap-and-Trade. . .

2

V ðE Þ = vE 2 ,

ð2:3Þ

where v is the “environmental concern” parameter (Krass et al., 2013). The parameter is of great significance, as it plays the role of converting a unit emission into a monetary unit of economic surplus and measuring the environmental concern degree of society toward the emitted pollution or the physical destructiveness of a unit emission. A higher value of v indicates more significant environmental damage incurred by one unit emission and thus more loss of economic surplus. From the perspective of the regulator, the objective is to set a reasonable cap C to maximize the social welfare of the considered system, as shown in Fig. 2.1. Social welfare is defined as the sum of customer surplus and the profit of the manufacturer through selling products minus the social damage to the environment. Note that we do not consider the cost or revenue of emission trading because both the outside market and the manufacturer are included in the considered system. Consequently, the social welfare function under a given cap C satisfies q

W ðC Þ =

ðα - βx - p Þdx þ ðp - cÞq - vE2

ð2:4Þ

0

where the first term on the right side is customer surplus, ( p - c)q is the profit of the manufacturer through selling products and vE2 measures the social damage of emissions to the environment. The regulator’s problem can be formulated as follows: max C ≥ 0 W ðC Þ: Let C be the optimal C = arg maxC ≥ 0W(C). 

2.4

cap

that

maximizes

ð2:5Þ social

welfare,

i.e.,

Optimal Decisions of the Manufacturer

In this section, we first develop the optimal decisions and then discuss their properties with respect to emission trading prices and emission intensity. For ease of discussion, we replace the production quantity q with the emission E in solving the problem. Define f(E) as the profit of the manufacturer through producing and selling products under a given total emission E. Since q = E/e, it is easy to verify that f ðE Þ = αE - βE 2 ,

ð2:6Þ

where α = ðα - cÞ=e and β = β=e2 . Here, α can be interpreted as the maximal potential profit per unit emission. As shown in the following analysis, it will play a key role in determining the optimal decisions of the manufacturer. Note that α, β > 0 because α > c and β > 0. The marginal profit of selling product by

2.4

Optimal Decisions of the Manufacturer

13

consuming emission permits is df ðEÞ=dE = α - 2βE. Based on the function f(E), Model (2.2) can be rewritten as Π=

max max E ≥ C π b ðEÞ = f ðE Þ - bE þ bC , max 0 ≤ E ≤ C ½π s ðE Þ = f ðE Þ - sE þ sC g,

ð2:7Þ

where π b(E) is the profit for the case of purchasing permits and π s(E) is the profit for the case of selling permits. Let E be the optimal solution to Model (2.4). The following lemma shows the properties of the optimal solutions to π b(E) and s π (E). Lemma 1 The optimal solutions to maxE ≥ Cπ b(E) and max0 ≤ E ≤ Cπ s(E) satisfy arg max E ≥ C π b ðE Þ = maxfC, C 1 g = maxf0, minðC 2 , CÞg,

and

arg max 0 ≤ E ≤ C π s ðEÞ

where C 1 = ðα - bÞ= 2β and C 2 = ðα - sÞ= 2β withC1 ≤ C2. The proofs of Lemma 1 (and the subsequent results) can be found in the Appendix. Note that when the total emission is C1 (C2), the marginal profit of selling product by consuming emission permits is df ðE Þ=dEjE = C1 = α - 2βC 1 (df ðEÞ=dEjE = C2 = α - 2βC2 ), which equals the unit purchasing (selling) price of permits. As will be seen later, C1 and C2 are two important thresholds for determining the operational decisions of the manufacturer. Lemma 1 shows the optimal emissions for the case of purchasing and selling permits, which will help us to characterize the optimal emission trading decisions and the optimal joint pricing and production decisions. Recall that α is the maximal potential profit per unit emission. By comparing it with s and b, we have the following results implied by Lemma 1. Lemma 2 The following results hold: (i) if α ≤ s, then the manufacturer will directly sell all the permits and never produce, (ii) if α ≤ b, then the manufacturer will never purchase permits to produce under any level of cap. Lemma 2 shows the relationship between the operational decisions and the relative magnitude among parameters. α ≤ s means that the maximal potential profit per unit emission is lower than the selling price. Therefore, the profit-maximizing manufacturer prefers to sell all the permits rather than produce. α ≤ b implies that the maximal potential profit per unit emission is lower than the purchasing price. As the profit of selling products is not enough to compensate for the cost of purchasing permits, the manufacturer will never purchase permits to produce under any level of cap.

14

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Production Planning and Cap-Setting Under Cap-and-Trade. . .

To avoid the speculation that the manufacturer never produces but directly sells the granted emission permits, we hereafter assume that α > s throughout this chapter. Next, we explore the optimal decisions for two cases: (1) s < α ≤ b and (2) α > b. The two cases represent the cases in which the maximal potential profit per unit emission is not so large and is large. In the case with s < α ≤ b, Lemma 1 indicates that the manufacturer will never purchase permits. We only need to focus on max0 ≤ E ≤ C[π s(E) = f(E) - sE + sC]. The following theorem summarizes the optimal decisions for this case: Theorem 1 If s < α ≤ b, the optimal total emission is E = min {C2, C}, and the optimal production quantity and price are q = min {C2/e, C/e} and p = max {α βC2/e, α - βC/e}, respectively. Theorem 1 indicates that if s < α ≤ b, then the decision of whether to sell permits or not follows a one-threshold policy. That is to say, if the cap exceeds the threshold C2, the manufacturer sells the permits down to C2. Otherwise, the manufacturer does not sell any permit. Recall that C2 is the critical cap where the marginal profit of the emission equals the unit permit selling price. If C > C2, the marginal profit of the emission is lower than the unit selling price of permits, then selling the permits of C - C2 units is more profitable; otherwise, it is better not to sell any permits, and the optimal total emission E is equal to the cap C. Theorem 1 also indicates that both the optimal emission and the optimal production quantity increase (throughout this chapter, we use “increase” and “decrease” in the non-strict sense, respectively) with respect to the cap, but the optimal product selling price decreases with respect to the cap. From Theorem 1, we can easily obtain the properties of the optimal decisions for the case with s < α < b, as summarized in the following proposition. Proposition 1 If s < α < b, the following results hold: (i) q decreases with respect to s, while p increases with respect to s if C > C2 (ii) both q and p are independent of s if C < C2. Proposition 1 indicates that if the cap is relatively large, then the manufacturer will produce less and set a high price when the permits’ selling price is high because the emission permits become relatively valuable “resources.” If the cap is relatively small, then the optimal production and price are independent of the permit selling price because there is no excess permit to be sold for the manufacturer. For the case with α > b, the optimal decisions of the manufacturer are given as follows: Theorem 2 If α > b, then the following results hold: (i) when C < C1, the optimal emission is E = C1, and the optimal production quantity and price are q = C1/e and p = α - βC1/e, respectively. (i) when C1 ≤ C ≤ C2, the optimal emission is E = C, and the optimal production quantity and price are q = C/e and p = α - βC/e, respectively.

2.4

Optimal Decisions of the Manufacturer

15

(ii) when C > C2, the optimal emission is E = C2, and the optimal production quantity and price are q = C2/e and p = α - βC2/e, respectively. Theorem 2 indicates that if α > b, then the emission trading decision follows a two-threshold policy. That is to say, if the cap is lower than the threshold C1, the manufacturer purchases permits up to C1; if the cap is higher than the threshold C2, the manufacturer sells permits down to C2; and if the cap is between C1 and C2, the manufacturer neither purchases nor sells any permits. Recall that C1 and C2 are the critical caps at which the marginal profit of the emission equals the purchasing price of permits b and the selling price s, respectively. If C < C1, the marginal profit of the emission (α - 2βC) is higher than the unit purchasing price of permits (b = α - 2βC 1 ), and it is better to purchase permits to produce more products. If C > C2, the marginal profit of the emission is lower than the unit selling price of permits s, then, selling permits C - C2 is more profitable. If C1 ≤ C ≤ C2, the marginal profit of the emission is lower than the unit purchasing price of permits b but higher than the unit selling price of permits s; thus, it is better not to purchase or sell any permits, so the optimal total emission E equals exactly the granted cap C. The lower and upper thresholds C1 and C2 are influenced by b and s, respectively. C1 decreases in b, and C2 decreases in s. As b and s become closer, the range (C1, C2) gets smaller and the two thresholds become one when b = s. It can also be penetrated from the aforementioned theorems that the manufacturer will always sell permits when the allocated permits exceed (α - c)e/2β, which equals the maximal value of C2. As proven above, the manufacturer sells permits when the initial cap is larger than C2. Therefore, the optimal operation decision will always be selling permits when the initial cap C exceeds (α - c)e/2β. Theorem 2 also implies that the optimal emission and the optimal production quantity increase with respect to the cap, and the optimal price decreases in the cap. From Theorem 2, we can also easily obtain the properties of the optimal decisions for the case with α > b, as summarized in the following proposition. Proposition 2 If α > b, the following results hold: (i) q decreases with respect to b, while p increases with respect to b if C < C1 (ii) both q and p are independent of b and s if C1 ≤ C ≤ C2 (iii) q decreases with respect to s, while p increases with respect to s if C > C2. Proposition 2 indicates that either the cap is relatively small or relatively large, the manufacturer always produces less and sets a high price when the permit purchasing or selling price is high due to the relatively valuable “resources.” In many regions and countries, manufacturers are encouraged by local governments to lower emission intensity to alleviate carbon emissions. In the following analysis, we discuss the impact of the emission intensity on the optimal production quantity, price, and emission.

16

2

Production Planning and Cap-Setting Under Cap-and-Trade. . . E

1000

1000

1000

800

800

800

600

600

C 550

600 400

C1

200 0

0

5

10

15

20

400

C2 25

C1

200

e

30

0

0

5

10

15

20

400

C2 25

200

e

30

0

0

5

10

15

C1

C2

20

25

e

30

Fig. 2.2 Optimal total emissions with different unit emission intensities. (a) C ≤ (α - c)2/(8bβ), (b) (α - c)2/(8bβ) < C ≤ (α - c)2/(8sβ), (c)C > (α - c)2/(8sβ)

Proposition 3 The optimal production quantity q decreases with respect to the emission intensity e, while the optimal price p increases with respect to the emission intensity e. Under cap-and-trade regulation, a larger emission intensity leads to a lower optimal production quantity but a higher optimal price. This is natural because (i) the emission permits are limited and not free, and (ii) a lower optimal production quantity is accompanied by a higher price. In contrast to the consistent monotonicity of the optimal production quantity and price with respect to the emission intensity, the monotonicity of the optimal total emission with respect to the emission intensity is not consistent, as shown in the following proposition. Proposition 4 The optimal emission E increases with respect to e when e ≤ e0, and decreases with respect to e when e ≥ e0, where e0 = (α - c)/2b if C ≤ (α - c)2/(8bβ), and e0 = (α - c)/2s ifC > (α - c)2/(8bβ). At first glance, it might seem that increasing the emission intensity would always increase the total emission of the manufacturer. However, as shown in Proposition 4, this is not true. Proposition 4 indicates that the optimal total emission always first increases and then decreases with respect to the emission intensity. In particular, the threshold depends on the maximal potential revenue of the product, the unit production cost, the purchasing or selling price of the permits, and the initial cap. To illustrate the conclusion proposed in Proposition 4 and explain it, we conduct a numerical example. We set α = 1004, c = 4, β = 4, s = 40, and b = 50. The relationship between the optimal total emissions and the emission intensity under three initial cap levels (C = 550, C = 700 and C = 800) is illustrated in Fig. 2.2 a, b, c. These three initial cap levels correspond to cases C ≤ (α - c)2/(8bβ), (α - c)2/ (8bβ) < C < (α - c)2/(8sβ) and C > (α - c)2/(8sβ), respectively. Both the last two cases can be integrated into the case C > (α - c)2/(8bβ) in Proposition 4. It is easy to verify that (α - c)2/(8bβ) and (α - c)2/(8sβ) are the two maximum values of C1 and C2, respectively. In Fig. 2.2 a, b, c, the solid curves represent the optimal total emission of the manufacturer under different values of the emission intensity; the dashed curves represent the values of C1 and C2, respectively; the dashed horizontal lines represent

2.5

Optimal Cap of the Regulator

17

the initial cap levels; and the dashed vertical lines represent two thresholds (e1, e2) of the emission intensity at which C1 and C2 arrive at their maximal values. Figure 2.2 shows that the optimal total emission of the manufacturer can be a certain part of the curves of C1, C2, or C. To explain the properties characterized in Proposition 4, one can just examine the values of C1 and C2 with respect to the emission intensity e. It is clear that both C1 and C2 first increase and then decrease with respect to the emission intensity e, and C1 ≤ C2 for all e. Take the case with C ≤ (α - c)2/(8bβ) as an example (see Fig. 2.2a). When e is quite low, C2 is also small, and C > C2. Then, the allocated permits are abundant, and the operational decisions are not affected by the cap. The optimal total emission equals C2 (the increasing part of C2), and the manufacturer sells the excess permits. As e further increases, C2 increases, and the cap is less than C2 but more than C1. In this case, the manufacturer does not purchase or sell any permits in the production process, and the total emission equals the cap (the horizontal line). If e further increases, the cap will be less than C1; then, the manufacturer purchases permits for production, and the optimal total emission equals C1 (the arched part of C1), which increases first and then decreases with respect to e. After that, C1 decreases to values that are less than the cap C, and the manufacturer again does not purchase or sell permits, i.e., the total emission is fixed at the cap C (the horizontal line). Finally, as e further increases, C2 decreases to values that are less than the cap C, and the manufacturer produces less and sells excess permits to keep the total emission at C2, which decreases in e (the decreasing part of C2). The cases with (α - c)2/(8bβ) < C ≤ (α - c)2/(8sβ) and C > (α - c)2/ (8sβ) are simpler than the case with C ≤ (α - c)2/(8bβ); thus, we omit them here. To summarize, the optimal total emission of the manufacturer increases with a relatively small emission intensity and decreases with a relatively large emission intensity. This conclusion implies that under cap-and-trade regulation, it is not always correct to encourage the manufacturer to invest in emission intensity reduction, from the perspective of minimizing the total emissions of the manufacturer. For those who produce with relatively green technologies (Krass et al. 2013), the emission abatement investment can be more attractive since the greener the manufacturers become, the less total emissions will be generated. However, for manufacturers that are relatively less green, it is not wise to encourage them to invest much for abatement since the smaller the emission intensity is, the more total emissions will be generated from the manufacturer.

2.5

Optimal Cap of the Regulator

In this section, we derive the optimal cap by incorporating the optimal decisions of the manufacturer into Model (2.5). Our interest lies in the impact of the value of v on the optimal cap and the decisions of the manufacturer. Additionally, we explore the property of the optimal cap with respect to the emission intensity. The following theorem characterizes the optimal cap.

18

2

Production Planning and Cap-Setting Under Cap-and-Trade. . .

Theorem 3 The optimal cap C satisfies: (i) If s < α ≤ b, then C 2 ðα - sÞ=2β, 1

when v ≤ βðα þ sÞ=2ðα - sÞ; C  =

α= β þ 2v when v > βðα þ sÞ=2ðα - sÞ. (ii) If α > b, then C  2 ðα - sÞ=2β, 1 α= β þ 2v

when v ≤ βðα þ sÞ=2ðα - sÞ ; C  =

when v 2 βðα þ sÞ=2ðα - sÞ, βðα þ bÞ=2ðα - bÞ

; C 2

0, ðα - bÞ=2β when v ≥ βðα þ bÞ=2ðα - bÞ. Theorem 3 formulates optimal caps for different environmental concern parameters. From Theorem 3, we can see that the optimal cap is decreasing relative to the value of v given a certain emission intensity. This occurs because the higher the value of v is, the higher the regulator’s desire to reduce emissions. Based on the three theorems, denoted by Ω(A, B) the equilibrium result, with A the optimal cap from the regulator and B the optimal total emission of the manufacturer, the equilibrium results of the game in this chapter can be formulated as follows. Table 2.1 illustrates that the optimal total emission equals the optimal cap except in the last case. As we proved before, the manufacturer sells permits down to C2 (ðα - sÞ=2β) when the cap exceeds C2 both when s < α ≤ b and α > b, or purchases permits to C1 (ðα - bÞ=2β) when the cap is less than C1 if α > b, or else makes no permit trading and uses up the allocated permits when the cap is less than C2 if s < α ≤ b or when the cap lies between C1 and C2 if α > b. Note that the minimal value of the optimal cap equals C2 when v ≤ βðα þ sÞ=2ðα - sÞ, so that the optimal total emission remains constant at C2 regardless of the optimal cap. With the increase in v, the optimal total emission equals the optimal cap when the optimal cap decreases to less than C2 if s < α ≤ b or when the cap lies between C1 and C2 if α > b. In particular, the manufacturer is supposed to purchase permits to C1 if the cap decreases to less than C1. Therefore, the optimal total emission should be ðα - bÞ=2β when the optimal cap lies in the region 0, ðα - bÞ=2β in the last case. In summary, the environmental concern parameter plays a key role in determining the amount of the given permits and the manufacturer’s production quantity. In addition, the optimal total emission also decreases with respect to the environmental concern parameter, which means that a larger environmental concern parameter causes less pollution. Apart from the influence of the environmental concern parameter, the optimal cap is likely to be impacted by the emission intensity as well. Therefore, we explore the properties of the optimal cap with respect to the emission intensity in the following section. Note that when v ≥ βðα þ bÞ=2ðα - bÞ and v ≤ βðα þ sÞ=2ðα - sÞ, the optimal cap over the corresponding interval results in different profits for the manufacturer but the same social welfare. However, considering that the emission permit is

α>b

Permit trading scenarios s βðα þ sÞ=2ðα - sÞ v ≤ βðα þ sÞ=2ðα - sÞ

Ω=

v ≤ βðα þ sÞ=2ðα - sÞ

ðα - sÞ=2β, 1 , ðα - sÞ=2β

Equilibrium results

Values of v

Table 2.1 The equilibrium results of the game with different environmental concern parameters

2.5 Optimal Cap of the Regulator 19

2 Production Planning and Cap-Setting Under Cap-and-Trade. . .

20

becoming an increasingly scarce resource, it is reasonable to conclude that the regulator will supply the manufacturer with the minimal cap in the corresponding region, which is convenient for monotonicity exploration. The proposition below presents the results. _

Proposition 5 Denote by e the unique feasible solution that satisfies v = βðα þ sÞ=½2ðα - sÞ ; then, the optimal cap C increases with respect to e when 0 < e ≤ e and decreases with respect to e when e > e, where. _

(i) if e ≥ ðα - cÞ=2s, e = ðα - cÞ=2s. _ _ (ii) if e < ðα - cÞ=2s, e = e . Intuitively, the optimal cap decreases with the emission intensity from the perspective of environmental protection. Surprisingly, Proposition 5 shows that the optimal cap is supposed to increase first and decrease later as the emission intensity increases. Furthermore, Proposition 5 also shows that when the environmental concern parameter decreases to a lower level, the region in which the optimal cap increases with the emission intensity is enlarged. The reason behind the non-monotonous relationship between the optimal cap and the emission intensity is that at the beginning, a small cap will be adequate for the production requirement. When the emission intensity increases, more permits should be allocated for more production to satisfy the demand from consumers. Meanwhile, relatively less environmental damage is caused as the emission intensity remains at a low level. Therefore, from the perspective of cap setting, the regulator is supposed to allocate more permits rather than restrict the permit provision as the emission intensity increases in a relatively low region. With the further increase of the emission intensity, the optimal cap is supposed to be limited to a lower level until no permit is offered to avoid more significant social welfare loss resulting from more serious environmental damage from a unit output.

2.6

Conclusion

This chapter first characterizes the optimal decisions of a self-pricing manufacturer operating under cap-and-trade regulation given unequal permit purchasing and selling prices. It is found that the decision of whether to purchase or to sell emission permits depends on the relative magnitude of the permit trading prices and the maximal potential profit brought by one unit permit. If the permit purchasing price is larger than the maximal potential profit brought by one unit permit, then the manufacturer will sell excess permits when the allocated cap is higher than a threshold and just use up the allocated permits when the cap is lower than the threshold. Otherwise, the manufacturer will purchase some permits when the cap is smaller than the lower threshold, sell some permits when the cap is larger than the upper threshold, and just use up the allocated permits when the cap lies between the two thresholds. If the emission trading prices are equal, as is assumed in many

Appendix

21

existing studies, the two thresholds will match together. Consequently, the manufacturer will either purchase or sell some permits unless the initial cap equals the threshold. By incorporating the optimal solutions of the manufacturer into the social welfare model, the optimal solution of the regulator is then achieved from a game-theoretical perspective. It is found that the optimal cap differs with different environmental concern parameters with respect to which the optimal cap decreases. The impacts of the emission intensity on both players’ optimal solutions are also analyzed. Surprisingly, we found that the optimal total emissions will first increase and then decrease as the emission intensity increases. This implies that under capand-trade regulation, it is not always right to encourage the manufacturer to invest to reduce the emission intensity from the perspective of minimizing the total emissions of the manufacturer. Likewise, the optimal cap increases first and decreases later with respect to the emission intensity rather than always decreasing. The reason is that when the emission intensity lies at a low level, increasing the cap avoids more loss of social welfare. When the emission intensity reaches a quite high level, fewer permits will be allocated from the regulator because otherwise significant social damage will be caused. This chapter attempts to incorporate emission trading regulations into a decisionmaking process with different emission trading prices and caps. Nevertheless, several limitations exist in this chapter, which can be extended in the future. First, we focus on one period in deriving the optimal decisions of the manufacturer. It is possible that the manufacturer is allowed to transfer redundant permits from one period to another. Second, the work can be extended to the case with multiple product types rather than only one type, as we considered. Other extensions could also be made, such as incorporating “green” technology investment decisions in reducing emissions. Furthermore, it is also meaningful to explore some practical ways to ascertain the environmental concern parameter and perform corresponding empirical studies.

Appendix Proof of Lemma 1 From Eq. (2.3), i.e., f ðEÞ = αE - βE 2 , we have that f(E) is strictly concave. Consequently, π b(E) and π s(E) are also strictly concave. It is easy to verify that (i) f(E) - bE = ðα - bÞE - βE 2 attains its maximum at point C 1 = ðα - bÞ=2β, and (ii) f ðE Þ - sE = ðα - sÞE - βE2 attains its maximum at point C 2 = ðα - sÞ=2β: It is clear that C1 ≤ C2 because s ≤ b. Since π b(E) = f(E) - bE + bC and π s(E) = f(E) - sE + sC are strictly concave, we have

22

2

Production Planning and Cap-Setting Under Cap-and-Trade. . .

arg max E ≥ C π b ðE Þ = maxfC, C1 g = maxf0, minðC 2 , C Þg:

and arg max 0 ≤ E ≤ C π s ðE Þ

Proof of Lemma 2 If α ≤ s, then α ≤ s ≤ b and C1 ≤ C2 ≤ 0. Recall that C ≥ 0. From Lemma 1, we have that argmaxE ≥ Cπ b(E) = max {C, C1} = C and argmax0 ≤ E ≤ Cπ s(E) = max {0, min(C2, C)} = 0. Since C is also a feasible solution to max0 ≤ E ≤ Cπ s(E), we have E = 0, and the manufacturer directly sells all the permits. If α ≤ b, then C1 ≤ 0. From Lemma 1, we know that argmaxE ≥ Cπ b(E) = max {C, C1} = C for any C because C ≥ 0. This implies that the manufacturer will never purchase permits under any level of cap. Proof of Theorem 1 Recall that Lemma 2 implies that the manufacturer will never purchase permits if s < α ≤ b:In the following discussion, we focus on π s(E) = f(E) sE + sC. Since α > s, C 2 = ðα - sÞ=2β > 0: Hence, Lemma 1 implies that argmax0 ≤ E ≤ Cπ s(E) = max {0, min(C2, C)} = min {C2, C}. The optimal emission is E = min {C2, C}. From E = eq and Eq. (2.1), we directly have q = min {C2/e, C/e}, and p = max {α - βC2/e, α - βC/e}. Proof of Theorem 2 If α > b, then α > b ≥ s, and C2 ≥ C1 > 0. Hence, Lemma 1 implies that arg max E ≥ C π b ðEÞ = maxfC, C1 g and

arg max 0 ≤ E ≤ C π s ðE Þ = minfC2 , Cg:

When C < C1, argmaxE ≥ Cπ b(E) = C1 and argmax0 ≤ E ≤ Cπ s(E) = C. Since C is also a feasible solution to maxE ≥ Cπ b(E), we have that E = C1. It is easy to verify that q = C1/e and p = α - βC1/e because E = C1. When C1 ≤ C ≤ C2, argmaxE ≥ Cπ b(E) = C and argmax0 ≤ E ≤ Cπ s(E) = C. Therefore, E = C. It is easy to verify that q = C/e and p = α - βC/e because E = C. When C > C2, argmaxE ≥ Cπ b(E) = C and argmax0 ≤ E ≤ Cπ s(E) = C2. Since C is also a feasible solution to max0 ≤ E ≤ Cπ s(E), we have that E = C2. It is easy to verify that q = C2/e and p = α - βC2/e because E = C2. Proof of Proposition 3 To study the impact of emission intensity on the optimal production quantity and price, we focus on Model (2.2) instead, i.e., Π = maxq ≥ 0{(α - βq - c)q + s(C - eq)+ - b(eq - C)+}. It can be verified that (α - βq - c)q is concave in q, s(C - eq)+ - b(eq - C)+ is concavely decreasing in q, and is submodular in (q, e). Consequently, (α - βq - c)q + s(C - eq)+ - b(eq - C)+ is convex in q and submodular in (q, e). It follows that the optimal production quantity q is decreasing in e. From Eq. (2.1), we have that the optimal price p is increasing ine.. Proof of Proposition 4 For ease of exposition, we rewrite C1 and C2 as C1(e) and C2(e), respectively. Combining Theorems 1 and 2, we have that

Appendix

23

maxfC 1 ðeÞ, 0g 

E =

C C 2 ð eÞ

C < maxfC 1 ðeÞ, 0g maxðC 1 ðeÞ, 0Þ ≤ C ≤ C 2 ðeÞ C > C2 ðeÞ:

ð2:8Þ

It follows that ðα - bÞ=2β = C 1 ≤ E  ≤ C 2 = ðα - sÞ=2β:

ð2:9Þ

Equation (2.9) implies that Model (2.2) can be rewritten as (replacing q with E/e): Π =

max C1 ≤ E ≤ C2 F ðe, E Þ þ sðC - E Þþ - bðE - C Þþ , F ðe, EÞ = ðα - cÞE=e - βE 2 =e2 g: ð2:10Þ

It is easy to verify that F(e, E) + s(C - E)+ - b(E - C)+ is concave in E. Since (i) ∂2F/∂E∂e = ½4βE - ðα - cÞe=e3 = 4βE - α =e increases with respect to E, (ii) 4βC 1 - α = α - 2b, and (iii) 4βC 2 - α = α - 2s, we have that (i) if α ≥ 2b, i.e., e ≤ (α - c)/2b, then ∂2F/∂E∂e ≥ 0 when C1 ≤ E ≤ C2; and (ii) if α ≤ 2s, i.e., e ≥ (α - c)/2s, then ∂2F/∂E∂e ≤ 0 when C1 ≤ E ≤ C2. Consequently, from Eq. (2.10), we have that the optimal emission E increases with respect to e when e ≤ (α - c)/2b, and decreases with respect to e whene ≥ (α - c)/2s.. For ease of exposition, we rewrite C1 and C2 as C1(e) and C2(e), respectively. It can be easily verified that C1(e) (C2(e)) is strictly convex with respect to e and arrives at its maximum (α - c)2/(8bβ) ((α - c)2/(8sβ)) at e = (α - c)/2b (e = (α - c)/2s). We discuss the impact of e on E when (α - c)/2b < e < (α - c)/2b in the following three cases: (1) If C ≤ (α - c)2/(8bβ), then the strict convexities of C1(e) and C2(e) imply that C ≤C1((α - c)/2b) ≤ C2(e) when (α - c)/2b < e < (α - c)/2b. Equation (2.8) suggests that E = C1(e) if C ≤ max {C1(e), 0} (note that C1(e) decreases with respect to e when e > (α - c)/2b) and E = C if C ≥ max {C1(e), 0}. Consequently, E decreases with respect to e. (2) If (α - c)2/(8bβ) < C < (α - c)2/(8bβ), then the strict convexities of C1(e) and C2(e) suggest that C > C1((α - c)/2b) > C1(e) when (α - c)/2b < e < (α - c)/ 2s. It is clear that C > 0. Equation (2.8) implies that E = C if C ≤ C2(e) and E = C2(e) if C ≥ C2(e) (note that C2(e) increases with respect to e when e < (α - c)/2s). Consequently, E increases with respect to e. (3) If C ≥ (α - c)2/(8sβ), then the strict convexities of C1(e) and C2(e) suggest that C ≥ C2((α - c)/2s) ≥ C2(e) when (α - c)/2b < e < (α - c)/2b. Equation (2.8) implies that E = C2(e) (note that C2(e) increases with respect to e when e < (α - c)/2s). Consequently, E strictly increases with respect to e.

24

2

Production Planning and Cap-Setting Under Cap-and-Trade. . .

In summary, we have that the optimal emission E first increases with respect to e when e ≤ e0, and decreases with respect to e when e ≥ e0, where e0 = (α - c)/2b if C ≤ (α - c)2/(8bβ), and e0 = (α - c)/2s ifC > (α - c)2/(8bβ). Proof of Theorem 3 From Eq. (2.4) and Theorems 1 and 2, it can be verified that ðiÞ If s < α ≤ b, = ðiiÞ

then W ðCÞ

αC - β=2 þ v C2

C ≤ C2 2

W ðC 2 Þ = ðα - sÞ 3βα - 2vα þ βs þ 2vs =8β C > C2

If α > b,

then W ðCÞ

W ðC1 Þ = ðα - bÞ 3βα - 2vα þ βb þ 2vb =8β =

ð2:11Þ

2

C < C1 C1 ≤ C ≤ C2

αC - β=2 þ v C 2 W ðC2 Þ = ðα - sÞ 3βα - 2vα þ βs þ 2vs =8β

2

ð2:12Þ

C > C2 :

Similar to the proof of Lemma 1, it can be verified that arg max C αC - β=2 þ v C 2 : 0 ≤ C ≤ C2 = min α= β þ 2v , C 2 ,

and

arg max C αC - β=2 þ v C 2 : C 1 ≤ C ≤ C2 = max C 1 , min α= β þ 2v , C 2

:

Recall that C1 = ðα - bÞ=2β and C 2 = ðα - sÞ=2β. Consequently, arg max C αC - β=2 þ v C2 : 0 ≤ C ≤ C 2 =

C 2 = ðα - sÞ=2β α= β þ 2v

v 2 0, βðα þ sÞ=2ðα - sÞ v 2 βðα þ sÞ=2ðα - sÞ, 1

ð2:13Þ

Appendix

25

arg max C αC - β=2 þ v C 2 : C 1 ≤ C ≤ C2 C 2 = ðα - sÞ=2β =

v 2 0, βðα þ sÞ=2ðα - sÞ

α= β þ 2v

v 2 βðα þ sÞ=2ðα - sÞ, βðα þ bÞ=2ðα - bÞ

C 1 = ðα - bÞ=2β

v 2 βðα þ bÞ=2ðα - bÞ, 1 :

ð2:14Þ

From Eqs. (2.11) and (2.13), we have that if s < α ≤ b, C = α= β þ 2v when v > βðα þ sÞ=2ðα - sÞ and C  2 ðα - sÞ=2β, 1

when v ≤ βðα þ sÞ=2ðα - sÞ.

From Eqs. (2.12) and (2.14), we have that if α > b, then C  2 0, ðα - bÞ=2β v ≥ βðα þ bÞ=2ðα - bÞ,

when

C = α= β þ 2v

when

v 2 βðα þ sÞ=2ðα - sÞ, βðα þ bÞ=2ðα - bÞ , and C 2 ðα - sÞ=2β, 1

when

v ≤ βðα þ sÞ=2ðα - sÞ. □ Proof of Proposition 5 According to Theorem 3, the optimal cap with respect to v is:

ðiÞ If s < α ≤ b, ðiiÞ If α > b,

C =

v ≤ βðα þ sÞ=½2ðα - sÞ

α= β þ 2v

v > βðα þ sÞ=½2ðα - sÞ

ð2:15Þ

C

ðα - sÞ=2β =

ðα - sÞ=2β

v ≤ βðα þ sÞ=½2ðα - sÞ

α= β þ 2v

βðα þ sÞ=½2ðα - sÞ < v < βðα þ bÞ=½2ðα - bÞ

0

v ≥ βðα þ bÞ=½2ðα - bÞ

ð2:16Þ

_

Denoting by e the unique feasible emission intensity that can be obtained from v = βðα þ sÞ=½2ðα - sÞ, we can rewrite (2.15) and (2.16) as a function of the emission intensity as follows: ðiÞ

If s < α ≤ b,

ðiiÞ If α > b,

½eðα - cÞ - se2 =2β eðα - cÞ=ðβ þ 2ve2 Þ

C =

C =

½eðα - cÞ - se2 =2β eðα - cÞ=ðβ þ 2ve2 Þ 0

_

0e

ð2:17Þ

_

0 e and C = e(α - c)/(β + 2ve2), ∂C/∂e = (α - c)(β - 2ve2)/ (β + 2ve2)2, since v > βðα þ sÞ=½2ðα - sÞ, we have that ∂C/∂e < 0, which means that the optimal cap is decreasing in e in this region. Synthetically: _

_

(i) If e ≥ ðα - cÞ=2s, the optimal cap is increasingly related to the emission intensity when 0 < e ≤ (α - c)/2s and is decreasingly related to the emission intensity when e > (α - c)/2s; _ (ii) If e < ðα - cÞ=2s, the optimal cap increases with respect to the emission inten_ sity when 0 < e ≤ e and decreases with respect to the emission intensity when _ e > e.

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Hoen, K. M. R., Tan, T., Fransoo, J. C., & Van Houtum, G. J. (2011). Effect of carbon emission regulations on transport mode selection under stochastic demand. Flexible Services and Manufacturing Journal, 1–26. Hovi, J., & Holtsmark, B. (2006). Cap-and-trade or carbon taxes? The feasibility of enforcement and the effects of non-compliance. International Environmental Agreements, 6, 137–155. Hua, G., Cheng, T. C. E., & Wang, S. (2011). Managing carbon footprints in inventory management. International Journal of Production Economics, 132, 178–185. Kim, H. J. (2014). A Lagrangian heuristic for determining the speed and bunkering port of a ship. Journal of the Operational Research Society, 65(5), 747–754. Krass, D., Nedorezov, T., & Ovchinnikov, A. (2013). Environmental taxes and the choice of green technology. Production and Operations Management, 22(5), 1035–1055. Letmathe, P., & Balakrishnan, N. (2005). Environmental considerations on the optimal product mix. European Journal of Operational Research, 167, 398–412. Mandell, S. (2008). Optimal mix of emission taxes and cap-and-trade. Journal of Environmental Economics and Management, 56, 131–140. Stavins, R. (1995). Transaction costs and tradeable permits. Journal of Environmental Economics and Management, 29, 133–148. Subramanian, R., Gupta, S., & Talbot, B. (2007). Compliance strategies under permits for emission. Production and Operations Management, 16(6), 763–779. Wey, K. D., & Yang, S. T. (2005). Simulating the effect of joint policies of emission trading and joint implementation under a monopoly market. Agriculture and Economics, 35, 27–43. Woerdman, E. (2001). Emission trading and transaction cost: Analyzing the flaws in the discussion. Ecological Economics, 38, 293–304. Yalabik, B., & Fairchild, R. J. (2011). Customer, regulatory, and competitive pressure as drivers of environmental innovation. International Journal of Production Economics, 131(2), 519–527. Yale, E. (2008). Taxing cap-and-trade environmental regulation. The Journal of Legal Studies, 37(2), 535–550. Zhang, B., & Xu, L. (2013). Multi-item production planning with carbon cap and trade mechanism. International Journal of Production Economics, 144, 118–127. Zhang, J. J., Nie, T. F., & Du, S. F. (2011). Optimal emission-dependent production policy with stochastic demand. International Journal of Society Systems Science, 3(1), 21–39.

Chapter 3

A Two-Period Carbon Tax Regulation for Manufacturing and Remanufacturing Production Planning

3.1

Introduction

With the increasing concern about carbon emissions, emission tax regulation and market-based emission trading have been established as two main schemes to control carbon emissions. The emission trading markets include the EU-ETS (Chang et al., 2015; Fan et al., 2016), Shenzhen Emissions Exchange (Cong & Lo, 2017), Chicago Climate Exchange, and Australia Climate Exchange. Emission taxes have been levied in many countries, such as the USA, France, etc. (Yenipazarli, 2016). In response to these regulations, sustainable development and environmentally friendly business have been taken as critical priorities by enterprises, and incorporating emission abatement into production planning becomes indispensable concerning manufacturers’ operational planning (Yenipazarli, 2016). Among the activities implemented by many manufacturers to enhance environmental sustainability, remanufacturing plays a critical role by which used products are recovered, processed, and sold again in the market (Fleischmann et al., 2000). Due to fewer raw materials and fewer manufacturing procedures, energy consumption and associated carbon emissions could be significantly reduced by remanufacturing, such as the remanufacturing of photocopiers and diesel engines (Sutherland et al., 2008). To motivate the implementation of remanufacturing and thus induce them to emit less, many governments employ the carbon tax regulation. For instance, firms in the USA receive no subsidies or tax credits to remanufacture yet pay emission taxes (Yenipazarli, 2016). More notably, the emission tax price or emission penalty may vary from time to time. In 2007, the carbon tax price in the city of Boulder was 0.0002$ per kWh, which increased to 0.0003$ in subsequent years for industrial consumers (Brouillard & Van Pelt, 2007). Under EU-ETS, a penalty per ton of CO2 not covered by the allowances increased from 40 € in the first phase (Jan. 2005 to Dec. 2007) to 100 € in the second phase (Jan 2008 to Dec. 2012) (Gong & Zhou, © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Dou et al., Operations Management for Environmental Sustainability, SpringerBriefs in Operations Management, https://doi.org/10.1007/978-3-031-37600-9_3

29

30

3 A Two-Period Carbon Tax Regulation for Manufacturing and. . .

2013). The penalty can also be viewed as an emission tax scheme. Therefore, manufacturers who are engaged in remanufacturing can be regulated by the carbon tax scheme with two tax prices over the stages of manufacturing and remanufacturing. The production decision of remanufacturing is closely linked to that of manufacturing in the sense that the collected returns used for remanufacturing are constrained by the production quantity in the manufacturing stage. The carbon tax adds to the correlation of the production decision over the two stages, which makes the production planning activities inherently more complex for remanufacturing. That is to say, the tax price over each stage becomes the determinant of production decisions in both stages. Therefore, to lower the overall emissions and maximize profits, production decisions should be made over the whole planning horizon with the incorporation of both tax prices. On the regulation side, it is more flexible for the regulator to strategically use carbon tax legislation with two tax prices. Compared with adjusting only one tax price throughout the planning horizon, changing the tax price during either the manufacturing or the remanufacturing stage may pay off in obtaining economic and environmental benefits. Thus, it is of great significance to disclose a more powerful tax price. Since the overall emission and profit are determined directly by the production quantities, the production performances in relation to manufacturing or remanufacturing features play the key role in defining the more powerful tax price. On the other hand, carbon emission regulation has the possibility of motivating the manufacturer to use green technologies. However, since the production decisions of manufacturing and remanufacturing are correlated, a smaller emission per unit product may enlarge the production in both stages, thus leading to an overall emission increment. Then, from the regulator’s perspective, it remains to be verified whether subsidizing the manufacturer to promote the use of green technology is efficient in reducing overall emissions. Furthermore, for cases with and without remanufacturing, the carbon tax influences production planning in different ways. Depending on the production decisions determined by the carbon tax, remanufacturing may lead to a negative environmental effect and profit shrinking because manufacturing cannibalizes the market demand for new products (Guide & Li, 2010). Therefore, to enhance the remanufacturing benefit both economically and environmentally, a rational tax price portfolio or the strategic use of tax prices needs to be founded. In this chapter, we consider the production planning decisions for a manufacturer under carbon tax regulation with two tax prices over the manufacturing and remanufacturing periods. Consumers in the market are heterogeneous in their willingness to pay and value remanufactured products less than new products. Using a two-period model, we consider two cases with and without remanufacturing. The remanufacturer only produces new products in both periods in the case without remanufacturing, while in the remanufacturing case, the manufacturer produces new products in the first period and sets up a mixed product line where new and remanufactured products coexist in the second period. Based on optimal production planning, we explore how the two tax prices, as well as remanufacturing-related

3.2

Literature Review

31

features, influence the optimal production decisions and emissions to achieve insights concerning emission abatement. To better understand how tax prices can be strategically used to achieve both the economic and environmental benefits of remanufacturing, the performances of the emission and profit increments of remanufacturing in relation to emission tax prices are also explored. The remainder of the paper is organized as follows. Section 3.2 includes a review of the related literature. Section 3.3 describes the model, and Sect. 3.4 gives the optimal production planning decisions under a two-period emissions tax regulation. Additionally, the structural properties of the optimal results are analyzed, based on which some managerial insights are highlighted. Section 3.5 presents some comparisons between cases with and without remanufacturing. Section 3.6 summarizes and concludes the paper. All the proofs are provided in the appendix.

3.2

Literature Review

In the literature, two main streams of research are related to our work, including research exploring operation decisions under carbon emission regulation and research addressing production planning with remanufacturing. In the former stream of research, operation decisions have been explored at the firm level in many studies. Zhang et al. (2011) address the problem of a manufacturer’s optimal production policy under stochastic demand in the cap-and-trade system. Benjaafar et al. (2013) introduce a series of simple and general models to illustrate how carbon footprint considerations could be incorporated into operational decisions. Hua et al. (2011) investigate how firms react in inventory management under carbon cap-and-trade based on the EOQ model, where the optimal order quantity is derived, and the impacts of regulation parameters on optimal solutions are examined. Zhang and Xu (2013) investigate the multi-item production planning problem with a cap-and-trade mechanism under stochastic demand. Additionally, many others study operation planning under carbon constraints on a supply chain level. Xu et al. (2017) investigate the two-product production and pricing problems in a make-to-order supply chain within cap-and-trade regulation. Combined with life cycle assessment, Chaabane et al. (2012) introduce mixed-integer linear programming into a sustainable supply chain to develop insights under cap-and-trade. Zakeri et al. (2015), Ji et al. (2017), and Cruz (2008) are among the researchers performing similar studies. Although operational decisions are analyzed from many perspectives in the above studies, as an effective way to reduce carbon emissions, remanufacturing is not considered. An extensive stream of studies on remanufacturing is performed in the operations management literature, which focuses mostly on production planning and economic implications. Ferrer and Swaminathan (2006) propose two-period and multiperiod production planning models where remanufactured and new products are perfect substitutes. Using a newsvendor model, Kaya (2010) considers a manufacturer that needs to offer an incentive to consumers to collect the right number of returns to be

32

3 A Two-Period Carbon Tax Regulation for Manufacturing and. . .

used in the remanufacturing process. Kim et al. (2006) develop a new model to discuss the remanufacturing process of reusable parts in reverse logistics. Ferguson and Toktay (2006) study pricing and remanufacturing decisions and derive conditions on costs under which remanufacturing is profitable. Debo et al. (2005) discuss the issue of joint pricing and production technology selection for manufacturable products. Zanoni et al. (2012) study the multiproduct economic lot scheduling problem with manufacturing and remanufacturing. Similarly, the issues of manufacturing-remanufacturing production and pricing decisions are also researched by Akçalı and Cetinkaya (2011), Chen and Chang (2013), Kenne et al. (2012), Mahmoudzadeh et al. (2013), and Xiong et al. (2014). Although remanufacturing decisions are modeled from different aspects in the above research, the environmental problem is not considered, or production decisions are not explored under carbon emission regulations. Remanufactured products consume less emissions and thus are effective in saving emission costs to protect the environment. The implications for emission prices on the production planning for remanufacturing and the economic and environmental effects could be interesting research problems, as are addressed in the following studies. Assuming limited information on demand distribution, Liu et al. (2015) present three optimization models to determine the remanufacturing quantity that maximizes the total profits under three common carbon emission regulation policies: (a) mandatory carbon emissions capacity, (b) carbon tax, and (c) cap and trade. Chang et al. (2015) establish two-period models in independent and substitutable demand markets, where the optimal production quantity and pricing decisions of a profit-maximizing remanufacturer are analyzed under a cap-and-trade mechanism. Using a leader-follower Stackelberg game model, Yenipazarli (2016) incorporates emission concerns into production and pricing issues in remanufacturing and examines the impact of emission- and legislation-related factors on operational decisions. Miao et al. (2018) address the problem of remanufacturing with trade-ins under a carbon tax policy and a cap-and-trade program, and the optimal pricing and production decisions are analyzed. Fahimnia et al. (2013) develop a unified optimization model for a closed-loop supply chain in which carbon emissions are expressed in terms of dollar carbon costs. The studies above analyzed the strategies for remanufacturing and present useful insights into the effect of carbon regulations. However, the emission prices are modeled as constant over the whole planning horizon. In practice, the emission regulation implemented may suggest different tax prices in the manufacturing and remanufacturing stages. Consistent with these studies, we model a quantitative profit-maximization problem consisting of manufacturing and remanufacturing, where the performance of the optimal production quantity and the optimal emission in relation to the features of manufacturing and emission regulation are explored. Our paper differs from the existing research in that we model a carbon tax regulation where the tax prices are different over the manufacturing and remanufacturing periods. In addition, we analyze the different impacts of the two tax prices on the optimal emission and profit to develop insights for the flexible use of the emission tax regulation from the

3.3 Modeling Framework

33

perspective of the regulator. That is to say, we explore which tax price is more effective for environmental protection and how to adjust the tax price(s) to enhance the benefit of remanufacturing both economically and environmentally.

3.3

Modeling Framework

We model a monopolistic manufacturer who produces new products in the first period, collects a certain ratio of end-of-life products for remanufacturing, and produces new products in the second period. Over the entire planning horizon, the manufacturer is constrained by a carbon tax regulation where the tax prices over the two periods are different. The manufacturer jointly makes the production decision over the two periods to maximize its profit. The notations in the modeling setup are summarized in Table 3.1. Notation: Variables and explanations. Assume that the new and remanufactured products are sold in the same market in the two periods. Since the characteristics and valuations of the new and remanufactured products are different, we consider the substitution between new and remanufactured products and assume a lower selling price of the remanufactured products, i.e., ϕp2n > q2r. Following Ferrer and Swaminathan (2010), the price functions of the new and remanufactured products are assumed to be p1 = Q - q1, p2n = Q - q2n - ϕq2r, and p2r = ϕ(Q - q2r - q2n). Based on these assumptions, we explore the manufacturer’s production decisions of the two periods. Specifically, we explore whether new products should be produced in period 2. What ratio of the collected returns should be used for remanufacturing? How do the two tax prices impact the production decision of each period? Furthermore, to explore the role of Table 3.1 Variables and explanations Variables Q e w c h γ ϕ ti q1, p1 q2n, q2r p2n, p2r Π E

Explanations The potential market size in each period The carbon emission for producing one unit of new product The carbon emission saving per unit remanufactured product The cost for producing one unit of new product The cost saving per unit remanufactured product The collection ratio (0 < γ < 1) Customers’ tolerance for remanufactured products (0 < ϕ < 1) The carbon tax price in period i, i = 1, 2 The new product quantity and the selling price in period 1 The new and remanufactured product quantities in period 2 The new and remanufactured product prices in period 2 The total profit of the manufacture over the two periods The total carbon emission over the two periods

3 A Two-Period Carbon Tax Regulation for Manufacturing and. . .

34

remanufacturing concerning emission reduction and profit improvement, two cases with and without remanufacturing are modeled.

3.3.1

No Remanufacturing Case

For the case without remanufacturing, the product line includes only all new products over the two periods. The profit-maximizing problem of the manufacturer in this case can be given by: max Πðq1 , q2n Þ = q1 ðp1 - c - et 1 Þ þ q2n ðp2n - c - et 2 Þ

ð3:1Þ

s:t: q1 ≥ 0, q2 ≥ 0 Maximizing Eq. (3.1) with the price functions that q1 = Q - p1, p2n = Q - q2n, the optimal production decisions in the two periods can be given as q1 = ðQ - c1 Þ=2, q2n = ðQ - c2 Þ=2, where c1 = c þ et 1 , c2 = c þ et 2 . To eliminate the uninteresting case where the tax price is too high that the manufacturer does not produce any product, we assume that ti < (Q - c)/e to ensure that qi > 0, i = 1, 2. Here, (Q - c)/e can be interpreted as the maximal potential profit from consuming one unit of emissions. Then, the optimal product prices can be given as p1 = ðQ þ c1 Þ=2, p2n = ðQ þ c2 Þ=2; the optimal total carbon emissions and the overall profit can be given as E0 = ½2eðQ - cÞ - e2 ðt 1 þ t 2 Þ=2 and  2 2 0 = ðQ - c1 Þ þ ðQ - c2 Þ =4, respectively.

3.3.2

Remanufacturing Case

In this case, the product line is mixed with new and remanufactured products. The manufacturer decides the quantities of the new and remanufactured products in two periods simultaneously. In period 2, the remanufactured product quantity is constrained by the new product quantity in period 1. The decision problem can be formulated as follows: max Πðq1 , q2n , q2r Þ = s:t:

q1 ðp1 - cÞ þ q2n ðp2n - cÞ þ q2r ½p2r - ðc - hÞ - t 1 eq1 - t 2 ½eq2n þ ðe - wÞq2r 

γq1 ≥ q2r ; q1 , q2n , q2r ≥ 0: ð3:2Þ

3.4

Results and Analyses

35

The first three terms denote the profit from selling new products in the two periods and remanufactured products in period 2. The last two terms represent the cost associated with the carbon tax regulation in the two periods. In the constraints, γq1 ≥ q2r implies that the remanufactured product quantity is not more than the collected returns from period 1. The optimality of Function (3.2) can be characterized by Karush-Kuhn-Tucker conditions. We use λ as the multiplier as the slack variable; then, the Lagrangian function for profit maximization can be rewritten as q1 ðQ - q1 - cÞ þ q2n ðQ - q2n - ϕq2r - cÞ max Πðq1 , q2n , q2r Þ = þ q2r ½ϕðQ - q2r - q2n Þ - ðc - hÞ - t 1 eq1 - t 2 ½eq2n þ ðe - wÞq2r  þ λðγq1 - q2r Þ λ ≥ 0; s:t:

ð3:3Þ

λðγq1 - q2r Þ = 0; q1 , q2n , q2r ≥ 0:

3.4

Results and Analyses

In this section, we derive the manufacturer’s optimal production decisions by maximizing Lagrangian function (3.3). Additionally, further analyses are performed to explore the characteristics of the optimal results. By defining different regions with the emission saving parameter w, the optimal production decisions are characterized in the following theorem: Theorem 1 Let w1 = fð1 - ϕÞ½c2 þ γϕðQ - c1 Þ - hg=t 2 , w2 = fðQ - c2 Þ - ϕγ ðQ - c1 Þ þ γγϕ½Qð1 - ϕÞ - hg=γγϕt 2 , w3 = [Q(1 - ϕ) - h]/ t2 and w4 = ½ð1 - ϕÞc2 - h=t 2 denote four different emission saving thresholds. Table 3.2 shows the optimal production decisions of the two periods: Table 3.2 illustrates four different regions defined by the emission-saving parameter. In region 1, the manufacturer uses all the collected returns for remanufacturing and does not make new products in period 2; in region 2, the manufacturer uses all the collected returns for remanufacturing and makes new products in period 2; in region 3, the manufacturer uses a proportion of collected returns for remanufacturing and makes new products in period 2; and in region 4, the manufacturer only makes new products in period 2. The optimal production decisions show that when all the collected returns are used for remanufacturing, the production decision is determined by both tax prices in each period. Otherwise, one tax price only determines the production decision of the corresponding period. Likewise, the cost savings per unit remanufactured product

36

3

A Two-Period Carbon Tax Regulation for Manufacturing and. . .

Table 3.2 The optimal production decisions of the manufacturer The emission savings w1 < w2 < w

w1 < w < w2

The optimal production decision in the two periods ð1 þ ϕγ ÞQ - c1 - γ ½c2 - ðh þ wt2 Þ  , q2n = 0 q1 = 2ðϕγγ þ 1Þ ð1 þ ϕγ ÞQ - c1 - γ ½c2 - ðh þ wt 2 Þ q2r = γ 2ðϕγγ þ 1Þ ðQ - c1 Þ þ γ ½ðh þ wt 2 Þ - ð1 - ϕÞc2   q1 = 2½1 þ γγϕð1 - ϕÞ q2n = ð Q c 1 Þ þ γ ½ðh þ wt 2 Þ - ð1 - ϕÞc2   q2r = γ 2½1 þ γγϕð1 - ϕÞ ðQ - c2 Þ½1þγγϕð1 - ϕÞ - ϕγ ðQ - c1 Þ - ϕγγ ½ðhþwt 2 Þ - ð1 - ϕÞc2  2½1þγγϕð1 - ϕÞ

w3 > w1 > w > w4

q1 =

Q - c1 2

, q2n =

Qð1 - ϕÞ - ðhþwt 2 Þ , q2r 2ð1 - ϕÞ

w3 > w1 > w4 > w

q1 =

Q - c1 2

, q2n =

Q - c2 2

=

ðhþwt 2 Þ - ð1 - ϕÞc2 2ϕð1 - ϕÞ

, q2r = 0

determine the new product quantity in period 1 only when all the collected returns are used for remanufacturing (i.e., the first two regions). Based on Theorem 1, we present some further analyses in the following section. Note that the production decision in region 4 is essentially the case without remanufacturing, and we focus on the first three regions. First, we explore how the two carbon tax prices impact the optimal production quantities in the two periods, and the results are summarized in Proposition 1. Proposition 1 The relations between the optimal product quantities and the carbon tax prices are shown in Table 3.3. Proposition 1 shows that q1 , q2n , and q2r are monotonously related to tax price t1 but conditionally monotonously related to tax price t2. In period 1 of all regions, a larger tax price t1 enlarges the emission cost for new products; thus, q1 decreases in t1. In period 2 of region 1, the emission cost of remanufacturing becomes higher with a larger t2; thus, fewer products would be remanufactured. In this region, all the collected returns are used for remanufacturing, and no new products are produced. Remanufacturing less suggests fewer new products in period 1 when t2 increases. In region 2, the manufacturer produces new products in period 2, but a larger t2 enlarges the emission cost, thus leading to fewer new products. However, if remanufacturing saves a large amount of emissions when w > e(1 - ϕ), the cost increment due to a larger t2 would be small, and producing more emissions in period 1 for more remanufacturing increases profitability. In contrast, when w < e(1 - ϕ), remanufacturing requires a large emission cost; thus, producing less remanufacturing in period 1 is more beneficial. In region 2, the emission cost increases for a larger t1; thus, the manufacturer produces less in period 1, and a profit loss is caused. Consequently, to better meet the market demand and compensate for the profit loss, the manufacturer should produce more new products in period 2. In regions 1 and 2, since all the collected returns are used for remanufacturing, less production in period 1 leads to less remanufacturing in period 2 when t1

3.4

Results and Analyses

37

Table 3.3 The impact of the two tax prices on the optimal production decisions Production quantity q1

q2n q2r

Region 1

Region 2

Region 3

∂q1 =∂t 1 < 0 ∂q1 =∂t 2 < 0

∂q1 =∂t 1 < 0 ∂q1 =∂t 2 > 0 if w > e(1 - ϕ) ∂q1 =∂t 2 < 0 if w < e(1 - ϕ) ∂q2n =∂t 1 > 0 ∂q2n =∂t 2 < 0 ∂q2r =∂t 1 < 0 ∂q2r =∂t 2 > 0 if w > e(1 - ϕ) ∂q2r =∂t 2 < 0 if w < e(1 - ϕ)

∂q1 =∂t 1 < 0 N/A

N/A N/A ∂q2r =∂t 1 < 0 ∂q2r =∂t 2 < 0

N/A ∂q2n =∂t 2 < 0 N/A ∂q2r =∂t 2 > 0 if w > e(1 - ϕ) ∂q2r =∂t 2 < 0 if w < e(1 - ϕ)

increases. In region 1, remanufacturing requires a higher emission cost when t2 increases; thus, the manufacturer remanufactures less in period 2. In regions 2 and 3, when remanufacturing saves a large number of emissions when w > e(1 - ϕ), the emission increment could be small for a larger t2. Therefore, remanufacturing enhances profitability. Otherwise, when w < e(1 - ϕ), remanufacturing incurs a high emission cost; thus, the manufacturer remanufactures less. The results above indicate that a higher carbon tax price does necessarily induce a lower level of production. The emissions that remanufacturing saves play a critical role in determining the product quantities. If the emission cost increment is small for remanufacturing with a larger tax price, then the overall profit could be enhanced effectively by remanufacturing more. Apparently, the total emissions over the two periods are significantly affected by the tax prices and the emission-saving parameter. In the following section, by exploring the properties of the optimal total emissions, we analyze how to use the carbon tax to control the total emissions and discuss whether it is effective to employ green technologies. The results are presented below. Proposition 2 Denote by Ej ( j = 1, 2, 3) the optimal total emissions in region j; then: (1) In region 1, ∂E1 =∂t i < 0, i = 1, 2. (2) In region 2, ∂E2 =∂t 1 < 0. When w < e(1 - ϕ), ∂E 2 =∂t 2 < 0, when w > e(1 ϕ), then if γ > e2[1 + γγϕ(1 - ϕ)]/{[e(1 - ϕγ) + γ(e - w)][w - e(1 - ϕ)]}, ∂E 2 =∂t 2 > 0; otherwise, ∂E2 =∂t 2 < 0. (3) In region 3, ∂E3 =∂t 1 < 0. When w < e(1 - ϕ), ∂E 3 =∂t 2 < 0, when w > e(1 ϕ), then ∂E 3 =∂t 2 < 0 if w > (e - w)[w - e(1 - ϕ)]/ϕe; otherwise, ∂E 3 =∂t 2 > 0. Proposition 2 shows that improving tax price t1 always decreases total emissions, while improving carbon tax price t2 may induce more emissions. Proposition 1 reveals that in region 1, the manufacturer provides fewer new and remanufactured products when ti (i = 1, 2) increases; thus, the total emission decreases with ti (i = 1, 2). In region 2, Proposition 1 indicates fewer new products in period 1 and fewer remanufactured products in period 2 when t1 increases.

38

3 A Two-Period Carbon Tax Regulation for Manufacturing and. . .

Although a larger t1 motivates more new products in period 2, the increment is small; thus, the total emissions decrease. On the other hand, when t2 increases, Proposition 1 indicates less production in both periods if w < e(1 - ϕ), thus leading to less total emissions. Otherwise, if w > e(1 - ϕ), the manufacturer produces more in period 1 and remanufactures more but produces fewer new products in period 2. In this situation, if considerable collected returns are remanufactured, the total emission increases. In contrast, a small number of collected returns are used for remanufacturing, and the total emissions decrease because the manufacturer produces fewer new products. In region 3, Proposition 1 indicates fewer new products and fewer (more) remanufactured products when w < e(1 - ϕ) (w > e(1 - ϕ)) for a larger t2 in period 2. Consequently, the total emission decreases if w < e(1 - ϕ). Otherwise, if w > e(1 - ϕ), although more collected returns are used for remanufacturing, the emission increment is small when w > (e - w)[w - e(1 - ϕ)]/ϕe, which is overweighed by the emission decrement resulting from fewer new products in period 2. Therefore, the total emissions decrease. In contrast, remanufacturing leads to a large emission increment so that the overall emission increases. The discussion above suggests that setting a higher tax price in period 1 is effective in controlling total emissions. However, raising the tax price in period 2 does not necessarily motivate fewer total emissions. If remanufacturing requires a high level of emissions and more collected returns are used for remanufacturing to reduce the losses caused by a higher tax price, more emissions could be generated over the two periods. Since each tax price has an effect on lowering total emissions, an interesting question is which tax price is more efficient in controlling total emissions. To this end, we compare the emission reduction achieved per unit increment of t1 and t2. Corollary 1 presents the results. Corollary 1 When the optimal total emission E j ( j = 1, 2, 3) decreases in both t1 and t2, then: (1) In region 1, ∂E 1 =∂t 1 > ∂E 1 =∂t 2 , while in region 3, ∂E 3 =∂t 1 < ∂E 3 =∂t 2 . (2) In region 2, ∂E2 =∂t 1 < ∂E2 =∂t 2 when w < e(1 - ϕ), and ∂E 2 =∂t 1 > ∂E2 =∂t 2 when w > e(1 - ϕ). The results show different emission reductions associated with a one-unit increase in t1 and t2. In region 1 (3.3), the marginal emission decrement is larger in relation to t1 (t2), while in region 2, the emission saved by remanufacturing determines the larger marginal emission decrement. In region 1, higher tax prices lead to less production in the two periods, and q1 decreases more with a marginal increase in t1. Since new products require more emissions, tax price t1 is more efficient in reducing total emissions. In region 3, a higher tax price t1 only leads to less production in period 1, while a higher tax price t2 leads to fewer new and remanufactured products in period 2. Hence, the marginal emission decrement is larger when associated with t2. In region 2, raising the tax

3.4

Results and Analyses

39

price t1 leads to fewer products in period 1 and more new products but fewer remanufactured products in period 2. In contrast, all production decreases with a higher tax price t2 when w < e(1 - ϕ); thus, the marginal emission decrement is larger associated with t2. Otherwise, when w > e(1 - ϕ), remanufacturing requires a small number of emissions; thus, the marginal emission decrement associated with t2 is smaller. From the regulator’s perspective, the strategy of raising one tax price could be employed to effectively control the total emissions instead of raising both tax prices simultaneously to avoid causing too much profit loss for the manufacturer. Specifically, if the manufacturer uses all (part of) the collected returns for remanufacturing but does not produce (and produces) new products in period 2, raising t1 (t2) reduces the overall emissions more efficiently. On the other hand, if all the collected returns are used for remanufacturing and new products are produced in period 2, raising t2 (t1) reduces the overall emissions more efficiently when w > e(1 - ϕ) (w < e(1 ϕ)). In practice, green technologies could be used for emission abatement. Concerning remanufacturing, what is interesting here is whether employing green technology during remanufacturing reduces the overall emission. We explore this by investigating the relationship between E j ( j = 1, 2, 3) and the emission-saving parameterw. Proposition 3 Denote by wj ( j = 1, 2, 3) the threshold for w in region j, then when w < wj ; ∂Ej =∂wj < 0 when w > wj , where ∂Ej =∂wj > 0 w2 = eð1 - ϕÞ w1 = e - fðQ - c - et 1 Þ þ γ ½ϕQ - ðc - hÞ - et 2 g=2γt 2 , and fðQ - c - et 1 Þ - γ ½cð1 - ϕÞ - h - et 2 g=2γt 2 w3 = eð1 - ϕÞ þ ½cð1 - ϕÞ - h=2t 2 . Proposition 4 shows that the overall emission could either increase or decrease in the emission-saving parameter w. A larger w indicates a lower emission cost per remanufactured product, due to which the production quantities increase in both periods in region 1. However, if remanufacturing only saves a small number of emissions, i.e., w < w1 , the production quantity increment could still cause higher total emissions. In contrast, w > w1 indicates that remanufacturing requires a low level of emissions; thus, the total emissions decrease as the production quantity increases. The total emissions in region 3 have similar characteristics. In region 2, Theorem 1 indicates more products in period 1 and more remanufactured products but fewer new products in period 2 when w increases. When w < w2 , remanufacturing requires a high level of emissions, thus leading to higher total emissions. Otherwise, when remanufacturing requires a low level of emissions (w < w2 ), fewer new products in period 2 lead to less total emissions. The discussion above indicates that employing green technology during remanufacturing may not be effective for reducing total emissions. If the initial level of remanufacturing is high, reducing the emissions of remanufacturing with green technologies enlarges the overall emissions. Therefore, from the regulator’s perspective, a subsidizing strategy could be taken to motivate the use of green

40

3 A Two-Period Carbon Tax Regulation for Manufacturing and. . .

technology during remanufacturing only when the original emission level of remanufacturing is low enough.

3.5

Comparisons of the Cases With and Without Remanufacturing

Remanufacturing promotes product recycling and helps save social costs. Nevertheless, what is notable is whether the environment gets better protected and whether the manufacturer’s profit improves after remanufacturing. Furthermore, can the regulator strategically use a carbon tax to combine the aims of protecting the environment and improving the manufacturer’s profitability under remanufacturing? In this section, we explore the characteristics of the emission and profit increments between two cases with and without remanufacturing concerning carbon tax prices. The two propositions below illustrate the results. Proposition 4 Denoted by ΔEj , j = 1, 2, 3 the optimal emission increment after remanufacturing, i.e., ΔE j = Ej - E 0 , let M = e - e and N = e(1 - ϕ)(1 - γϕ); then:

1 þ 4ð1 þ ϕγγ Þ - 1 =2γ

(1) In region 1, ∂ΔE 1 =∂t 1 < 0, ∂ΔE 1 =∂t 2 < 0 when w < M; ∂ΔE 1 =∂t 1 < 0, ∂ΔE1 =∂t 2 > 0 when M < w < e(1 - ϕγ); ∂ΔE 1 =∂t 1 > 0, ∂ΔE 1 =∂t 2 > 0 when w > e(1 - ϕγ). (2) In region 2, ∂ΔE 2 =∂t 1 < 0, ∂ΔE 2 =∂t 2 < 0 when w < N; ∂ΔE 2 =∂t 1 > 0, ∂ΔE2 =∂t 2 < 0 when N < w < e(1 - ϕ); and ∂ΔE 2 =∂t 1 > 0, ∂ΔE 2 =∂t 2 > 0 when w > e(1 - ϕ). (3) In region 3, ∂ΔE 3 =∂t 2 < 0. This proposition shows that depending on the emissions saved by remanufacturing, the emission increment is conditionally monotonous in relation to the carbon tax prices. Therefore, the total emission increment can be enlarged when raising the carbon tax price. Specifically, when the emission savings per unit remanufactured product are small (large) enough, i.e., w < M or w < N (w > e(1 ϕγ) or w > e(1 - ϕ)), raising either tax price leads to a smaller (larger) emission increment. Otherwise, the emission increment changes conversely when the two tax prices are raised. In region 3, a higher tax price in period 2 leads to a smaller increase in total emissions. Here is an example. Suppose that Q = 700, c = 200, h = 150, e = 200, γ = 0.95, ϕ = 0.75, t2 = 2.43 (t1 = 2.42). For cases of w < M, M < w < e(1 - ϕγ) and w > e(1 - ϕγ), we set w = 11, 20, 60. The relationship between the optimal emission increment and tax prices is shown in Figs. 3.1 and 3.2. Suppose that Q = 500, c = 200, h = 150, e = 50, γ = 0.4, ϕ = 0.5, t2 = 5 (t1 = 2). For cases w < M, M < w < e(1 - ϕγ) and w > e(1 - ϕγ), we set w = 19.5, 22, 30. The optimal emission increment with different carbon tax prices is shown in Fig. 3.3.

3.5

Comparisons of the Cases With and Without Remanufacturing 600

2750

580 2740

550 520

2730

E1*490

2720

460 2710

430 400 2.41

2.415

2.42

2.425

t1

2700 2.43

41

502

2734

501.5

2732

501

2730

500.5

2728

E1* 500

2726

499.5

2724

499

2722

498.5 2.43

2.432

2.434

2.436

t2

2.438

2720 2.44

Fig. 3.1 The optimal emission increment with different t1(t2) in region 1

1.13055

10 4

1.138

10 4

1.1305

1.136

1.13045

E1*

E1*

1.1304

1.134

1.13035

1.132

1.1303 1.13025 2.41

2.415

2.42

t1

2.425

2.43

1.13 2.43

2.432

2.434

2.436

t2

2.438

2.44

Fig. 3.2 The optimal emission increment with different t1(t2) in region 1 when w > e(1 - ϕγ)

Recall that in the first two regions, all the collected returns are used for remanufacturing; thus, both tax prices are the determinants of production decisions. When w is small, (i.e., w < M or w < e(1 - ϕ)(1 - γϕ)), remanufacturing requires a high emission cost, which would become even larger if the tax prices are raised. Therefore, fewer new and remanufactured products are provided, resulting in a smaller increase in total emissions. In contrast, if w is large, (i.e., w > e(1 - ϕγ) or w > e(1 - ϕ)), remanufacturing incurs a small emission cost; thus, higher tax prices would not lead to a large emission cost increment and producing more enhances profitability. Consequently, remanufacturing brings a larger increment to the total emissions. On the other hand, for a moderate value of w, the variations in the emission increments in relation to the carbon tax prices are inconsistent. The emission cost becomes relatively higher when M < w < e(1 - ϕγ) (N < w < e(1 - ϕ)) compared with the situation in which w > e(1 - ϕγ) (w > e(1 - ϕ)). In region 1, a larger t1 incurs a higher emission cost, leading to smaller quantities of both new products in period 1 and remanufactured products in period 2; thus, the total emissions decrease. However, in region 2, t2 influences the production quantity in both periods in the case of remanufacturing, while only the production decision in period 2 is affected in

42

3

A Two-Period Carbon Tax Regulation for Manufacturing and. . .

450

320

400

300

350

280

E2*

E2*

260

300

240

250 200

2

2.2

2.4

t1

2.6

2.8

3

220

4

4.2

4.4

t2

4.6

4.8

5

Fig. 3.3 The optimal emission increment with different t1(t2) in region 2

the case without remanufacturing. With a higher emission cost caused by a larger t2, the overall production decreases more in the case of remanufacturing; thus, the emission increment is smaller. This result suggests that for certain small (larger) emission savings per unit remanufactured product, raising (lowering) the carbon tax prices simultaneously could be taken as an effective measure by the regulator to diminish the emission increment under remanufacturing. Otherwise, raising both tax prices leads to opposite changes in the emission increment, and then strategically raising one tax price and lowering the other decrease the emission increment effectively. Proposition 5 Denoted by Δ j , j = 1, 2, 3 the optimal profit increment after remanufacturing, i.e., Δ j = j - 0 , then Δ j > 0 and: 1. In region 1, ∂Δ 1 =∂t 1 < 0, ∂Δ 1 =∂t 2 > 0. 2. In region 2, ∂Δ 2 =∂t 1 < 0 ; ∂Δ 2 =∂t 2 > 0 when w > e(1 - ϕ), and ∂Δ 2 =∂t 2 < 0 when w < e(1 - ϕ). 3. In region 3, ∂Δ 3 =∂t 2 < 0. Proposition 5 demonstrates that remanufacturing improves the manufacturer’s profit, and a larger t1 leads to less profit increment, while a larger t2 could either lead to less or more profit increment. Here is an example. Suppose that Q = 500, c = 200, h = 40, e = 50, w = 30, γ = 0.4, ϕ = 0.8, t2 = 5. Figure 3.4 shows the optimal profit increment with different t1 in regions 1 and 2. Suppose Q = 500, c = 200, e = 50, γ = 0.4, and h = 40, w = 30, ϕ = 0.8, t1 = 4 for the case w > e(1 - ϕ); h = 150, w = 24, ϕ = 0.5, t1 = 2 for the case w < e(1 ϕ). Figure 3.5 shows the optimal profit increment with different t2 in region 2. Suppose Q = 500, c = 200, e = 50, h = 150, and w = 18, ϕ = 0.5, γ = 0.4, t1 = 2. Figure 3.6 shows the optimal profit increment with different t2 in region 3. In region 1, although the new products are not manufactured in period 2, the manufacturer produces more new products in period 1 and more remanufactured products in period 2 compared with the case without remanufacturing, which brings

Comparisons of the Cases With and Without Remanufacturing

Fig. 3.4 The optimal profit increment with different t1 in regions 1 and 2. (a) w > e(1 - ϕ) and (b) w < e(1 - ϕ)

* 1 * 2

3100 3000 2900 2800 2700 3

3.1

* 1 * 2

2320

Optimal profit increment

Optimal profit increment

2340

2300 2280 2260 5

5.02

5.04

t2

43

3200

Optimal profit increment

3.5

5.06

5.08

5.1

3.2 t1 3.3

3.4

3.5

1422 1420 1418 1416 1414

* 1 * 2

1412 1410 5.02

5.04

t2

5.06

5.08

Fig. 3.5 The optimal profit increment with different t2 in regions 1 and 2

more overall profit. In region 2, both new and remanufactured products are produced; thus, higher profit can be achieved. In region 3, the production quantities in period 1 are the same in both cases. However, the remanufactured products and a larger quantity of new products in period 2 improve the total profit in the case of remanufacturing. The tax price t1 determines the production decisions in both periods in the case with remanufacturing but only impacts the production decision in period 1 in the case without remanufacturing. Recall that Proposition 1 indicates that a larger tax price t1 causes a decrease in production for both new and remanufactured products in the first two regions, and in region 2, the production decrement outweighs the new production increment in period 2; thus, the profit increment decreases in the first two regions. When the tax price t2 increases, all the production quantities decrease in both cases. However, in region 1, the production decrease in the case with

44

3

A Two-Period Carbon Tax Regulation for Manufacturing and. . .

Fig. 3.6 The optimal profit increment with different t2 in region 3

Optimal profit increment

225

* 3

220 215 210 205 200 5

5.02

5.04

t2

5.06

5.08

5.1

remanufacturing outweighs that in the case without remanufacturing; thus, the profit increases. In region 2 of the case with remanufacturing, when w > e(1 - ϕ), the manufacturer produces fewer new products in period 2 but more remanufactured products and more new products in period 1 for a larger tax price t2. In contrast, in the case without remanufacturing, a larger tax price t2 only leads to a smaller product quantity in period 2. Consequently, the overall profit increment becomes larger. On the other hand, when w < e(1 - ϕ), all the production quantities decrease in the case of remanufacturing, and then the profit increment decreases. Likewise, in region 3, there is a larger overall production decrement in the case with remanufacturing with a larger tax price t2; thus, the profit increment decreases. The result suggests that different profit increments after remanufacturing can be led to by changing the two tax prices. Combining the three points in Propositions 5, it can be implied that the economic benefit does not necessarily conflict with environmental protection. Under remanufacturing, changing the tax price improves the manufacturer’s profit and lowers emissions at the same time (e.g., raising the tax price t2 when w < e - e 1 þ 4ð1 þ ϕγγ Þ - 1 =2γ in region 1 or lowering the tax price t1 when e(1 - ϕ)(1 - γϕ) < w < e(1 - ϕ) in region 2). Therefore, from the perspective of the regulator, the emission tax price could be strategically used to pursue both the economic and environmental benefits concerning remanufacturing.

3.6

Conclusion

Many companies have organized their product lines based on remanufacturing capabilities, for example, manufacturers of printer cartridges, single-use cameras, medical equipment, and many other products. In this chapter, we study the optimal production decisions in a hybrid manufacturing-remanufacturing system under a

3.6

Conclusion

45

carbon tax regulation where the tax prices in manufacturing and remanufacturing periods are different. We explore the characteristics of the optimal results and make some comparisons between cases with and without remanufacturing. Our research reveals several unintuitive consequences. For the production decision, depending on the emission level of remanufacturing, a higher carbon tax in the remanufacturing period does not necessarily induce a lower level of production. Improving the carbon tax in the first period always decreases the total emissions, while more emissions may be caused when improving the tax price in the second period. In situations where the overall emissions are reduced with higher tax prices, there could be different marginal emission decrements. Additionally, the overall emissions in the case of remanufacturing could either increase or decrease in relation to the emissions saved by remanufacturing. Compared with the case without remanufacturing, the optimal emission and the manufacturer’s profit increment could either increase or decrease with a higher carbon tax price. From the manufacturer’s perspective, the results above suggest that for a small emission cost of remanufacturing, remanufacturing more with a higher carbon tax price effectively reduces the overall profit loss. In addition, employing green technology during remanufacturing may not be effective in lowering the emission cost when the original emission level of remanufacturing is high enough. For regulators, levying a heavy carbon tax in the first period can be an effective way of controlling overall emissions. However, if the manufacturer uses more collected returns for remanufacturing, raising the tax price in the second period would motivate the manufacturer to emit more. To more effectively control the overall emissions, the two tax prices could be raised selectively according to the manufacturer’s production decision and the characteristics of remanufacturing. In addition, subsidizing the manufacturer to motivate the use of green technology during remanufacturing only pays off in reducing the total emissions when remanufacturing requires a low level of emissions. Moreover, the two-period carbon tax regulation has the potential to match the goals of improving the manufacturer’s profit and lowering the overall emissions under remanufacturing. That is, charging lower or higher tax prices over the manufacturing or remanufacturing period reduces emissions and enhances total profit. Our study can be extended in a few ways for future research. For instance, instead of capturing carbon tax regulation with two tax prices in the two periods, the capand-trade regulation with distinct emission buying and selling prices in the two periods can also be modeled. In this situation, the initial emission cap and the trading prices could play a critical role in determining the optimal decisions and environmental performance. Additionally, the use of green technology could also be considered to derive insights into how to allocate emission reduction targets.

46

3

A Two-Period Carbon Tax Regulation for Manufacturing and. . .

Appendix Proof of Theorem 1 The optimality conditions can be given as ∂Π ∂Π and q = ðQ - 2q1 - cÞ - et 1 þ λγ = 0, q = ðQ - 2q2n - 2ϕq2r - cÞ - et 2 = 0, 1

∂Π q2r

2n

= ϕðQ - 2q2r - 2q2n Þ - ðc - hÞ - t 2 ðe - wÞ - λ = 0.

(1) When λ > 0, λ(γq1 - q2r) = 0 indicates that γq1 = q2r, and substituting γq1 = q2r into the above equations, we have ðQ-c-et1 Þ þ γ ½ðh þ wt 2 Þ- ð1-ϕÞðc þ et2 Þ 2½1 þ γγϕð1-ϕÞ ðQ-c-et1 Þ þ γ ½ðh þ wt2 Þ- ð1-ϕÞðc þ et2 Þ q2r =γ 2½1 þ γγϕð1-ϕÞ ðQ-c-et2 Þ½1 þ γγϕð1-ϕÞ-ϕγ ðQ-c-et1 Þ-ϕγγ ½ðh þ wt2 Þ- ð1-ϕÞðc þ et2 Þ q2n = 2½1 þ γγϕð1-ϕÞ ðh þ wt 2 Þ- ð1-ϕÞðc þ et 2 Þ-γϕð1-ϕÞðQ-c-et 1 Þ λ= ½1 þ γγϕð1-ϕÞ

q1 =

cþet 2 Þ - γϕð1 - ϕÞðQ - c - et 1 Þ λ = ðhþwt2 Þ - ð1 - ϕÞ½ð1þγγϕ > 0, we obtain that ð1 - ϕÞ ð1 - ϕÞðcþet 2 Þþγϕð1 - ϕÞðQ - c - et 1 Þ - h = w1 . Additionally, from q1 > 0, we obtain w> t2 γ ð1 - ϕÞðcþet 2 Þ - ðQ - c - et 1 Þ - γh = w. w1 - w = ½1þγγϕð1 - ϕγtÞ2ðQ - c - et1 Þ, recall the that w > γt 2 c assumption that Q e > t 1 , w1 - w > 0; thus, w > w holds. Likewise, from q2n > 0, we can obtain that ðQ - c - et 2 Þ½1þγγϕð1 - ϕÞ - ϕγ ðQ - c - et 1 Þþγγϕð1 - ϕÞðcþet 2 Þ - γγϕh w< = w2 . γγϕt 2 1 Þ - ðQ - c - et 2 Þ w1 - w2 = ½1 þ γγϕð1 - ϕÞ ϕγðQ - c - etγγϕt ; thus, w1 > w2 when 2 ð1 - ϕγ ÞðQ - cÞ ð1 - ϕγ ÞðQ - cÞ t 2 - ϕγt 1 > , and w1 < w2 when t 2 - ϕγt 1 < . For the condie e ð1 - ϕγ ÞðQ - cÞ ð1 - ϕγ ÞðQ - cÞ tion of t 2 - ϕγt 1 > , it can be derived that t 1 > given that e e c t2 = t1. Recall that we assume t i < Q , (i = 1, 2) to ensure a positive production e

From

quantity in the case without remanufacturing. We neglect the situation of t 1 > ð1 - ϕγ ÞðQ - cÞ and arrive at the conclusion that w1 < w2. e Therefore,

(i) When w1 < w < w2, then q1 > 0, q2n > 0. Thus, the optimal production quantities are ðQ-c-et 1 Þ-γ ð1-ϕÞðc þ et 2 Þ þ γ ðh þ wt 2 Þ 2½1 þ γγϕð1-ϕÞ ðQ-c-et 1 Þ-γ ð1-ϕÞðc þ et 2 Þ þ γ ðh þ wt 2 Þ  q2r =γ ; 2½1 þ γγϕð1-ϕÞ ðQ-c-et2 Þ½1 þ γγϕð1-ϕÞ-ϕγ ðQ-c-et 1 Þ-ϕγγ ½ðh þ wt 2 Þ- ð1-ϕÞðc þ et 2 Þ q2n = 2½1 þ γγϕð1-ϕÞ q1 =

Appendix

47

(ii) When w1 < w2 < w, then q1 > 0, q2n < 0. Thus, the optimal production ð1 þ ϕγ ÞQ - ðc þ et 1 Þ - γ ½ðc - hÞ þ t 2 ðe - wÞ q1 = 2ðϕγγ þ 1Þ  = 0 q quantities are 2n . ð 1 þ ϕγ ÞQ ð c þ et Þ γ ½ ð c h Þ þ t ð e w Þ  1 2 q2r = γ 2ðϕγγ þ 1Þ (2) When λ = 0, λ(γq1 - q2r) = 0 indicates that γq1 ≥ q2r, substitute λ = 0 into the first-order conditions, then we obtain that q1 =

h þ wt 2 - ð1 - ϕÞðc þ et 2 Þ Qð1 - ϕÞ - h - wt 2 Q - c - et 1 ; q2n = ; q2r = 2 2ϕð1 - ϕÞ 2 ð 1 - ϕÞ

γϕð1 - ϕÞðQ - c - et 1 Þþð1 - ϕÞðcþet 2 Þ - h = w1 . t2 Likewise, q2n > 0 requires that w < Qð1 -t2ϕÞ - h = w3 , and q2r > 0 requires that c 2Þ - h w > ð1 - ϕÞðcþet = w4 . w3 - w4 = ð1 - ϕÞ ðQ - ct2- et2 Þ. Since Q t2 e > t 2 , w3 > w4. w1 - w3 = ð1 - ϕÞ eðt2 - γϕt1 Þ - tð2Q - cÞð1 - γϕÞ, thus w1 < w3 provided that t 2 - γϕt 1 < ð1 - γϕeÞðQ - cÞ. w1 - w4 = γϕð1 - ϕÞðtQ2 - c - et1 Þ, thus w1 > w4. Synthetically,

The condition γq1 ≥ q2r requires that w ≤

w3 > w1 > w4. Therefore,

(i) When w3 > w1 > w > w4, q1 > 0, q2n > 0, q2r > 0. Thus, the optimal production quantities can be obtained as q1 = Q - c2- et1 , q2n = Qð1 -2ðϕ1Þ--ϕhÞ- t2 w

q2r = hþt2 w -2ϕðð11--ϕϕÞÞðcþet2 Þ. (ii) when w3 > w1 > w4 > w, q1 > 0, q2n > 0, q2r < 0. Thus, the optimal production quantities can be obtained as: q1 = Q - c2- et1 , q2n = Q - c2- et2 , q2r = 0.

Proof of Proposition 1 According to the optimal production quantity in Proposition 1, the first derivatives of the optimal production quantity in relation to the carbon tax prices can be obtained as follows: In ∂q2r ∂t 1

∂q = γ ∂t11

region ∂q < 0, ∂t2r2

1,

∂q1 ∂t 1

=

-e 2ðϕγγþ1Þ

< 0,

∂q1 ∂t 2

=

- γ ðe - wÞ 2ðϕγγþ1Þ

0, ∂t2r2 > 0 if w > e(1 - ϕ); ∂t21 < 0, ∂t2r2 < 0 if w < e(1 ∂t 2   ∂q ∂q e - wϕγγ ϕ). ∂t2n1 = eϕγ > 0, ∂t2n2 = 2½1-þγγϕ ð1 - ϕÞ < 0.  ∂q1 ∂q2n ∂q ∂q2r - eð1 - ϕÞ -e In region 3, ∂t1 = 2 < 0, ∂t2 = 2ð1--wϕÞ < 0, ∂t2r2 = w2ϕ ð1 - ϕÞ ; thus, ∂t 2 > 0 ∂q when w > e(1 - ϕ), and ∂t2r2 < 0 when w < e(1 - ϕ).

Proof of Proposition 2 Based on the optimal production quantities, the optimal total emissions in each region can be derived as follows:

48

3

In

region

A Two-Period Carbon Tax Regulation for Manufacturing and. . .

ð1þϕγ ÞQ - ðcþet 1 Þ - γ ½ðc - hÞþt 2 ðe - wÞ ; 2ðϕγγþ1Þ    In region 2:E2 = e q1 þ q2n

=

E1 = eq1 þ ðe - wÞq2r = ½e þ ðe - wÞγ  

1:

þ q2r ðe - wÞ

½eð1 - ϕγ Þ þ γ ðe - wÞ½ðQ - c - et 1 Þ - γ ð1 - ϕÞðc þ et 2 Þ þ γ ðh þ wt 2 Þ 2½1 þ γγϕð1 - ϕÞ eðQ - c - et 2 Þ ; 2

þ

In region 3:E3 = e q1 þ q2n þ q2r ðe - wÞ =

eϕð1-ϕÞðQ-c-et 1 Þ þ eϕQð1-ϕÞ þ ðe-wÞðh þ t2 wÞ-eϕðh þ t 2 wÞ- ð1-ϕÞðe-wÞðc þ et 2 Þ ; 2ϕð1-ϕÞ

In region 4: E4 = e q1 þ q2n = 2eðQ - cÞ -2 e ðt1 þt2 Þ; Thus, the first derivatives of the optimal total emissions in relation to the carbon tax prices are as follows: ∂E  ∂E  ðe - wÞγ  Þ½eþðe - wÞγ  < 0, ∂t21 = - γ ðe -2ðwϕγγ < 0. In region 1, ∂t11 = - e2½eþ ðϕγγ þ1Þ þ1Þ 2

∂E 2 ∂t 2

γ ½eð1 - ϕγ Þþγ ðe - wÞ½w - eð1 - ϕÞ - e2 ½1þγγϕð1 - ϕÞ . Thus, if w < e(1 2½1þγγϕð1 - ϕÞ ∂E 2 ∂E  if γ > ϕ), ∂t2 < 0. Otherwise, if w > e(1 - ϕ), then ∂t22 > 0 ∂E 2 e2 ½1þγγϕð1 - ϕÞ ½eð1 - ϕγ Þþγ ðe - wÞ½w - eð1 - ϕÞ; otherwise, ∂t 2 < 0. ∂E  ∂E 3 e 2 ϕð 1 - ϕÞ ½w - eð1 - ϕÞðe - wÞ - weϕ . Then, if In region 3: ∂t13 = -2ϕ ð1 - ϕÞ < 0, ∂t 2 = 2ϕð1 - ϕÞ ∂E 3 w < e(1 - ϕ), ∂t2 < 0. Otherwise, if w > e(1 - ϕ), then when ∂E  ∂E  ðe - wÞ½w - eð1 - ϕÞ - e ð 1 - ϕÞ  > w, ∂t23 > 0; when ðe - wÞ½wϕe < w, ∂t21 < 0. ϕe

In region 2:

=

Proof of Corollary 1 (1) In region 1, (2) In

region

∂E 1 ∂t 1

=

2,

- e½eð1 - ϕγ Þþγ ðe - wÞ 2½1þγγϕð1 - ϕÞ

(a) When

w

∂E  ∂E  e½eþðe - wÞγ  ∂E 1 γ ðe - wÞ½eþðe - wÞγ  ; thus, ∂t11 - ∂t21 > 0; 2ðϕγγ þ1Þ , ∂t 2 = 2ðϕγγ þ1Þ ∂E 2 ∂E  ½w - eð1 - ϕÞ - e2 ½1þγγϕð1 - ϕÞ = γ½eð1 - ϕγ Þþγðe - w2Þ½1þγγϕ , ∂t12 = ð1 - ϕÞ ∂t 2

< 0; therefore,
0 2½1þγγϕð1-ϕÞ

.

Appendix

49

(3) In region 3,

∂E 3 ∂t 1

=

- e2 ϕð1 - ϕÞ ∂E 3 2ϕð1 - ϕÞ , ∂t 2

(a) When w > e(1 - ϕ) and

∂E 3 ∂t 2

(b) When w < e(1 - ϕ), then

=

½w - eð1 - ϕÞðe - wÞ - weϕ . 2ϕð1 - ϕÞ

< 0, then

∂E 3 ∂t 1

-

∂E 3 ∂t 2

∂E 3 ∂t 1

=

-

∂E 3 ∂t 2

Then, - ½eð1 - ϕÞ - w2 2ϕð1 - ϕÞ

= 2

- ½eð1 - ϕÞ - w 2ϕð1 - ϕÞ

< 0.

< 0.

Proof of Proposition 3 The relationship between the optimal total emissions and the emission savings per remanufactured product can be derived as follows: ∂E 1 ∂E  c - et 1 Þ - γ ½ϕQ - ðc - hÞ = γ t2 ½eþ2ðe - wÞγ - ðQ2ð-ϕγγþ1 . Thus, ∂w1 > 0 when Þ ∂w ∂E  ½ϕQ - ðc - hÞ - et 2 , and ∂w1 < 0 otherwise. w < e - ðQ - c - et1 Þþγ2γt 2 ∂E  2 Þþγ ðhþwt 2 Þþγt 2 ½eð1 - ϕγ Þþγ ðe - wÞ In region 2, ∂w2 = - γ½ðQ - c - et1 Þ - γð1 - ϕÞð2cþet . Thus, ½1þγγϕð1 - ϕÞ  ∂E 2 ∂E 2 ðQ - c - et 1 Þ - γ ½cð1 - ϕÞ - h - et 2 > 0 when w < eð1 - ϕÞ ; otherwise, ∂w < 0. 2γt 2 ∂w ∂E 3 ð1 - ϕÞðcþ2et 2 Þ - 2wt 2 - h In region 3, ∂w = ; thus, when w < eð1 - ϕÞ þ cð1 -2tϕ2Þ - h, 2ϕð1 - ϕÞ ∂E 3 ∂E  > 0; otherwise, ∂w3 < 0. ∂w

In region 1,

Proof of Proposition 4 In region 1, the optimal total emission increment after remanufacturing can be formulated as E 1 - E 0 = ½e þ γ ðe - wÞ  ðQ - c - et 1 Þþγ ½ϕQ - ðc - hÞ - t 2 ðe - wÞ 2ð1þϕγγ Þ

- e ðQ - c - et1 Þþ2 ðQ - c - et2 Þ ; then, we obtain the first ∂ðE 1 - E0 Þ = derivatives of the emission increment in relation to the tax prices as ∂t 1   2 ∂ðE 1 - E0 Þ eγ ½w - eð1 - ϕγ Þ ðe - wÞ½eþγ ðe - wÞ and = e ð1þϕγγÞ -2γð1þϕγγ . 2ð1þϕγγ Þ Þ ∂t 2 Defining f(w) = e2(1 + ϕγγ) - γ(e -pw)[e + γ(e - w)], theptwo roots of f(w) = 0 can

p

be

derived

as

eþ

e 1-

1þ4ð1þϕγγ Þ 2γ

,e þ

e 1þ

1þ4ð1þϕγγ Þ 2γ

.

Since

1þ4ð1þϕγγ Þ > 0, we can conclude that f(w) > 0 when e p 2γ p e 1þ4ð1þϕγγ Þ - 1 e 1þ4ð1þϕγγ Þ - 1 . < w < e and f(w) < 0 when w < e 2γ 2γ p p e 1þ4ð1þϕγγ Þ - 1 2γγϕþ1 - 1þ4ð1þϕγγ Þ - ðe - eϕγ Þ = e < 0, synthetiSince e 2γ 2γ p e 1þ4ð1þϕγγ Þ - 1 ∂ðE 1 - E0 Þ , then < cally, we can obtain that when w < e 2γ ∂t 1 p     e 1þ4ð1þϕγγ Þ - 1 ∂ðE 1 - E0 Þ ∂ðE 1 - E0 Þ < 0 ; when < w < eð1 - ϕγ Þ, then < 0, 2γ ∂t 2 ∂t 1 ∂ðE 1 - E0 Þ ∂ðE 1 - E 0 Þ ∂ðE 1 - E 0 Þ 0, > 0; and when w > e(1 - ϕγ), then > 0, > 0. ∂t 2 ∂t 1 ∂t 2 e 1þ

In region 2, the optimal total emission increment after remanufacturing can be formulated as: E 2 - E 0 = ½eð1 - ϕγ Þþγ ðe - wÞ½ðQ - c - et 1 Þ - γ ð1 - ϕÞðcþet 2 Þþγ ðhþwt 2 Þ - eðQ - c - et 1 Þ½1þγγϕð1 - ϕÞ : 2½1þγγϕð1 - ϕÞ

Then, the first derivatives of the emission increment in relation to the tax prices are ∂ðE 2 - E 0 Þ ∂ðE 2 - E 0 Þ eð1 - ϕÞð1 - γϕÞ ðe - wÞ½w - eð1 - ϕÞ = eγ½w2-½1þγγϕ , and = γ½eð1 - ϕγ2Þþγ . Thereð 1 - ϕÞ  ½1þγγϕð1 - ϕÞ ∂t 1 ∂t 2 ∂ðE 2 - E 0 Þ ∂ðE 2 - E0 Þ < 0, < 0 when w < e(1 - ϕ)(1 - γϕ); fore, we can obtain that ∂t 1 ∂t 2

3 A Two-Period Carbon Tax Regulation for Manufacturing and. . .

50 ∂ðE 2 - E 0 Þ ∂t 1 ∂ðE 2 - E 0 Þ ∂t 1

> 0,

∂ðE 2 - E 0 Þ ∂t 2 ∂ðE 2 - E 0 Þ ∂t 2

< 0 when e(1 - ϕ)(1 - γϕ) < w < e(1 - ϕ); and

> 0, > 0 when w > e(1 - ϕ). In region 3, the optimal total emission increment after remanufacturing can be 1 - ϕÞ - w - ½h - cð1 - ϕÞg formulated as E 3 - E 0 = ½w - eð1 - ϕÞft2 ½eð2ϕ . Thus, ð1 - ϕÞ 2 ∂ðE 3 - E 0 Þ = - ½w2ϕ-ð1eð-1 -ϕÞϕÞ < 0. ∂t 2 Proof of Proposition 5 The profit increment between the cases with remanufacturing and the case without remanufacturing is as follows: (1)

2

t2 <  2

(2)

2

 3

ϕ2 γ 2 ð1 - ϕÞϕγ 2 ðQ - c - et 1 Þ2 > 0; 4γ 2 ϕ2 fðQ - c - et 1 Þþγ ½ðhþwt 2 Þ - ð1 - ϕÞðcþet 2 Þg2 - ½1þγγϕð1 - ϕÞðQ - c - et 1 Þ2  . 0= 4½1þγγϕð1 - ϕÞ γγϕð1 - ϕÞðQ - c - et 1 Þ2     2, w > w1; thus, 2 - 0 > 20 w = w1 = 4

ð1 - ϕγ ÞðQ - cÞ e

-

region (3)

2

- ðc - hÞ - t 2 ðe - wÞg - 0 = fðQ - c - et1 Þþγ½4ϕQ - ðQ - c - et1 Þ þ4 ðQ - c - et2 Þ , in ð1þϕγγ Þ region 1, w > w2 ; thus, 2 Þ - ϕγ ðQ - c - et 1 Þ ½ϕQ - ðc - hÞ - t 2 ðe - wÞ > ðγγϕþ1ÞðQ - c - etγγϕ . Therefore, ½ðγγϕþ1Þ - γ2 ϕ2 ðQ - c - et2 Þ2 - γ2 ϕ2 ðQ - c - et1 Þ2     . Since 10> 10 w = w2 = 4γ 2 ϕ2  1

-

 0

=

þ ϕγt 1 ;

 1

-

 0

>

½ϕQ - ðc - hÞ - ðe - wÞt 2 ½ϕðcþet2 Þ - ðc - hÞ - ðe - wÞt2  4ϕð1 - ϕÞ

þ

In > 0.

ϕðQ - c - et2 Þ½Qð1 - ϕÞ - h - wt 2  4ϕð1 - ϕÞ

2

ϕð1 - ϕÞðQ - c - et 2 Þ . Recall that in region 3, w > w4; thus, we can obtain that 4ϕð1 - ϕÞ ϕðQ - c - et 2 Þ½Qð1 - ϕÞ - h - wt 2  ½ϕðcþet2 Þ - ðc - hÞ - ðe - wÞt2    þ ½ϕQ - cþh - et2 þw4 t24ϕ 30> 4ϕð1 - ϕÞ ð1 - ϕÞ

-

ð1 - ϕÞðQ - c - et 2 Þ2 4ð1 - ϕÞ

=

ð1 - ϕÞðQ - c - et2 Þ2 4ð1 - ϕÞ

-

ð1 - ϕÞðQ - c - et 2 Þ2 4ð1 - ϕÞ

= 0.

The relationship between the profit increment and tax prices is explored as   ∂ð Þ ½ϕQ - c - et 2 þhþwt 2  1 0 follows. In region 1, = 2eγ ϕγðQ - c - et1 Þ4-ð1þϕγγ , recall that in Þ ∂t 1 this region, w > w 2; thus,     ∂ð ∂ð Þ Þ ½ϕγ ðQ - c - et 1 Þ - ðQ - c - et 2 Þ 1 0 1 0 < = 2e < 0. Similarly, we 4γϕ ∂t 1 ∂t 1 ∂ð



w = w2 

Þ 2wγ2 ½ϕQ - ðc - hÞ - t2 eþt2 wþ2γwðQ - c - et1 Þ 2eðQ - c - et2 Þ 0 = þ . can obtain that 4ð1þϕγγ Þ 4 Since and w > w1, [ϕQ - (c - h) - t2e + t2w] > [ϕQ - (c - h) - t2e + t2w1] > 0,   ∂ð 1 Þ 0 > 0. and ∂t 2   ∂ð 2 Þ - wt 2 þγϕð1 - ϕÞðQ - c - et 1 Þ 0 In region 2, = 2eγ ð1 - ϕÞðcþet2 Þ -4h½1þγγϕ , and since ð1 - ϕÞ ∂t 1   ∂ð 2 Þ ð 1 ϕ Þ ð cþet Þ h w t þγϕ ð 1 ϕ Þ ð Q c et Þ 2 1 2 1 0 w > w1, then < 2eγ = 0. Addition4½1þγγϕð1 - ϕÞ ∂t 1   2 ∂ð Þ 2γ ½ ð hþwt Þ ð 1 ϕ Þ ð cþet Þ  ½ w e ð 1 ϕ Þ  2 2 2 0 ally, = . Given w > w1, it is easy to 4½1þγγϕð1 - ϕÞ ∂t 2 obtain that [(h + wt2) - (1 - ϕ)(c + et2)] > γϕ(1 - ϕ)(Q - c - et1) > 0. Therefore,     ∂ð ∂ð Þ Þ 2 0 2 0 > 0 when w > e(1 ϕ), and < 0 when w < e(1 - ϕ). ∂t 2 ∂t 2 ∂t 2 1

References

In

51

region

∂ð





Þ - 2ðc - hÞ - 2ðe - wÞt 2  0 = - ðe - wÞ ½ϕQþϕðcþet2 Þ4ϕ ð1 - ϕÞ ∂t 2 ϕ½wþ2eð1 - ϕÞðQ - c - et 2 Þ . Recall that in this region, 4ϕð1 - ϕÞ

3,

3

- eϕ½Qð14ϕ-ðϕ1Þ--ϕhÞ - wt2  w4 < w < w3; thus, [ϕQ + ϕ(c + et2) - 2(c - h) - 2t2e + 2t2w] > [ϕQ + ϕ(c + et2) t2e + 2t2w] > [ϕQ + ϕ(c + et2) - 2(c - h) - 2t2e + 2t2w4] =ϕ(Q - c - et2) > 0 and   ∂ð 3 Þ 0 [Q(1 - ϕ) - h - wt2] > [Q(1 - ϕ) - h - w3t2] = 0. Therefore, < 0. ∂t 2

References Akçalı, E., & Cetinkaya, S. (2011). Quantitative models for inventory and production planning in closed-loop supply chains. International Journal of Production Research, 49(8), 2373–2407. Benjaafar, S., Li, Y., & Daskin, M. (2013). Carbon footprint and the management of supply chains: Insights from simple models. IEEE Transactions on Automation Science and Engineering, 10(1), 99–116. Brouillard, C., & Van Pelt, S. (2007). A community takes charge: Boulder’s carbon tax. City of Boulder. Chaabane, A., Ramudhin, A., & Paquet, M. (2012). Design of sustainable supply chains under the emission trading scheme. International Journal of Production Economics, 135(1), 37–49. Chang, X., Xia, H., Zhu, H., Fan, T., & Zhao, H. (2015). Production decisions in a hybrid manufacturing-remanufacturing system with carbon cap and trade mechanism. International Journal of Production Economics, 162, 160–173. Chen, J. M., & Chang, C. I. (2013). Dynamic pricing for new and remanufactured products in a closed-loop supply chain. International Journal of Production Economics, 146(1), 153–160. Cong, R., & Lo, A. Y. (2017). Emission trading and carbon market performance in Shenzhen, China. Applied Energy, 193, 414–425. Cruz, J. M. (2008). Dynamics of supply chain networks with corporate social responsibility through integrated environmental decision-making. European Journal of Operational Research, 184(3), 1005–1031. Debo, L. G., Toktay, L. B., & Van Wassenhove, L. N. (2005). Market segmentation and product technology selection for remanufacturable products. Management Science, 51(8), 1193–1205. Fan, J., Li, J., Wu, Y., Wang, S., & Zhao, D. (2016). The effects of allowance price on energy demand under a personal carbon trading scheme. Applied Energy, 170, 242–249. Fahimnia, B., Sarkis, J., Dehghanian, F., Banihashemi, N., & Rahman, S. (2013). The impact of carbon pricing on a closed-loop supply chain: An Australian case study. Journal of Cleaner Production, 59, 210–225. Ferguson, M. E., & Toktay, L. B. (2006). The effect of competition on recovery strategies. Management Science, 15, 351–368. Ferrer, G., & Swaminathan, J. (2006). Managing new and remanufactured products. Management Science, 52, 15–26. Ferrer, G., & Swaminathan, J. M. (2010). Managing new and differentiated remanufactured products. European Journal of Operational Research, 203(2), 370–379. Fleischmann, M., Krikke, H. R., Dekker, R., & Flapper, S. D. P. (2000). A characterization of logistics networks for product recovery. Omega, 28(6), 653–666. Gong, X., & Zhou, S. X. (2013). Optimal production planning with emissions trading. Operations Research, 61(4), 908–924. Guide, V. D. R. J., & Li, J. (2010). The potential for cannibalization of new products sales by remanufactured products. Decision Sciences, 41, 547–572. Hua, G., Cheng, T. C. E., & Wang, S. (2011). Managing carbon footprints in inventory management. International Journal of Production Economics, 132(2), 178–185.

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Ji, J., Zhang, Z., & Yang, L. (2017). Carbon emission reduction decisions in the retail-/dualchannel supply chain with consumers’ preference. Journal of Cleaner Production, 141, 852–867. Kaya, O. (2010). Incentive and production decisions for remanufacturing operations. European Journal of Operational Research, 201, 442–453. Kenne, J. P., Dejax, P., & Gharbi, A. (2012). Production planning of a hybrid manufacturing– remanufacturing system under uncertainty within a closed-loop supply chain. International Journal of Production Economics, 135(1), 81–93. Kim, K., Song, I., Kim, J., & Jeong, B. (2006). Supply planning model for remanufacturing system in reverse logistics environment. Computers and Industrial Engineering, 51(2), 279–287. Liu, B., Holmbom, M., Segerstedt, A., & Chen, W. (2015). Effects of carbon emission regulations on remanufacturing decisions with limited information of demand distribution. International Journal of Production Research, 53, 532–548. Mahmoudzadeh, M., Sadjadi, S. J., & Mansour, S. (2013). Robust optimal dynamic production/ pricing policies in a closed-loop system. Applied Mathematical Modelling, 37(16), 8141–8161. Miao, Z., Mao, H., Fu, K., & Wang, Y. (2018). Remanufacturing with trade-ins under carbon regulations. Computers and Operations Research, 89, 253–268. Sutherland, J. W., Adler, D. P., Haapala, K. R., & Kumar, V. (2008). A comparison of manufacturing and remanufacturing energy intensities with application to diesel engine production. CIRP Annals-Manufacturing Technology, 57(1), 5–8. Xiong, Y., Li, G., Zhou, Y., Fernandes, K., Harrison, R., & Xiong, Z. (2014). Dynamic pricing models for used products in remanufacturing with lost-sales and uncertain quality. International Journal of Production Economics, 147, 678–688. Xu, X., Zhang, W., He, P., & Xu, X. (2017). Production and pricing problems in make-to-order supply chain with cap-and-trade regulation. Omega, 66, 248–257. Yenipazarli, A. (2016). Managing new and remanufactured products to mitigate environmental damage under emissions regulation. European Journal of Operational Research, 249(1), 117–130. Zakeri, A., Dehghanian, F., Fahimnia, B., & Sarkis, J. (2015). Carbon pricing versus emissions trading: A supply chain planning perspective. International Journal of Production Economics, 164, 197–205. Zanoni, S., Segerstedt, A., Tang, O., & Mazzoldi, L. (2012). Multi-product economic lot scheduling problem with manufacturing and remanufacturing using a basic period policy. Computers and Industrial Engineering, 62(4), 1025–1033. Zhang, J. J., Nie, T. F., & Du, S. F. (2011). Optimal emission-dependent production policy with stochastic demand. International Journal of Society Systems Science, 3(1–2), 21–39. Zhang, B., & Xu, L. (2013). Multi-item production planning with carbon cap and trade mechanism. International Journal of Production Economics, 144(1), 118–127.

Chapter 4

A Joint Analysis of the Environmental and Economic Performances of Closed-Loop Supply Chains Under Carbon Tax Regulation

4.1

Introduction

In addition to economic sustainability (Doane & MacGillivray, 2001; Duman et al., 2017), environmental sustainability has been a great concern in recent decades, and growing environmental concerns and regulations have become impetuses for green policies (Tozanlı et al., 2020). In many regions, the cap-and-trade scheme (He et al., 2017; Pan et al., 2019; Thompson et al., 2018) or carbon tax regulation (Krass et al., 2013) is established. For instance, firms in the USA that receive no subsidies or tax credits to remanufacture have to pay emission tax (Yenipazarli, 2016). In 2007, the carbon tax price in the city of Boulder was 0.0002$ per kWh for industrial consumers (Brouillard & Van Pelt, 2007). Growing environmental awareness coupled with stricter regulations has fueled the need for integrating sustainability into supply chain and logistics activities (Tozanli et al., 2017). In response, environmentally friendly business is taken as a critical priority by enterprises, among which incorporating emission abatement into production planning becomes indispensable in operational decisions (Yenipazarli, 2016). Among the implemented activities, remanufacturing has become a dominant tendency in a low-carbon and sustainable economy (Mukhopadhyay & Ma, 2009), by which used products are recollected, processed, and sold again (Fleischmann et al., 2000). Due to fewer raw materials and fewer manufacturing procedures, energy consumption and associated carbon emissions could be significantly reduced, such as photocopiers and diesel engines (Sutherland et al., 2008). Accordingly, the closed-loop supply chain (CLSC) involving remanufacturing plays an important role in environmental protection (Miao et al., 2017). In practice, various channels have been implemented to collect used products. Some manufacturers, such as Hewlett Packard, Canon, and Xerox, collect used products directly from customers. For instance, Xerox provides prepaid mailboxes for customers to return used products (Xerox Corporation, 2001). Other © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Dou et al., Operations Management for Environmental Sustainability, SpringerBriefs in Operations Management, https://doi.org/10.1007/978-3-031-37600-9_4

53

54

4 A Joint Analysis of the Environmental and Economic Performances. . .

manufacturers, such as Eastman Kodak Company, collect single-use cameras through retailers (Das & Chowdhury, 2012). Each time a camera is returned to Kodak, the retailer is reimbursed a fixed fee (Savaskan et al., 2004). Additionally, in the auto industry, independent third parties (i.e., dismantlers), such as the GENCO Distribution System, are handling used-product collection (Savaskan et al., 2004). For different reverse channels in a CLSC, the collection rate varies since the collection activities are taken by different entities (i.e., the manufacturer, the retailer, or the independent third party). As some studies have proven (e.g., Savaskan et al., 2004), the reverse channel choice in a CLSC affects the forward channel decisions. Hence, under emission regulation, the forward and reverse channel decisions among different CLSCs are shaped by regulation in distinct ways. Then, considering the emission constraint, how can production and collection decisions be made in each CLSC? What are the roles of the emission-related factors in determining the decisions? How will CLSCs perform in terms of environmental protection? On the other hand, as is modeled in previous studies (e.g., Chang et al., 2015), to meet market demand, new products are also manufactured in the remanufacturing period, which indicates that the overall production quantity could be enlarged. As such, although remanufacturing requires less emissions, will remanufacturing in a CLSC necessarily mean eco-efficiency? Furthermore, considering economic performance, does a CLSC exist that can be both economically and environmentally better off to achieve Pareto improvement? If one CLSC is the most eco-efficient but another performs the best economically, are there any strategies that can be employed by the regulator (government) to promote the choice of the most eco-efficient CLSC? To explore the issues described above, in this chapter, we formulate models for three CLSCs: (1) the manufacturer is engaged in collection; (2) the retailer is engaged in collection; and (3) an independent third party is engaged in collection. In each supply chain, the operational decisions, the entire profit, and the entire emissions are derived. To explore how remanufacturing affects supply chain performances, we model the scenario without remanufacturing as the benchmark. Then, the optimal decisions between scenarios with and without remanufacturing are compared. To find out whether a CLSC with remanufacturing can be environmentally and economically better off, we compare all supply chain emissions and profits. Moreover, to unveil the impacts of the emission intensities of both the new and remanufactured products and to discuss the government’s strategy of motivating the most eco-efficient CLSC, some numerical studies are conducted. The remainder of this chapter is organized as follows. Section 4.2 includes a review of the related literature. Section 4.3 describes the models and gives the optimal decisions of each supply chain. In addition, the properties of the optimal results are analyzed, based on which some managerial insights are highlighted. Section 4.4 presents some comparisons between cases with and without remanufacturing. Section 4.5 presents the numerical studies. Section 4.6 summarizes and concludes the paper. All the proofs are provided in the Appendix.

4.2

Literature Review

4.2

55

Literature Review

Two main streams of research are related to our work. One stream is the research exploring operational decisions concerning remanufacturing at both the firm level and the supply chain level. The other stream is the research studying the related environmental issues.

4.2.1

Operational Decisions Concerning Remanufacturing

In the literature, many studies focus on the operational decisions and economic implications of remanufacturing on a firm level. Ferguson and Toktay (2006) study pricing and remanufacturing decisions and derive the conditions under which remanufacturing is profitable. Ferrer and Swaminathan (2006) set up two-period and multiperiod models to study production planning concerning remanufacturing. Kaya (2010) uses a newsvendor model to explore the right amount of returns to be used in the remanufacturing process. Zanoni et al. (2012) proposed a novel basic period approach to study the multiproduct economic lot scheduling problem with manufacturing and remanufacturing opportunities. Xiong et al. (2014) propose a dynamic pricing policy to investigate the remanufacturing problem of pricing singleclass used products. Other studies, such as Mahmoudzadeh et al. (2013), Franke et al. (2006), Mitra (2016), and Han et al. (2013), have also explored the operational decisions related to remanufacturing in different settings. From a supply chain perspective, Chen and Chang (2012) study joint decisions on pricing and production lot-sizing in a closed-loop supply chain. Kenne et al. (2012) propose a manufacturing/remanufacturing policy under uncertainty within a CLSC. By developing analytical models using Lagrangian relaxation and dynamic programming schemes, Chen and Chang (2013) study the dynamic pricing for new and remanufactured products in a CLSC. Akçalı and Cetinkaya (2011) provide a comprehensive exposition of state-of-the-art quantitative models for inventory and production planning for CLSC systems. Savaskan et al. (2004) address the problem of choosing the appropriate reverse channel structure for collecting used products from customers. Chen et al. (2015) present a two-period stochastic CLSC model to help original equipment manufacturers develop their remanufacturing strategy. Zhao et al. (2019) consider manufacturer remanufacturing and retailer remanufacturing in a closed-loop supply chain, where pricing, service, and recycling decisions are analyzed. Han et al. (2017) study collection channel and production decisions in a CLSC from the perspective of both firm profit and system robustness. Wei et al. (2019) study a remanufacturing supply chain with dual collection channels under a dynamic setting, and the effects of profit discounts and collection competition on firms’ pricing decisions, collection rates, and profits are analyzed. Although the economic aspects of remanufacturing are well explored in the above research, the environmental problem is not considered. Since remanufactured

56

4 A Joint Analysis of the Environmental and Economic Performances. . .

products consume less emissions and thus are effective for environmental protection, the implications of the environmental aspects of remanufacturing need further exploration. In the following section, we review some of the studies that explore the environmental implications of remanufacturing.

4.2.2

Environmental Implications Concerning Remanufacturing

Assuming limited information on demand distribution, Liu et al. (2015) present three optimization models to determine the remanufacturing quantity that maximizes the total profits under mandatory carbon emissions capacity, carbon tax, and cap-andtrade regulation. Chang et al. (2015) establish two-period models to analyze a remanufacturer’s optimal production quantity and pricing under a cap-and-trade mechanism, where both the independent and substitutable relationships between the remanufactured and new products are considered. Using a leader-follower Stackelberg game model, Yenipazarli (2016) incorporates emission concerns into production and pricing issues in remanufacturing, and the impact of emission-related factors on operational decisions is examined. Wang et al. (2018) characterize the optimal carbon emission tax policy through a two-period model, where the new products and remanufactured products are assumed to be clearly distinguishable. Miao et al. (2017) analyze the optimal pricing and production decisions by addressing the problem of remanufacturing with trade-ins under carbon tax policy and the cap-and-trade program. Differentiated from the research above, we study the optimal operational decisions considering remanufacturing under carbon tax regulation from a CLSC perspective, and we try to discuss the structural priority of CLSCs by jointly measuring both economic and environmental performance. To the best of our knowledge, little research has been conducted to study remanufacturing in a CLSC under emission regulations. Behnam et al. (2013) develop a unified optimization model for a CLSC with carbon cost to investigate the effects of emission tax on the optimal production decision of manufacturing and remanufacturing. Xu and Wang (2018) explore the decision strategy and profit distribution of a CLSC. In this chapter, the retailer is engaged in remanufacturing, while in our paper, remanufacturing is undertaken by the manufacturer. Sarkar et al. (2017) propose a multi-echelon CLSC model to study the impacts of transportation and carbon emission costs, and the best returnable transport items management policies under the influence of these costs are devised. In this paper, third-party logistics provide transportation and collection services. In contrast, we formulate three CLSCs where the manufacturer uses the returns collected by himself, the retailer, and an independent third party. Drawing on the existing research, this chapter provides a framework to investigate the CLSC considering remanufacturing and environmental sustainability and provides insights for a better understanding and management of reverse channels

4.3

Modeling

57

under carbon tax regulation. We contribute to the CLSC research in the sense that (1) we model three main ways of collecting used products under carbon tax regulation; (2) we try to find the optimal reverse channel both economically and environmentally; (3) we explore whether remanufacturing in a CLSC can be eco-efficient or not compared with the case without remanufacturing; and (4) we discuss the government’s strategies when no CLSC can be both economically and environmentally better off.

4.3

Modeling

We consider three CLSCs where the manufacturer, the retailer, and the independent third party are engaged in used product collection. In the first period, new products are manufactured. In the second period, used products are collected for remanufacturing, and new products are also manufactured. Afterward, the second period repeats. In the subsequent period, used products from the former period are collected, and new products are manufactured. Thus, to simplify the research problem and follow the existing research (e.g., Chang et al., 2015; Miao et al., 2017), we focus our attention on the first two periods and set up the model from a two-period perspective. The manufacturer is constrained by the carbon tax regulation over the two periods. Following Savaskan et al. (2004), the decision-making process is modeled as a Stackelberg game where the manufacturer is the leader and the retailer and the independent third party is the follower. All supply chain members have access to full information. The notations in the modeling setup are summarized in Table 4.1. Notation: Variables and explanations

4.3.1

Benchmark Case

To explore whether remanufacturing can be eco-efficient on a whole CLSC level, we first model a benchmark case without remanufacturing. Assuming the demand function is q0 = α - βp0, the profits of the retailer and the manufacturer are ΠR = ( p0 - w0)q0, ΠM = ðw0 - cn Þq0 , where cn (cn = cn þ ten) denotes the marginal production and emission costs of the new products. Maximizing the profit of the retailer, the optimal response is p0 = (α + βw0)/2β; thus, q0 = α - βw0 (α = α=2, β = β=2). Maximizing the manufacturer’s profit with the production decision of q0 = α - βw0 , the optimal wholesale price can be given as w0 = α þ βcn =2β. Thus, q0 = α - βcn =2, p0 = 3α þ βcn =4β, and the optimal total emissions and profit of the supply chain over two periods can be derived as E 0 = en α - βcn , Π0 = 3 α - βcn

2

=4β.

58

4

A Joint Analysis of the Environmental and Economic Performances. . .

Table 4.1 Variables and explanations Variable α en, er wi cn, cr β τ CL t φ b S q0, p0 q1, p1 q2, p2 q2n, q2r ΠiM , ΠiR , ΠiT Π0, E0 Π1, Π2, Π3 E1, E2, E3

4.3.2

Explanation The potential market size in each period The carbon emission for producing one unit of new and remanufactured product The wholesale price of one unit of product in period i, (i = 1, 2) The cost for producing one unit of new and remanufactured product cn > cr The price sensitivity of the new product The collection ratio (0 < τ < 1) The scaling parameter The carbon tax price in over the two periods The unit cost of collecting and handling a returned product The reward given by the manufacturer for each unit of collection The profit subsidy of the government The product quantity and the selling price in the benchmark case The product quantity and the selling price in period 1 The product quantity and the selling price in period 2 The new and remanufactured production quantity in the second period The profit of the manufacture, the retailer, the independent third party in period i The profit and emissions of the supply chain in case without remanufacturing The entire profit of the three types of CLSCs The entire emissions of the three types of CLSCs

Remanufacturing Cases

In this section, we present three CLSCs with reverse channels in which the manufacturer, the retailer, or the independent third party collects used products (Fig. 4.1). In the literature, some claim that remanufactured products are perceived to be of lower quality than those newly produced by some customers (e.g., Ullah & Sarkar, 2020). In contrast, other studies consider that the quality of remanufactured products can be attained as manufactured ones (e.g., Ferrer & Swaminathan, 2006; Sarkar et al., 2019), the disposable camera is a good example (Ferrer & Swaminathan, 2006). In the modern manufacturing industry, due to high-technology development, many materials used in new products are recyclable. For instance, most of the metal aluminum recycled from the old iPhone will be used as 100% recycled metal, and the cobalt recovered from the iPhone battery can be used to make new ones.1 When these materials are used for remanufacturing, the remanufactured products are able to have the same quality as the new ones. Thus, following the second case, we assume that the manufactured and remanufactured products are of the same quality, and there is no price difference between them.

1

https://www.apple.com.cn/cn/environment/

4.3

Modeling

59

Consumer market

Retailer

Manufacturer

Used products

(a) Manufacturer collection Manufacturer

Consumer market

Retailer

Used products

Used products

(b) Retailer collection

Manufacturer

Retailer

Used products

Third party

Consumer market Used products

(c) Third-party collection Forward flow Reverse flow

Fig. 4.1 Three CLSCs with remanufacturing. (a) Manufacturer collection, (b) Retailer collection, (c) Third-party collection

Manufacturer Collection In this scenario, the manufacturer collects used products from consumers. The profits of the manufacturer and the retailer in the first and second periods are formulated as follows: Π1M = ðw1 - cn Þq1 Π1R = ðp1 - w1 Þq1 Π2M = ðw2 - cn Þq2n þ ðw2 - cr Þq2r - C L τ2 - φτq1

,

Π2R = ðp2 - w2 Þq2 where q1 = α - βp1; CLτ2 + φτq1 is the cost of collection characterized as a function of the return rate (Savaskan 2004) and cr is the production and emission costs per unit remanufactured product (i.e., cr = cr þ ter ). Note that q2r = τq1 and q2n = q2 - τq1; then, Π2M = ðw2 - cn Þq2 þ ðcn - cr - φÞτq1 - CL τ2 , and the entire profits of the retailer and the manufacturer over the two periods are reformulated as ΠR = ( p1 - w1)q1 + ( p2 - w2)q2, ΠM = ½ðw1 - cn Þ þ ðcn - cr - φÞτq1 þ ðw2 - cn Þq2 - C L τ2 . Maximizing these two profit functions sequentially, we obtain the following proposition:

60

4

A Joint Analysis of the Environmental and Economic Performances. . .

Proposition 1 When 4C L > βðcn - cr - φÞ2 , let α = α=2, β = β=2, the optimal wholesale prices and the optimal collection rate are derived as w1 = 2C L αþβcn - αβðcn - cr - φÞ

2

β 4C L - βðcn - cr - φÞ

2

, w2 =

αþβcn 2β

, τ =

α - βcn

ðcn - cr - φÞ

4C L - βðcn - cr - φÞ

, and the optimal

2

production quantities and the retail prices in the two periods are q1 = 2C L α - βcn 4C L - βðcn - cr - φÞ

2

, q2 =

α - βcn 2

, p1 =

C L 3αþβcn - αβðcn - cr - φÞ β 4CL - βðcn - cr - φÞ

2

2

, p2 =

3αþβcn 4β

:

Combining Proposition 1 and the benchmark case, we can obtain that w1 < w2 = w0 , q1 > q2 = q0 and p1 < p2 = p0 , i.e., the wholesale and retail prices in the first (second) period are lower (equal) than (with) those in the benchmark case. When the manufacturer undertakes collection, the production and emission cost savings are internalized in its profit; thus, remanufacturing improves the profit. To achieve this goal, the manufacturer increases production in the first period, which leads to a lower wholesale price. Accordingly, the retailer purchases more from the manufacturer and sells with a lower retail price. In the second period, since the new and remanufactured products are sold at the same price, when remanufacturing is completed, the realized demand is the same as in the benchmark case. Therefore, the wholesale and retail prices in the second period are the same as in the benchmark case. The results indicate that remanufacturing lowers product prices, which creates benefits for consumers.

Retailer Collection In this scenario, the retailer collects the used products, which are then delivered to the manufacturer with a reward of b per unit collection. The profits of the retailer and the manufacturer in the two periods are formulated as follows: Π1R = ðp1 - w1 Þq1 Π1M = ðw1 - cn Þq1 Π2R = ðp2 - w2 Þq2 - C L τ2 - φτq1 þ bτq1 Π2M = ðw2 - cn Þq2n þ ðw2 - cr Þτq1 - bτq1

:

Then, the entire profits of the manufacturer and the retailer can be given as ΠM = ½w1 - cn þ ðcn - cr - bÞτq1 þ ðw2 - cn Þq2 , ΠR = ðp1 - w1 Þq1 þ ðp2 w2 Þq2 - C L τ2 - φτq1 þ bτq1 , where q2 = α - βp2. Maximizing these two profit functions sequentially, we obtain the following proposition:

4.3

Modeling

61

Proposition 2 When 2CL > βðcn - cr - φÞ2 , the optimal wholesale prices, the optimal collection rate, and the optimal reward are w1 = w2 = ð cn - cr - φ Þ

α - βcn

2 2C L - βðcn - cr - φÞ

2

C L 3αþβcn - 2αβðcn - cr - φÞ

2

, p1 =

2β

, τ =

, b = cn - cr , and the optimal production quantities and the

retail prices in the two periods areq1 = α - βcn 2

αþβcn

2β 2C L - βðcn - cr - φÞ

2

, p2 =

C L α - βcn ½2C L 3αþβcn 4β

βðcn - cr - φÞ2 , q2 =

:

Note that this proposition shows that the manufacturer does not extract any benefit from remanufacturing since the optimal delivery fee equals the total cost saved by remanufacturing (i.e., b = cn - cr ). The savings are all passed to the retailer. When the retailer undertakes collection, the retailer earns not only p1 - w1 by each unit of product but also b - φ through each collection. Therefore, compared with the benchmark case, the retailer has the incentive to reduce the retail price to enlarge the demand and thus to obtain more collection. For the manufacturer, although there is no direct benefit from remanufacturing, the market demand in the first period is enlarged; thus, profit increases. To extract the maximal profit, the manufacturer would like to raise the wholesale price, which arrives at the highest level when it increases to be the same as in the benchmark case. Otherwise, if the price is higher than in the benchmark case, the retailer’s profit would be damaged. In the second period, as in the former case, the wholesale and retail prices are the same as in the benchmark case. Synthetically, we can derive that w1 = w2 = w0 , p1 < p2 = p0 , and q1 > q2 = q0 . This shows that in the reverse channel of retailer collection, remanufacturing significantly impacts forward channel decisions, while remanufacturing period decisions remain unchanged compared with the benchmark case.

The Third-Party Collection In this scenario, the third party collects used products, which are then delivered to the manufacturer for remanufacturing with the reward of b per unit collection. The profits of the retailer, the manufacturer, and the third party are formulated as follows:

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Π1R = ðp1 - w1 Þq1 Π1M = ðw1 - cn Þq1 :

Π2R = ðp2 - w2 Þq2 Π2M = ðw2 - cn Þq2n þ ðw2 - cr Þτq1 - bτq1 2 T = ðb - φÞτq1 - C L τ

Then, the profits of the retailer and the manufacturer over the two periods can be given as ΠR = ( p1 - w1)q1 + ( p2 - w2)q2, ΠM = ðw1 - cn Þq1 þðw2 - cn Þðq2 - τq1 Þ þ ðw2 - cr Þτq1 - bτq1 . Maximizing these two profit functions sequentially, we obtain the following proposition: Proposition 3 When 8CL > βðcn - cr - φÞ2 , the optimal wholesale prices, the optimal collection rate, and the optimal reward are 2 4C L αþβcn - αβðcn - cr - φÞ ðcn - cr - φÞ α - βcn ðcn - cr þφÞ  , w2 = αþβcn , τ = w1 = 2 2 , b = 2 β 8CL - βðcn - cr - φÞ 2β 8C L - βðcn - cr - φÞ ; the optimal production quantities and the optimal retail prices in the two periods are

q1 =

=

4CL α - βcn 8C L - βðcn - cr - φÞ

2

, q2 =

α - βcn

2CL 3α þ βcn - αβðcn - cr - φÞ2 β 8CL - βðcn - cr - φÞ

2

2

, p2 =

, p1 3α þ βcn : 4β

Combining Proposition 3 and the benchmark case, we also obtain that w1 < w2 = w0 , q1 > q2 = q0 and p1 < p2 = p0 . When the third party undertakes the collection, the collection decision is directly driven by the reward from the manufacturer. A larger reward promotes collection and thus improves the manufacturer’s profit from remanufacturing. However, a larger reward means more cost; thus, the reward cost and profit must be balanced such that the manufacturer extracts half of the gains from remanufacturing and passes the other half to the third party. Since the manufacturer obtains some direct benefit from remanufacturing, as in Case 3.2.1, compared with the benchmark case, a larger number of new products are manufactured in the first period, which leads to lower wholesale and retail prices. Similar to the former two cases, in the second period, the demand is realized as the benchmark case; thus, the prices remain unchanged. In Propositions 2 and 3, we can also find that ∂b/∂t > 0, ∂b/∂en > 0, and ∂b/ ∂er < 0, which means that for a larger emission tax and a larger emission intensity of a new (remanufactured) product, the manufacturer offers more (less) reward. When the emission intensity en (er) increases, manufacturing (remanufacturing) becomes

4.3

Modeling

63

less eco-efficient and less beneficial. Therefore, the manufacturer offers more (less) reward for the collection to enlarge (reduce) the scale of remanufacturing. When the tax price becomes larger, manufacturing incurs more emission cost as en > er. Then, remanufacturing becomes more beneficial; thus, a larger reward is offered by the manufacturer to motivate more collections. To illustrate the impacts of the emission-related factors (i.e., the emission tax and the emission intensities), some sensitivity analyses are conducted. Since the production quantity in the second period is the same as that in the benchmark case, we only present the results for the first period. Proposition 4 The following results hold: (1) The relationship between the optimal collection rate (the optimal production quantity of the first period) and the carbon tax price is (i) When

ðen - er Þ en


0, then ∂τ ∂t (iii) When

ðen - er Þ en

∂q1 ∂t

>

2

XC L þ~β c~n - c~r - φ

XC L þ~β c~n - c~r - φ

2 

, then ∂τ < 0, ∂t

2

XC L - ~β c~n - c~r - φ

~β c~n - c~r - φ

(ii) When

XC L - ~β c~n - c~r - φ

~β c~n - c~r - φ

ðen - er Þ en


0.

(2) The relationship between the optimal collection rate (the optimal production quantity of the first period) and the emission intensity of a new product is (i) When ~α - ~β c~n < ~β c~n - c~r - φ

(ii) When

~β c~n - c~r - φ

XC L - ~β c~n - c~r - φ

XC L þ~β c~n - c~r - φ XC L - ~β c~n - c~r - φ

XC L þ~β c~n - c~r - φ

2

2 

2

< ~α - ~β c~n
0, ∂en1 < 0. ∂en (iii) When ~α - ~β c~n >

XC L - ~β c~n - c~r - φ 2 c~n - c~r - φ

2 

∂τ , ∂e > 0, n

∂q1 ∂en

> 0.

(3) The relationship between the optimal collection rate (the optimal production quantity of the first period) and the emission intensity of a remanufactured 

∂q

< 0, ( ∂e1r > 0), where X = 4, 2, 8 in the case of manufacturer product is ∂τ ∂er collection, retailer collection, and third-party collection, respectively.

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In the results, (en - er)/en can be explained as the emission reduction rate (ERR) of remanufacturing. With a larger tax price, the emission cost increases. Thus, fewer new products are manufactured, and the collection will decrease. However, when the ERR increases to a moderate level such that remanufacturing becomes more eco-efficient, enlarging remanufacturing can be more beneficial. Therefore, when the tax price is raised, fewer new products are manufactured, but the collection increases. When the ERR reaches a very high level, remanufacturing becomes very eco-efficient. Then, although a larger tax price causes more emission costs, the manufacturer expands the production scale in the first period; thus, more used products can be collected in the second period. A smaller value of α - βcn indicates a larger new product emission intensity; thus, the production scale in the first period is reduced, and a large emission cost will still be caused in the second period, although remanufacturing saves emissions; thus, the collection decreases. When α - βcn is large and the new product emission intensity becomes low, remanufacturing becomes more eco-efficient; thus, the collection rate increases. When α - βcn becomes very large, remanufacturing can be very eco-efficient; thus, the emission cost remains low even as the emission intensity increases. Therefore, enlarging the production scale for both new and remanufactured products can be more profitable; thus, either the new product quantity or the collection rate increases. The logic behind the phenomenon that the optimal collection rate decreases with the emission intensity er is easy to understand. Remanufacturing becomes less eco-efficient when er increases; thus, the collection decreases. Meanwhile, as new products become relatively more profitable, enlarging the new product quantity enhances profitability.

4.4

Comparisons

In this part, we make comparisons in two dimensions, i.e., the supply chain emissions in cases with and without remanufacturing and the economic and environmental performances of the CLSCs.

4.4.1

Environmental Impact of Remanufacturing

To explore whether remanufacturing can be more eco-efficient, we compare the entire supply chain emissions between the remanufacturing cases and the benchmark case. Proposition 5 Denote by M1, M2, M3 the three threshold values of 4CL - ~β c~n - c~r - φ

2

N

=4C L ~α - ~β c~n , N 2C L - βðcn - c - φÞ2 =C L α - βcn ,

4.4

Comparisons

65

and N 8CL - βðcn - cr - φÞ2 =8C L α - βcn , where N = βðcn - cr - φÞ, respectively, then when (en - er)/en < Mi, E i > E0 ; otherwise, Ei < E 0 , i = 1, 2, 3. Although remanufacturing saves emissions, Proposition 5 shows that remanufacturing in a CLSC does not necessarily lead to better environmental protection. When the ERR is larger than a threshold, remanufacturing protects the environment. However, when the ERR is smaller than the threshold, remanufacturing causes more emissions. A large ERR indicates that remanufacturing is very eco-efficient and that all emissions can be reduced. However, when ERR is small, remanufacturing slightly reduces emissions; thus, the emission intensity er is still large. Recall that compared with the benchmark case, a larger number of new products are remanufactured in the CLSCs; thus, more emissions are generated. The discussion suggests that to better protect the environment, production technology is required to effectively lower emissions during the remanufacturing process. Otherwise, the environment would be damaged rather than being protected.

4.4.2

Entire Emissions Among the CLSCs

The analysis above shows that all three CLSCs can be eco-effective if the ERR is large enough. To determine which CLSC performs the best environmentally, we compare all supply chain emissions. To make the comparison more tractable, the following lemma is given first. Lemma 1 The following results hold: (1) When 2βðcn - cr - φÞ2 < 4C L < 3βðcn - c - φÞ2 , then M2 < M1 < M3. (2) When 6βðcn - cr - φÞ2 < 8C L < 7βðcn - cr - φÞ2 , then M1 < M2 < M3. (3) When 8C L > 7βðcn - cr - φÞ2 , then M1 < M3 < M2. Lemma 1 illustrates the relationships among the three thresholds given in Proposition 5. With these relationships, we obtain the following results of comparison. Table 4.2 shows that when the ERR is small enough, none of the CLSCs is eco-efficient. When the ERR increases, more CLSCs become eco-efficient. As discussed above, a small ERR means that remanufacturing saves emissions slightly. Thus, when the manufacturer produces more in the first period, all the CLSCs generate more emissions. When the ERR becomes larger, more and more emissions can be saved; thus, more CLSCs become eco-efficient. When more CLSCs are eco-efficient, it remains to be determined which CLSC yields the best environmental performance. In the following section, we make further comparisons to find the most eco-efficient CLSC. Proposition 6 When two supply chains are eco-efficient with remanufacturing,

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A Joint Analysis of the Environmental and Economic Performances. . .

Table 4.2 The entire emissions comparison in cases with and without remanufacturing Threshold value M2 < M1 < M3

M1 < M2 < M3

M1 < M3 < M2

ERR (en - er)/en < M2 M2 < (en - er)/en < M1 M1 < (en - er)/en < M3 (en - er)/en > M3 (en - er)/en < M1 M1 < (en - er)/en < M2 M2 < (en - er)/en < M3 (en - er)/en > M3 (en - er)/en < M1 M1 < (en - er)/en < M3 M3 < (en - er)/en < M2 (en - er)/en > M2

Optimal emission relationship E i > E 0 , i = 1, 2, 3 E 1 > E 0 , E 2 < E 0 , E 3 > E 0 E 1 < E 0 , E 2 < E 0 , E 3 > E 0 E i < E 0 , i = 1, 2, 3 E i > E 0 , i = 1, 2, 3 E 1 < E 0 , E 2 > E 0 , E 3 > E 0 E 1 < E 0 , E 2 < E 0 , E 3 > E 0 E i < E 0 , i = 1, 2, 3 E i > E 0 , i = 1, 2, 3 E 1 < E 0 , E 2 > E 0 , E 3 > E 0 E 1 < E 0 , E 2 > E 0 , E 3 < E 0 E i < E 0 , i = 1, 2, 3

2 4CL - ~β c~n - c~r - φ

denoted by M0 the threshold value of

~α - ~β c~n

c~n - c~r - φ

2

2C L - ~β c~n - c~r - φ 8CL - 3~β c~n - c~r - φ

2

2

, then

(1) When M2 < M1 < (en - er)/en < M3 and E2 < E 0 , E 1 < E0 , then E 2 < E 1 < E0 . (2) When M1 < M2 < (en - er)/en < M3 and E2 < E 0 , E 1 < E0 , then (a) If M2 < M0 < (en - er)/en, E2 < E 1 < E 0 . (b) If (en - er)/en < min {M0, M3}, E1 < E 2 < E 0 . (3) When M1 < M3 < (en - er)/en < M2 and E1 < E 0 , E 3 < E0 , then E 1 < E 3 < E0 .

Proposition 7 When all the CLSCs are eco-efficient with remanufacturing, then (1) When M2 < M1 < M3 < (en - er)/en, then E2 < E1 < E 3 < E0 . (2) When M1 < M2 < M3 < (en - er)/en, then (a) If M2 < M0 < M3 < (en - er)/en, then E2 < E 1 < E 3 < E0 . (b) If M2 < M3 < M0 < (en - er)/en, then E2 < E 1 < E 3 < E0 . (c) If M2 < M3 < (en - er)/en < M0, then E1 < min E2 , E 3 < E 0 . (3) When M1 < M3 < M2 < (en - er)/en, then (a) If M2 < M0 < (en - er)/en, then E2 < E 1 < E 3 < E0 . (b) If M2 < (en - er)/en < M0, then E1 < min E2 , E 3 < E 0 . Proposition 6 (Proposition 7) shows which CLSC is more eco-efficient (the most eco-efficient) when two of them (all three CLSCs) better protect the environment. Recall that Proposition 5 gives the condition under which the CLSC can be eco-efficient. In Proposition 6, when M2 < M1 < (en - er)/en < M3 (M1 < M3 < (en -

4.4

Comparisons

67

er)/en < M2), the ERR satisfies the condition that the manufacturer (the third-party) collection can be eco-efficient but is far beyond the condition that the retailer (manufacturer) collection is eco-efficient. That is to say, the retailer (manufacturer) collection can be more eco-efficient given the ERR, i.e., E 2 < E 1 < E0 (E 1 < E 3 < 0). However, when M1 < M2 < (en - er)/en < M3, retailer collection can still be more eco-efficient. Recall that in the retailer collection scenario, all the remanufacturing savings are passed to the retailer; thus, more used products are collected, and less entire emissions may be generated given a relatively large ERR. Therefore, when (en - er)/en > M0 > M2 > M1, retailer collection can still be more eco-efficient. Otherwise, if (en - er)/en < min {M0, M3} that the ERR is relatively small, the manufacturer collection will be more eco-efficient. The logic behind the results in Proposition 7 can be explained in a similar way. When M2 < M1 < M3 < (en - er)/en, the ERR of remanufacturing is far beyond the level at which retailer collection is eco-efficient; thus, it becomes the most eco-efficient reverse channel. However, when M1 < M2 < M3 < (en - er)/en and M1 < M3 < M2 < (en - er)/en, since the retailer has the largest incentive for collection, the entire emissions can still be the least with an ERR larger enough than M2. That is why retailer collection is the most eco-efficient structure when M2 < M0 < M3 < (en - er)/en (M2 < M3 < M0 < (en - er)/en) and when M2 < M0 < (en - er)/en. Otherwise, if ERR is not large enough (i.e., M1 < M2 < M3 < (en - er)/en < M0 and M1 < M3 < M2 < (en - er)/en < M0), the manufacturer collection will be the most eco-efficient reverse channel. To better illustrate the results, we conduct some numerical examples. The basic parameters are set as α = 1000, β = 2, cn = 20, cr = 15, en = 10, φ = 5. For the first situation in which M2 < M1 < M3 < (en - er)/en, let er = 9.8, CL = 0.4; for t 2 (0, 0.7), the result is shown in Fig. 4.2a. For the second situation that M1 < M2 < M3 < (en - er)/en < M0, let er = 9.97CL = 0.26; for t 2 (0, 2), the result is shown in Fig. 4.2b. For the third situation in which M1 < M3 < M2 < (en er)/en < M0, the parameters are set as er = 9.97, CL = 0.1; for t 2 (0, 2), the result is shown in Fig. 4.2c. Synthetically, either the manufacturer collection or the retailer collection could be the most eco-efficient reverse channel. As we illustrated previously, only half of the remanufacturing savings are passed to the third party, while the manufacturer or the retailer extracts all the savings in the other two channels. As a result, the collection scale is larger in the manufacturer collection or the retailer collection, leading to better environmental performance.

4.4.3

Entire Profits Among the CLSCs

To unveil whether there exists a CLSC that achieves both economic and environmental improvements, we compare the total profits among the CLSCs.

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10000

9600 9400

8000

9200

6000

9000 4000

8800

E1* 2000 E2* E3* E0* 0

0

E1* E2* 8600 E3* E0*

t 0.1

0.2

8400 0.3

0.4

0.5

0.6

0.7

t

0

0.5

1

1.5

2

10000 9500 9000 8500 8000

E1* E2* E3* E0*

7500 7000

0

t 0.5

1

1.5

2

Fig. 4.2 The entire emissions comparison among the CLSCs. (a) M2 < M1 < M3 < (en - er)/en, (b) M1 < M2 < M3 < (en - er)/en < M0, (c) M1 < M2 < M2 < (en - er)/en < M0

Proposition 8 The supply chain profit gets improved with remanufacturing, i.e., Πj > Π0 , j = 1, 2, 3, and the profit relationship among the three CLSCs is Π2 > Π1 > Π3 . Proposition 8 shows that remanufacturing improves the supply chain’s economic performance, and retailer collection performs the best. In our setting, we assume that the price of the remanufactured product is the same as that of a manufactured product. Since remanufacturing consumes fewer production and emission costs, higher profit can be obtained through remanufacturing; thus, Πj > Π0 , j = 1, 2, 3. Furthermore, as the retailer has a full incentive for collection, the benefit from remanufacturing comes to the maximum for the supply chain; thus, retailer collection achieves the highest supply chain profit. From the expression of the supply chain profits, it can be concluded that a larger market potential (α) or a lower degree of price sensitivity (β) improves the supply chain profit. In terms of the cost-related components, i.e., the production costs (cn,

4.5

Numerical Study

69

cr), the unit cost of collecting and handling a returned product (φ), the scaling parameter (CL), the carbon tax price (t), and the emission intensities (en, er), a supply chain profit decrease would be caused when these parameters become larger. Therefore, lowering the production emission intensities by employing “green technologies” or releasing a product for which consumers’ price sensitivity is low contributes to the supply chain profit. Now that retailer collection has the potential to create the highest levels of economic and environmental performance, an interesting question is whether there are any incentives to motivate both the manufacturer and the retailer to choose this channel. To search the answer, we further compare the manufacturer’s and the retailer’s profits, and we obtain the following result. Proposition 9 Both the manufacturer’s and the retailer’s profits are higher in the scenario of retailer collection than in the other two CLSCs, i.e., 1 3 2 1 3 Π2 R > max ΠR , ΠR , ΠM > max ΠM , ΠM . This proposition indicates that there exists an internal incentive inside the supply chain that motivates both the leader and the follower to choose the same reverse channel. Since all the remanufacturing savings are passed to the retailer, the profit increment for the retailer is larger compared with the other two cases. Although none of the savings is extracted by the manufacturer, the whole market demand is enlarged. In addition, considering that half of the remanufacturing savings are obtained by the manufacturer when the third party undertakes the collection and that costs must be paid when the manufacturer undertakes the collection himself, retailer collection also better improves the manufacturer’s profit. Combining the comparisons of economic and environmental performances, we find that remanufacturing improves the supply chain’s performance both economically and environmentally when it saves enough emissions, and retailer collection could be the optimal reverse channel to achieve Pareto improvement. If the remanufacturing technologies are not well developed and the ERR is not large enough, a profit subsidy policy can be employed by the government (i.e., S = Π2 - Π1 ) to promote retailer collection.

4.5

Numerical Study

Through numerical studies, in this section, we attempt to learn how the optimal emissions change with the product emission intensities and how to strategically set the carbon tax price when subsidizing the supply chain for better environmental protection.

70

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4

A Joint Analysis of the Environmental and Economic Performances. . .

Impacts of the Emission Intensities on All Emissions

In this part, we explore the impacts of the emission intensities on the entire supply chain’s emissions. The basic parameters are set as α = 1000, β = 2, cn = 20, cr = 15, φ = 5, CL = 13, t = 2. Let en = 10, and er = 9; then, for er 2 (9.5, 10) and en 2 (9, 9.1), we obtain the emissions of the three CLSCs with different er and en shown in Figs. 4.3 and 4.4. Figure 4.3 shows that the optimal emissions increase with the emission intensity er, while Fig. 4.4 interestingly shows that the optimal emissions first increase and then decrease with the emission intensity en. Recall that in Proposition 4, we demonstrate that although a larger emission intensity er leads to a lower collection rate, the production scale in the first period is improved; thus, more emissions are generated. On the other hand, Proposition 4 shows that when en increases from a relatively low level, remanufacturing becomes more beneficial; thus, the manufacturer enlarges the collection for remanufacturing, which also leads to more emissions. However, when en reaches a very high level, the first-period production scale decreases because of the improved emission cost. Meanwhile, in the second period, fewer used products will be collected, as remanufacturing also causes more emission costs, as the original emission intensity en is very large. Therefore, all emissions decrease. The results above suggest that lowering the emission intensity of remanufactured products saves emissions, while lowering the emission intensity of new products may cause damage to the environment. Only when the original emission intensity is relatively small can reducing the emission intensity be effective in realizing emission abatement.

Fig. 4.3 Optimal supply chain emissions with different er

10000 9000 8000

E 1* E *2 E 3*

7000 6000 5000 4000 9.5

9.6

9.7

9.8

9.9

10

4.5

Numerical Study

Fig. 4.4 Optimal supply chain emissions with different en

71

8360 8340 8320 8300 8280

E1* E2* E3*

8260 8240

4.5.2

9

9.02

9.04

en 9.06

9.08

9.1

Government’s Subsidy and Tax Price

In addition to subsidies, the carbon tax price is another important measure for emission control. Then, what is the relationship between them, and how should we strategically take measures for better environmental protection? To search the answer, we conduct another numerical study. With the parameters that α = 1000, β = 2, cn = 20, cr = 15, en = 10, er = 8, φ = 6, CL = 13, for t 2 (0, 1), we obtain the results shown in Fig. 4.5. From Fig. 4.5, we can observe that both supply chain emissions and profit decrease in the carbon tax price in the scenario of manufacturer collection, and the subsidy is concavely related to the tax price. Because the emission cost is small with low tax prices, the manufacturer would like to improve the production scale. As we illustrated, the demand in the retailer collection scenario is large, which leads to a large emission cost increment when the tax price increases. In this situation, remanufacturing is supposed to be reduced; thus, profit decreases. Comparatively, the demand is lower in the scenario of manufacturer collection. A small emission cost increment occurs when the tax price is raised. Therefore, the profit decrement is smaller. To this end, the profit gap between retailer collection and manufacturer collection decreases with low tax prices. When the tax price becomes larger, the emission cost is enlarged; thus, the production scales decrease in both scenarios. Considering that more used products are collected when the retailer undertakes the collection, the profit decrement is smaller as remanufacturing improves the profit. Therefore, the profit gap increases with high tax prices. The results suggest that to motivate manufacturer collection when ERR is small, the government is able to set two tax prices with the same subsidy. If necessary, the government can choose a larger tax price to better protect the environment without

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Fig. 4.5 Entire emissions (profit) in Case 3.2.1 and the subsidy related to the tax price

105

4 3

E1*

2

S * 1 * 2

1 0 -1

t 0

0.2

0.4

0.6

0.8

1

offering more subsidies. Additionally, the government can lower emissions but subsidize less by raising the tax price when it lies in a relatively small scope (e.g., t < 0.5). Otherwise, if the tax price is relatively large (e.g., t > 0.5), although emissions can be decreased, more subsidies must be offered by the government.

4.6

Conclusion

Many companies have organized remanufacturing production lines to achieve environmental sustainability, such as the manufacturers of printer cartridges, single-use cameras, medical equipment, etc. Under carbon tax regulation, we modeled three CLSCs with reverse channels of manufacturer collection, retailer collection, and third-party collection. The economic and environmental performances of the CLSCs are compared. To explore the impacts of remanufacturing, a benchmark case without remanufacturing is modeled. For each CLSC, the equilibrium results are derived, and the impacts of emission-related factors are analyzed. Additionally, numerical analyses are conducted to explore the government’s policy concerning environmental protection and the relationship between the entire supply chain emissions and the emission intensities of both new and remanufactured products. Our results show that compared with the benchmark case, with remanufacturing, the first-period pricing may vary, but the second-period pricing remains unchanged. The emission reduction rate of remanufacturing plays a key role in decision-making. The collection rate and the first-period product quantity are piecewise monotonously related to the tax price and emission intensities. Among the CLSCs, either

Appendix

73

manufacturer collection or retailer collection can be the best reverse channel, while third-party collection is least preferred in terms of environmental protection. Combining the economic performances, it shows that retailer collection can be both environmentally and economically better off to achieve a Pareto improvement. Through numerical studies, we show that for the three CLSCs, a higher emission intensity of remanufactured products leads to more emissions, while a larger emission intensity of new products may either lead to more or less emissions. In addition, if manufacturer collection is the most eco-efficient channel but does not perform the best economically, a profit subsidy policy can be employed by the government to motivate manufacturer collection. Interestingly, we show that the subsidy is concavely related to the carbon tax price, which suggests that with one subsidy, the government can set two tax prices. Our results indicate that to realize better environmental protection through remanufacturing, the technology must be well developed. Otherwise, remanufacturing may harm the environment. From the government’s perspective, the tax price may not be effective in reducing emissions. When remanufacturing becomes very eco-efficient, the manufacturer will expand the production scale; thus, more emissions are generated. Additionally, when manufacturer collection is the most eco-efficient but retailer collection is the most economically efficient, a profit subsidy can be employed to motivate manufacturer collection. With one subsidy, two tax prices can be chosen by the government, with the larger price set for better environmental protection. Moreover, employing “green technologies” to lower the emission intensity of remanufactured products effectively reduces the entire emissions, while lowering the emission intensity of new products pays off only when the original emission intensity is low enough. Some limitations exist in our study. For instance, our models are developed from a two-period perspective, and extending the model to a multiperiod planning horizon can be more meaningful to derive insights for environmental protection in the long run. In addition, we assume that there is no price difference between the remanufactured products and the new products, while more insights can be derived from modeling different prices between them. For future research, the environmental performance of the CLSC under cap-and-trade regulation with distinct emission buying and selling prices is also worthy of exploration. Additionally, how to strategically use green technology during the manufacturing or remanufacturing process is another interesting topic.

Appendix Proof of Proposition 1 The first-order conditions of the manufacturer’s profit in ∂ΠM relation to the wholesale price are = ~α - ~βw1 - ~β w1 - c~n þ ∂w1

4 A Joint Analysis of the Environmental and Economic Performances. . .

74

∂ΠM ∂w2

c~n - c~r - φ τ,

∂ΠM ∂τ

= α - βw2 - βðw2 - cn Þ,

= ð c n - c r - φÞ α - β

w1 Þ - 2C L τ, and the Hessian matrix of ΠM is ∂ΠM ∂ΠM ∂ΠM ∂w1 ∂w1 ∂w1 ∂w2 ∂w1 ∂τ ∂ΠM ∂ΠM ∂ΠM H ðw1 ; w2 ; τÞ = ∂w2 ∂w1 ∂w2 ∂w2 ∂w2 ∂τ ∂ΠM ∂ΠM ∂ΠM ∂τ∂w1 ∂τ∂w2 ∂τ∂τ ~ - 2β 0 - ~β c~n - c~r - φ = : 0 - 2~β 0 - 2CL - ~β c~n - c~r - φ 0 2

Then, jH j = 2β βðcn - cr - φÞ2 - 4C L ; thus, H is negative definite when |
(2)

∂q1 ∂t

= 2βC L

ðen - er Þ en

2

βðcn - cr - φÞ þ4C L - βen ðcn - cr - φÞ 4CL - βðcn - cr - φÞ

ðen - er Þ α - βcn

βðcn - cr - φÞ 4C L - βðcn - cr - φÞ 4CL þβðcn - cr - φÞ

α - βcn

2

2

4C L - βðcn - cr - φÞ

4C L - βðcn - cr - φÞ

2

∂q1 ∂t

; thus,





, ∂τ > 0; otherwise, ∂τ < 0. ∂t ∂t

ðcn - cr - φÞðen - er Þ - en 4CL - βðcn - cr - φÞ

2 α - βcn

2

2 2

2

;

2 2

when

∂q1 ∂t

< 0. ðcn - cr - φÞ 2 2 2tβ α - βcn ðcn - cr - φÞ - t βðcn - cr - φÞ - α - βcn 4C L - βðcn - cr - φÞ ∂τ (3) ∂e = then: 2 2 n 4C L - βðcn - cr - φÞ 2 α - βcn βðcn - cr - φÞ þ4C L  ∂τ > ðcn - cr - φÞ, ∂e > 0; otherwise, ∂τ < 0. when 2 ∂en n β 4C L - βðcn - cr - φÞ 2 - t α - βcn 4C L - βðcn - cr - φÞ 2tβðcn - cr - φÞ α - βcn ðcn - cr - φÞ  (4) ∂τ = , thus 2 2 2 2 ∂er 4CL - βðcn - cr - φÞ 4C L - βðcn - cr - φÞ ∂τ < 0; ∂er >

2 α - βcn

(5) Since in q1 =

,

> 0; otherwise,

thus,

2C L α - βcn 2

4CL - βðcn - cr - φÞ

, only βðcn - cr - φÞ2 contains er, which

decreases with er; thus, we can obtain that (6)

∂q1 ∂en

= 2βtC L

∂q1 ∂er

> 0.

2ðcn - cr - φÞ α - βcn - 4C L - βðcn - cr - φÞ 4C L - βðcn - cr - φÞ

2

;

2 2

2ðcn - cr - φÞ α - βcn > 4C L - βðcn - cr - φÞ2 , ∂q1 ∂en

>0 ;

when otherwise,

< 0. βðcn - cr - φÞ 4C L - βðcn - cr - φÞ

4C L - βðcn - cr - φÞ

2

Let X 1 = X2 =

∂q1 ∂en

thus,

4C L þβðcn - cr - φÞ

α - βcn

- 4C L - βðcn - cr - φÞ

2 α - βcn

2

ð cn - cr - φ Þ

; then, X 1 -

2

2ðcn - cr - φÞ 4C L þβðcn - cr - φÞ

Let X 3 =

, X2 =

2

2

; therefore, X1 < X2.

βðcn - cr - φÞ 4C L - βðcn - cr - φÞ 4C L þβðcn - cr - φÞ

βðcn - cr - φÞ - 4C L

2

2

, X4 =

4C L - βðcn - cr - φÞ 2ðcn - cr - φÞ

2

, then X 3 -

2

X4 =

2ðcn - cr - φÞ 4C L þβðcn - cr - φÞ

2

; thus, X3 < X4.

For the cases of retailer collection and third-party collection, the proof process is similar to the case of manufacturing collection; thus, we omit the detailed proofs for the two cases. We obtain similar sensitivity analysis results as the case of the manufacturer collection, and only the threshold values are different. Proof of Proposition 5 Denoted by E j , j = 1, 2, 3 the total emissions in the three supply chains, from the equilibrium results in the three supply chains, the total emissions in each supply chain can be given as follows:

78

4

E1

E3

2en CL α - βcn

=

E2 =

=

A Joint Analysis of the Environmental and Economic Performances. . .

4C L - βðcn - cr - φÞ

-

2

-

2 2C L - βðcn - c - φÞ2 16CL - βðcn - cr - φÞ2

en α - βcn

ðcn - cr - φÞ

4CL - βðcn - cr - φÞ2

4CL - βðcn - c - φÞ2

en α - βcn

2

2CL ðen - er Þ α - βcn

2 8CL - βðcn - cr - φÞ

CL ðen - er Þ α - βcn

2

þ

en α - βcn 2

ðcn - cr - φÞ

2 2C L - βðcn - cr - φÞ2 -

2

2

4CL ðen - er Þ α - βcn

2

2

::

ðcn - cr - φÞ

8CL - βðcn - cr - φÞ2

2

2

ðcn - cr - φÞ en α - βcn , 2 2 2 4C L - βðcn - cr - φÞ 2 en βðcn - cr - φÞ 4CL - βðcn - cr - φÞ - 4C L ðen - er Þ α - βcn . Then, = α - βcn ðcn - cr - φÞ 2 2 2 4C L - βðcn - cr - φÞ 2 βðcn - cr - φÞ 4CL - βðcn - cr - φÞ ; otherwise, when when ðen e-n er Þ < E 1 > E 0 Then, E1 - E 0 =

2en C L α - βcn

4C L - βðcn - cr - φÞ

2C L ðen - er Þ α - βcn

-

2

4C L α - βcn

ðen - er Þ en

>

βðcn - cr - φÞ 4CL - βðcn - cr - φÞ

, E1 < E 0 .

4C L α - βcn

Similarly, we have. α - βcn ðcn - cr - φÞ E 2 - E 0 =

therefore: when

en βðcn - c - φÞ 2C L - βðcn - c - φÞ 2 2C L - βðcn - c - φÞ

en β ð c n - c r - φ Þ

E 3 - E 0 = α - βcn

and when

2

2

8C L - βðcn - cr - φÞ

2

2

C L α - βcn

βðcn - cr - φÞ 8C L - βðcn - cr - φÞ 8CL α - βcn

2

>

>

- 8CL ðen - er Þ α - βcn

ð en - er Þ en ,

ðen - er Þ en ,

- C L ðen - er Þ α - βcn

2 2

2 8C L - βðcn - cr - φÞ

βðcn - c - φÞ 2C L - βðcn - c - φÞ

2

ðcn - cr - φÞ

2 2

, ,

E 2 > E 0; otherwise, E2 < E 0;

ΔE > 0; otherwise, ΔE < 0.

Proof of Lemma 1 By comparing M1, M2, M3, we can obtain that M1 - M3 =

-β

2

ðcn - cr - φÞ

8C L α - βcn

3

< 0,

- βðcn - cr - φÞ 4C L - 3βðcn - c - φÞ 4C L α - βcn

M1 - M2 =

2

, M2 - M3 =

βðcn - c - φÞ 8CL - 7βðcn - c - φÞ 8C L α - βcn

2

, then

(1) If 2βðcn - cr - φÞ2 < 4C L < 3βðcn - c - φÞ2 , M1 > M2 and M2 < M3, then M 2 < M 1 < M 3. (2) If 6βðcn - cr - φÞ2 < 8C L < 7βðcn - cr - φÞ2 , then M1 < M2 and M2 < M3; thus, M1 < M2 < M3. (3) If 8CL > 7βðcn - cr - φÞ2 , then M1 < M2 and M2 > M3; thus, M1 < M3 < M2.

Appendix

79

Proof of Proposition 6 Simplifying the gap between the entire emissions in the case of manufacturer collection and retailer collection, we have the following:

E1 - E 2 =

-

C L ðen - er Þ α - βcn ðcn - cr - φÞβðcn - cr - φÞ2 8CL - 3βðcn - cr - φÞ2 2CL - βðcn - cr - φÞ2

2

4C L - βðcn - cr - φÞ2

2

2CL βðcn - cr - φÞ2 en 4CL - βðcn - cr - φÞ2 2CL - βðcn - cr - φÞ2 2

2CL - βðcn - cr - φÞ2

Then, letting Ψ = when ðen e-n er Þ > Ψ,

2 4C L - βðcn - cr - φÞ

2

2C L - βðcn - cr - φÞ

α - βcn ðcn - cr - φÞ 8C L - 3βðcn - cr - φÞ  E 1 > E 2 ; otherwise, E 1 < E 2 .

2

2

, we can conclude that

(1) When E2 < E 0 , E 1 < E0 , M2 < M1 < M3, then M 2 < M 1 < paring Ψ and M 2, we can 4C L - 3βðcn - c - φÞ

2

2C L - βðcn - cr - φÞ

:

2

4CL - βðcn - cr - φÞ2

ð en - er Þ en

< M 3 . Comobtain that

2 2

< 0. 2 ðcn - cr - φÞ 8CL - 3βðcn - cr - φÞ 2 2 2 4C L - βðcn - cr - φÞ 2C L - βðcn - cr - φÞ    Thus, ðen e-n er Þ > 2 , and E 2 < E 1 < E 0 . α - βcn ðcn - cr - φÞ 8C L - 3βðcn - cr - φÞ (2) When E2 < E 0 , E 1 < E0 and M1 < M2 < (en - er)/en < M3, then when Ψ - M2 =

C L α - βcn

4CL > 3βðcn - c - φÞ2 ,

4CL - 3βðcn - c - φÞ

2

ðcn - cr - φÞ

C L α - βcn

2C L - βðcn - cr - φÞ

2 2

8C L - 3βðcn - cr - φÞ

2

> 0,

thus

Ψ > M2, then. (a) If M 2 < Ψ


let

ð en - er Þ en ,

Φ=

βðcn - cr - φÞ 4C L - βðcn - cr - φÞ α - βcn

32C L 2 - β

2

8C L - βðcn - cr - φÞ

2

2

ð cn - cr - φ Þ

;

4

then,

if

E 1 > E 3 ; otherwise, E1 < E3 . Comparing Φ and M1, we can obtain

that Φ - M 1 = -

β

2

ðcn - cr - φÞ

4C L α - βcn

3

4C L - βðcn - cr - φÞ

32C L - β 2

2

2 2

ðcn - cr - φÞ

ðen - er Þ en

< 0. Thus,

4

> Φ, and

E 1 < E 3 < 0. Proof of Proposition 7 (1) When M2 < M1 < M3, and (en - er)/en > M3, then Ψ < M2, then (en - er)/ en > Ψ, so E2 < E 1 < 0. Meanwhile, Φ < M1, then (en - er)/en > Φ; thus, E1 < E 3 < 0. Therefore, E 2 < E 1 < E3 < 0. (2) When M1 < M2 < M3 and (en - er)/en > M3, if (a) M2 < Ψ < M3, then Ψ < (en - er)/en, and Φ < (en - er)/en, then E 2 < E1 < E 3 < 0 ; (b) if M3 < Ψ < (en - er)/en, then E 2 < E1 < 0. Meanwhile, since (en - er)/en > Φ, E2 < E 1 < E 3 < 0. (c) if Ψ > (en - er)/en, then E1 < E 2 < 0, and because (en er)/en > Φ, E 1 < E3 < 0. Therefore, E1 < min E2 , E 3 < 0. (3) When M1 < M3 < M2 and (en - er)/en > M2, since Ψ > M2, when 8CL > 7βðcn - cr - φÞ2 , then a) if M2 < Ψ < (en - er)/en, then E 1 > E 2 , and because (en - er)/en > Φ, E2 < E 1 < E 3 < 0; b) when Ψ > (en - er)/en, then E1 < E 2 . Since E1 < E 3 < 0, E 1 < min E 2 , E3 < 0. Proof of Proposition 8 In the case of manufacturer collection, the profits of the manufacturer and the retailer are ΠR = ðp1 - w1 Þq1 þ ðp2 - w2 Þq2 =

2C L C L ~α - ~β c~n

~β 4C L - ~β c~n - c~r - φ

w1 - c~n þ c~n - c~r - φ τ q1 þ w2 - c~n q2 - CL τ2 = þ

α - ~β c~n ~ 4~β

2

:, then

Π1

- Π0

= ΠM

ΠR

þ

2

- Π0

=

C L α - βcn

2

2

þ

C L ~α - ~β c~n

~α - ~β c~n 8~β

ΠM =

2

2

~β 4C L - ~β c~ 2

2

n - c~r - φ 

6C L - βðcn - cr - φÞ

β 4C L - βðcn - cr - φÞ

2

2 2

, thus

Π1 - Π0 > 0. In the case of retailer collection, the profits of the manufacturer and retailer are. ΠR = ½ðp1 - w1 Þ þðb - φÞτq1 þ ðp2 - w2 Þq2 - C L τ2 = ~α - ~β c~n 8~β

C L ~α - ~β c~n

2

4~β 2C L - ~β c~n - c~r - φ

2

þ

2

ΠM = w1 - c~n þ c~n - c~r - b τ q1 þ w2 - c~n q2 = C L ~α -

2CL - ~β c~n - c~r - φ Π2 = ΠR þ ΠM =

2

þ

~α - ~β c~n 4~β

3C L α - βcn

~β c~n

2

2~β

2

;

2

4β 2C L - βðcn - cr - φÞ

2

þ

thus,

3 α - βcn 8β

we

have

that

2

,

and

Appendix

Π2

- Π0

81

=

3C L α - βcn

2

4β 2CL - βðcn - cr - φÞ

> 0.

2

In the case of third-party collection, the profits of the manufacturer, the retailer, and the third-party company are. ΠM = ½ðw1 - cn Þ þ τðcn - cr - bÞq1 þ ðw2 - cn Þq2 =

ΠR = ðp1 - w1 Þq1 þ ðp2 - w2 Þq2 ΠR =

= ðb - φÞτq1 - C L τ = 2

T

 3

 0

-

Π1 ,

Comparing Π1 - Π2 =

Π1 -

 3

=

=

2

2

þ

8β

24C L - βðcn - cr - φÞ 2 2

- C L α - βcn

Π3 ,

and 2

þ

8β

2

2

α - βcn

β 8CL - βðcn - cr - φÞ

Π2

2

CL α - βcn

2

8C L þβðcn - cr - φÞ

β 8C L - βðcn - cr - φÞ

,

> 0. we

can

obtain

2

that

2

βðcn - cr - φÞ 8C L - βðcn - cr - φÞ

2

2

2 2

2

4β 2CL - βðcn - cr - φÞ2 4C L - βðcn - cr - φÞ2 8CL C L α - βcn

2

α - βcn

ðcn - cr - φÞ2

8C L - βðcn - cr - φÞ2

C L α - βcn

2

β 8C L - βðcn - cr - φÞ2

C L α - βcn

16C L - βðcn - cr - φÞ2

4β 8C L - βðcn - cr - φÞ2

8C L C L α - βcn

Thus, the supply chain profit is. 2 2 α - βcn 16C L - βðcn - cr - φÞ  þ = 2 3 4β 8C L - βðcn - cr - φÞ therefore,

2

α - βcn

0

Synthetically, Π2 > Π1 > Π3 . Proof of Proposition 9 Denote by ΠMj , ΠRj the profit of the manufacturer and retailer in scenario j ( j = 1, 2, 3); then For ΠM1 - ΠM2 =

ΠM2 - ΠM3 =

the - CL α - βcn

manufacturer, 2

βðcn - cr - φÞ

2

2β 2C L - βðcn - cr - φÞ2 4C L - βðcn - cr - φÞ2 3C L α - βcn

2

max ΠM1 , ΠM3 ;

>0

82

4

A Joint Analysis of the Environmental and Economic Performances. . .

ΠR2

- ΠR1

ΠR2

- ΠR3

=

For the retailer, =

~ - ~β c~n CL α 4~β 2C L - ~β c~n - c~r - φ C L ~α - ~β c~n

2

2

~β 2 c~n - c~r - φ

2

~β c~n - c~r - φ

4~β 2C L - ~β c~n - c~r - φ

2

4

4C L - ~β c~n - c~r - φ 2

2

16C L þ~β c~n - c~r - φ 8C L - ~β c~n - c~r - φ

2

2

>0 ;

2

2

>0

thus, we can obtain that ΠR2 > max ΠR1 , ΠR3 .

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Xiong, Y., Li, G., Zhou, Y., Fernandes, K., Harrison, R., & Xiong, Z. (2014). Dynamic pricing models for used products in remanufacturing with lost-sales and uncertain quality. International Journal of Production Economics, 147, 678–688. Xu, L., & Wang, C. (2018). Sustainable manufacturing in a closed-loop supply chain considering emission reduction and remanufacturing. Resources, Conservation and Recycling, 131, 297–304. Yenipazarli, A. (2016). Managing new and remanufactured products to mitigate environmental damage under emissions regulation. European Journal of Operational Research, 249(1), 117–130. Zanoni, S., Segerstedt, A., Tang, O., & Mazzoldi, L. (2012). Multi-product economic lot scheduling problem with manufacturing and remanufacturing using a basic period policy. Computers and Industrial Engineering, 62(4), 1025–1033. Zhao, J., Wang, C., & Xu, L. (2019). Decision for pricing, service, and recycling of closed-loop supply chains considering different remanufacturing roles and technology authorizations. Computers & Industrial Engineering, 132, 59–73.

Chapter 5

Does Implementing Trade-In and Green Technology Together Benefit the Environment?

5.1 5.1.1

Introduction Background and Motivation

Environmental sustainability has been a great concern in business operations. For governments, carbon taxation policies or emission trading schemes (ETSs) have been established in many counties around the world (He et al., 2015, 2017). Under climate regulations, establishing an environmentally friendly business operation becomes a priority within enterprises (Yenipazarli, 2016). To meet the environmental standards enforced by governments, green technologies have become a critical area because they can effectively lower emissions of pollutants. Table 5.1 shows many commonly observed green technologies that can reduce the production emission intensity (i.e., the emissions from manufacturing each unit of product). In the industry, we can also observe many examples. In China, Gree invested more than one billion RMB in carbon-reducing green technologies in 2008 to create better product designs with innovative greener products.1 In the USA, Apple focuses on making energy-efficient products with the wide use of “renewable energy.” Apple also strives hard to reduce carbon emissions associated with the “steel” through innovative techniques.2 From another aspect, to better achieve the goal of environmental protection, many governments offer subsidies for sustainability (Han et al., 2020). For instance, in April 2020, the Chinese government subsidized 22,500 RMB for an electrical car with an endurance mileage larger than 400 km.3 In May 2020,

1

http://www.gree.com.cn/public/200908/pop_jsp_catid_1261_id_44306.shtml https://www.apple.com/environment/pdf/products/iphone/iPhone_11_Pro_PER_sept2019.pdf 3 http://www.gov.cn/zhengce/zhengceku/2020-04/23/5505502/files/f5fc2592b25e4ff3a5ba01770 dd5842e.pdf 2

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Dou et al., Operations Management for Environmental Sustainability, SpringerBriefs in Operations Management, https://doi.org/10.1007/978-3-031-37600-9_5

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Table 5.1 Green technologies commonly observed Green technology The use of renewable energy Enhance recycling of materials Green chemistry

Specific examples Solar power, hydropower, wind power Rare earth elements, precious metals, 100% recycled tina Biodegradable plastics, green chemical processesb

a

https://www.apple.com/environment/pdf/products/iphone/iPhone_11_Pro_Max_PER_sept2019. pdf b https://www.acs.org/content/acs/en/greenchemistry/what-is-green-chemistry/examples.html

the French government increased the subsidy from 6000 € to 7000 € for each individual electrical car.4 Other than green technologies, trade-in programs are widely implemented. Under a typical trade-in program, consumers who bring the used products to the company will get cash redeemed when they buy the newer versions of the products. As a part of extended producer responsibility (EPR) and to encourage consumers to buy new-version products, many firms implement trade-in programs. For instance, Apple launched the trade-in program, officially known as the “Apple Reuse and Recycling Program” (Liu et al., 2019), in 2016. Through the official platform VMALL.com, consumers of Huawei can return their old products and purchase any other Huawei products with trade-in rebates. In November 2020, Samsung implemented a trade-in program for intelligent hardware products via both online and offline channels.5 Indeed, an interaction exists between green technologies and trade-in programs. Specifically, when green technologies, such as 100% recycled tin and bioplastics, are used during the manufacturing process, products are recyclable and can be reused to manufacture new products. For instance, the aluminum recycled from the iPhone will be used as 100% recycled metal on MacBook Air; the “cobalt” recovered from the iPhone battery can be used to make new ones.6 Hence, in addition to its marketing attribute, trade-in can be regarded as an effective way to collect used products to realize recycling originating from green technologies, thus helping protect the environment. In practice, trade-in is implemented in two ways, namely, manufacturer-collect (M-collect) or retailer-collect (R-collect) schemes. For instance, Hewlett-Packard (HP) Corporation, as the manufacturer, encourages consumers to return their used computers and peripherals directly (Miao et al., 2017) to HP (i.e., an M-collect scheme). Consumers of Apple can return used products under trade-in to retailers who sell Apple’s products (i.e., an R-collect scheme). Dell also collects returned products from the retail side (Ramani & De Giovanni, 2017). As other studies have proven, reverse channel choice affects forward channel decisions in a closed-loop supply chain (CLSC) (e.g., Savaskan et al., 2004). Thus, when the trade-in program

4

http://news.sina.com.cn/w/2020-05-27/doc-iircuyvi5195161.shtml http://support-cn.samsung.com/campaign/event/2020galaxyactivity/yjhx/index.html 6 https://www.apple.com.cn/cn/environment/ 5

5.1

Introduction

87

Table 5.2 The four strategies under exploration

Strategies 1 With GT Without GT M-collect R-collect

X

2

3 X

X X

X

4 X X

X

is implemented in different schemes (e.g., R-collect and M-collect), the forward channel decision varies. Furthermore, if green technology (GT) is used during the manufacturing process, differences in the decisions of the emission abatement level, production planning, and trade-in rebate may emerge. As a result, it is important to study the role played by the R-collect and M-collect schemes. Motivated by the observed popularity of GT and the existence of different tradein collection schemes (e.g., M-collect and R-collect) under emission regulations in practice, some natural questions arise: Does implementing GT and trade-in together help reduce emissions more than just implementing one of them? Does the trade-in collection scheme (i.e., M-collect versus R-collect) play a role? To answer these questions, four strategies are considered in this chapter: (1) the R-collect scheme without GT; (2) the M-collect scheme without GT; (3) the R-collect scheme with GT; and (4) the M-collect scheme with GT. The first two strategies are taken as benchmark cases to examine the impacts of GT. See Table 5.2 for the details of these four strategies. We can illustrate GT-related strategies using real-world scenarios. For instance, for Strategy 3, the GT can be viewed as the biobased plastic technology used in the manufacturing of iPhone 11 Pro, and Apple iPhones implement trade-in under the R-collect scheme. For Strategy 4, we can observe that HP uses GT for renewable energy and adopts the M-collect trade-in scheme.7

5.1.2

Research Questions and Major Findings

To highlight the focal points of this study, we present the core research questions as follows: 1. Considering that GT reduces production emission intensity, will implementing GT together with trade-in necessarily benefit the environment and consumers? 2. If GT is eco-efficient, which trade-in collection scheme (i.e., R-collect or M-collect) together with GT will perform better for the environment?

7 https://archive.eetindia.co.in/www.eetindia.co.in/ART_8800491654_1800008_NT_d0b2286d. HTM

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3. With the variation in the carbon tax rate, which strategy is superior from the perspectives of environmental performance, economic performance, and social welfare? 4. From the government’s perspective, when pursuing better environmental protection, how can we design a “carrot-and-stick” policy combining carbon taxes and subsidies to best entice supply chain members and consumers to establish a greener strategy? Through exploring the above research questions, several important insights are obtained. For instance, to enhance supply chain profitability, the manufacturer and retailer should cooperate in the trade-in program, and GT should be used during the manufacturing process. However, more emissions might be generated by implementing GT in each trade-in scheme, which is harmful to the environment. In addition, within different schemes, depending on the emission tax rate, implementing GT does not always enhance the supply chain’s profits or social welfare. From the perspective of environmental protection, Strategy 1 or Strategy 4 should be advocated by the government. We find that a well-designed “carrot-andstick” policy can help entice supply chain members to establish a greener strategy. In particular, the carbon tax (“stick”) can be adjusted to achieve the right environmental greenness level, and subsidies (“carrots”) can be good supplements to motivate the supply chain and consumers to favor the greener strategy.

5.1.3

Contribution Statements and Organization

To the best of our knowledge, we are the first to explore the environmental performance of trade-in programs considering GT together. Our findings challenge the conventional wisdom on whether implementing the trade-in program while using GT together always benefits the environment. In addition, the role played by the government and the proper setting of policies to improve the environment are uncovered. We also indicate how the government can strategically use the “carrotand-stick” policy to achieve the greener strategy. These findings contribute to the literature and provide valuable guidance to policymakers. The remainder of the paper is organized as follows. Section 5.2 presents a concise review of the related literature. Section 5.3 describes the model, gives the optimal decisions, and uncovers the structural properties of the optimal solutions. Section 5.4 presents comparisons and discussions among different strategies. Section 5.5 discusses the government’s policies. Section 5.6 examines extended models for robustness checks. Section 5.7 summarizes and concludes the paper. All the proofs are provided in the Appendix.

5.2

Literature Review

5.2 5.2.1

89

Literature Review Trade-In Programs

In the literature on trade-in programs, many analytical studies focusing on the economic benefits of trade-in have been published over the past few years. For instance, Yin et al. (2015) analyze the optimal prices of two “successive-generation” products. The authors uncover the conditions under which trade-in programs are beneficial. Agrawal et al. (2016) study the price discrimination problem considering trade-in programs. The authors identify the cases in which the customized trade-in rebate should be offered. Miao et al. (2017) model trade-in programs in three CLSCs (namely, those with centralized collection, retailer collection, and manufacturer collection). They provide conditions for each collection strategy to be optimal. Feng et al. (2019) model a dual channel with a single manufacturer to implement trade-in. The authors show that the trade-in program can intensify or mitigate the double marginalization effect if the retailer initially decides the trade-in rebate. Sheu and Choi (2019) develop a generalized consumer choice behavior model to determine the “syncretic value-oriented” prices and trade-in rebates in a competitive market. They propose the implementation of an “extended consumer responsibility” program. Hu et al. (2019) explore the optimal pricing decisions for the nextgeneration products and analytically derive the optimal trade-in rebate in the context of “limited trade-in duration.” The authors interestingly find that the optimal rebate value decreases with the trade-in duration. Cao et al. (2019) consider the optimal trade-in strategy for a direct-sales platform that owns a “self-run store” and hosts a “third-party store.” The authors prove that offering high quality and setting a low selling price for products can do more harm than good for the platform. Bian et al. (2019) explore the optimal “extended warranty strategy” (EWT) with trade-in service and the “traditional extended warranty” (EWR). The authors show that EWT should never be offered at a higher price than EWR, and EWT will outperform EWR if the handling cost for used products is sufficiently small. Most recently, Cao et al. (2020a) examine “gift card payment” and “cash payment” schemes for implementing trade-in. The authors show that the residual value of used products as well as the “scale of replacement” consumers are critical. In addition to the economic perspective, some studies explore the environmental impacts of trade-in strategies. For instance, Miao et al. (2018) analytically investigate new and remanufactured product pricing decisions and the optimal trade-in rebate in the presence of “carbon tax and cap-and-trade” regulations. Zhang and Zhang (2018) study the impacts of consumer purchasing behaviors on the environment under a trade-in program. The authors uncover that trade-in has a negative impact on the environment and social welfare when consumers are forward looking and strategic. Cao et al. (2020b) focus on exploring the optimal “trade-in and warranty” strategies for new and remanufactured products with the consideration of carbon tax regulation.

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Similar to many of the above examined studies, this chapter also analytically explores trade-in strategies considering both the economic and environmental perspectives. However, totally different from them, we evaluate the environmental performance of the trade-in program by considering the usage of GT under the government’s carbon tax regulation. This has not been studied in the extant literature.

5.2.2

Closed-Loop Supply Chains

In sustainable operations, CLSC management, including topics such as sourcing (Dai et al., 2020), coordination (Huang et al., 2002), and product returns (Mukhopadhyay & Setoputro, 2007), is probably the most widely studied area. In a popular paper, Savaskan et al. (2004) address the channel leadership choice of the reverse channel for used products collection. Savaskan and Wassenhove (2006) explore the interaction between a manufacturer’s reverse channel choice and strategic product pricing decisions in the forward channel. Then, Akçalı and Cetinkaya (2011) review the quantitative operations literature on inventory and production planning for CLSCs. The authors identify and propose new research avenues in CLSCs with a focus on inventory and production planning. Using optimal control theory based on stochastic dynamic programming, Kenne et al. (2012) analytically explore the production planning and control of a single product CLSC system. Chen and Chang (2013) investigate pricing behavior in a two-period setting for both new and remanufactured products in a CLSC system. Reimann et al. (2019) analyze how to lower remanufacturing costs via “process innovation.” They find that both underinvestment and overinvestment may be created with “process innovation.” Wu and Zhou (2019) revisit the effects of “buyer-specific” pricing and the entry of third-party remanufacturers. Contrary to common beliefs, they show that third-party remanufacturing could lead to a “triple win,” and a “buyer-specific” pricing scheme would be better than a uniform pricing scheme. In addition to the above-reviewed research, some prior studies specifically focus on exploring environmental problems in CLSCs, and we review some as follows. Utilizing data from a company located in Australia, Behnam et al. (2013) complete a comparative analysis for the respective environmental influences. The authors reveal that variations in cost and environmental impacts occur over a certain range of carbon pricing. Xu and Wang (2018) investigate the optimal retail price, emission reduction rate, and recycling rate considering consumer preferences. The authors show how the “self-profit maximization” objective affects the operations performance of the CLSC. Most recently, Dhanorkar (2019) use a “quasi-experimental setup” to investigate the environmental benefits of Internet-enabled consumer-toconsumer CLSCs. Similar to the above CLSC research, we also build analytical models from a CLSC perspective. However, different from them, we consider the trade-in program. In addition, the usage of GT for lowering the production emission intensity in different reverse channels is also considered in our research.

5.2

Literature Review

5.2.3

91

Emission Abatement Decisions

As the pioneering work, Subramanian et al. (2007) model a three-stage game in which firms invest in emission abatement, join a share auction for permits, and produce the demanded output. The authors interestingly show that changing the number of available permits influences abatement in a dirty industry less than that in a cleaner one. Krass et al. (2013) study several important aspects of using environmental taxes to motivate the choice of emission-reducing technologies. They find that while an initial increase in taxes may motivate a switch to greener technology, further raising the tax may motivate a “reverse switch.” Considering that the manufacturer can reduce emissions by using the GT, Xu et al. (2017) study the optimal production and emission abatement decisions under cap-and-trade regulation. The authors show that if the emission trading price increases, the optimal production quantities and the optimal abatement levels will first decrease and increase, respectively, and then remain constant. Ji et al. (2017) focus on exploring an O2O retail supply chain with low-carbon considerations. They examine consumers’ low-carbon preferences in the modeling setup and discuss the optimal emission reduction policies. Drake (2018) and Huang et al. (2020) consider the emission abatement problem with the use of technology related to “carbon leakage.” In particular, Drake (2018) demonstrates that “carbon leakage” can arise despite the presence of carbon tariffs, while Huang et al. (2020) show that border-tax policies can effectively reduce “carbon leakage.” Most recently, Haehl and Spinler (2020) evaluate technology and capacity choices under regulatory uncertainty. They show that an emission cap can help reduce emissions effectively, whereas an emission tax is still important in reducing the regulation cost. Following the above research, we also explore emission abatement decisions under carbon emission regulations. In particular, we try to reveal the emission abatement level when GT is employed. However, our research context is different from the prior studies in which emission abatement decisions are made. The research gap regarding whether implementing trade-in with GT would do more harm than good to the environment is still open. This chapter hence aims to bridge this important literature gap.

5.2.4

Government Policies for Environmentally Sustainable Operations

Among the literature concerning environmental protection in operations, the government’s policies are mainly discussed in terms of emission regulation. Drake et al. (2016) analytically study the impact of “carbon tax and cap-and-trade” regulations on a firm’s technology choice and production capacity decisions. The authors also uncover the effects of the emissions price level as well as government subsidies. Sunar and Plambeck (2016) address the emission allocation rules among coproducts. The authors show that the government should maximize social welfare for the region

92

5 Does Implementing Trade-In and Green Technology Together Benefit. . .

with climate policies in deciding whether and how to implement the optimal “border adjustment” decision. He et al. (2017) explore production planning strategies from the manufacturer’s perspective. The authors also examine the optimal cap-setting decision of the government and derive the optimal cap that maximizes social welfare considering different “emission permit buying and selling prices.” Hammami et al. (2017) study the effects of consumer environmental awareness and environmental regulations on emission intensity and product prices. In their analysis, the authors analytically explore how the carbon tax level can be set strategically to maximize social welfare from the government’s perspective. Jung and Feng (2020) investigate the government’s subsidy for firms’ green technology and its impact on the environment and social welfare. Interestingly, the subsidy is shown to be detrimental to the environment if the government only considers the environmental benefits of technology and its costs. In the above-reviewed works, the regulator’s strategies, including permit allocation, tax setting, or subsidies, are established toward the manufacturer. However, the regulator’s strategy for consumers needs more attention. To enrich this stream of research, we not only discuss regulation policies toward the manufacturer but also explore how to subsidize consumers with respect to special carbon tax rates for better environmental protection.

5.3 5.3.1

Basic Models Benchmark Cases

In a two-stage supply chain (Teunter et al., 2018) context, we first present two models for strategies where GT is not used, i.e., (i) the R-collect scheme and (ii) the M-collect scheme. In the observed real-world practices (e.g., trade-in programs of Apple or Huawei), trade-in programs keep running after being launched. When a new generation of product is released, consumers decide whether to purchase the new product, trade in for them, or do not buy. Then, with trade-in, the manufacturer collects used products and disassembles them for recycling in the future. In the literature, models describing two consecutive generations of products (or two periods) have been built to analyze trade-in decisions (see, e.g., Agrawal et al., 2012; Miao et al., 2017; Liu et al., 2019; Zhang & Zhang, 2018), where potential trade-in consumers are those who purchased first-generation products. However, as observed in current practice, products have been updated for many generations; thus, trade-in consumers may also come from earlier periods. For instance, when the iPhone 12 series is released, all consumers who have the iPhone 8 to iPhone 11 series can potentially be engaged in the trade-in program. To better describe this industrial situation and keep our focus on “how to use green technologies and how to make trade-in decisions simultaneously,” we have modeled a “general case for one generation of products.” The notation used is summarized in Table 5.3.

5.3

Basic Models

93

Table 5.3 Notation Notation α e0 θ wn t cn v λ pir qin, pin qit, pit Πi, Ei

Meaning The potential market size for new products The initial product emission intensity The maximum number of consumers who would return used products The wholesale price of one unit of new product The carbon tax rate The cost for producing one unit of new product The residual value of each unit of returned product of the manufacturer The coefficient of the emission abatement cost The retailer’s reimbursement in Strategy i, (i = 1, 3) The new product quantity and the retailing price in Strategy i, (i = 1, 2, 3, 4) The returned product quantity and return rebate in Strategy i, (i = 1, 2, 3, 4) The supply chain profit and emissions in Strategy i, (i = 1, 2, 3, 4)

R-Collect Scheme Without GT (Strategy 1) In Strategy 1, the manufacturer produces products while the retailer undertakes trade-in activities. After collection, the retailer obtains a reimbursement from the manufacturer for each unit of return. In the decision-making process, the retailer is involved in a Stackelberg game with the manufacturer acting as the game leader. The manufacturer decides the wholesale price and reimbursement, and then the retailer decides the retail price and trade-in rebate. Consumers evaluate the rebate and the new product retail price to decide whether to engage in the trade-in program. Following Genc and De Giovanni (2018), demands include the new product demand q1n and the trade-in demand q1t, for which we assume p1n = α - q1n and ( p1n p1t) = θ - q1t, respectively. Note that trade-in consumers may potentially be those who purchased products of many previous generations other than a proportion of those who just purchased the former generation products; we do not model a constraint between θ and α. The retailer’s decision problem is to maximize the profits from selling the product to new consumers and trade-in consumers, which can be formulated as follows: max

= q1n ðp1n - w1n Þ þ q1t ðp1n - w1n þ p1r - p1t Þ:

ð5:1Þ

1R ðq1n , q1t Þ

In Eq. (5.1), the two terms represent the profits from new product retailing and the trade-in program, in which the net margin from each new consumer is p1n - w1n; for each trade-in consumer, the retailer additionally pays the rebate p1t and earns p1r by shipping the returned product back to the manufacturer. Maximizing Eq. (5.1), the retailer’s best response can be obtained as q1n = ðα - w1n Þ=2,  q1t = ðθ - w1n þ p1r Þ=2.

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Through product distribution, the manufacturer obtains the net profit w1n - cn from each new consumer, earns the residual value of v, and pays p1r to the retailer for each returned product. Therefore, with the retailer’s response, the decision problem of the manufacturer is formulated as follows: max

= q1n ðw1n - cn Þ þ q1t ðv - p1r þ w1n - cn Þ - te0 q1n þ q1t :

ð5:2Þ

1M ðw1n , p1r Þ

In Eq. (5.2), the first two terms are the profits from product distribution and the trade-in program, while the last term describes the carbon tax resulting from manufacturing products with the quantity of q1n þ q1t .

M-Collect Scheme Without GT (Strategy 2) In Strategy 2, the retailer sells the product, and the manufacturer implements tradein. The manufacturer decides the wholesale price and trade-in rebate, and the retailer reacts and decides the retail price. The retailer’s decision problem is formulated as follows: max

= ðq2n þ q2t Þðp2n - w2n Þ:

ð5:3Þ

2R ðq2n Þ

Note that in Eq. (5.3), p2n = α - q2n. Maximizing the profit function, we obtain the retailer’s response that q2n = ðα - w2n - q2t Þ=2. Then, the decision problem of the manufacturer is formulated as follows: max

= q2n ðw2n - cn Þ þ q2t ðv þ w2n - cn - p2t Þ - te0 q2n þ q2t :

ð5:4Þ

2M ðw2n , q2t Þ

In Eq. (5.4), observe that q2t = θ - ( p2n - p2t). The meaning of each term is similar to that of Eq. (5.2), and hence, we omit them for the sake of brevity. Maximizing the manufacturer’s profit functions in Eqs. (5.2) and (5.4), we obtain the following theorem. Theorem 1 The equilibrium results in Strategies 1 and 2 can be summarized in Table 5.4. Theorem 1 presents the optimal decisions for each trade-in scheme when the GT is not used. First, the optimal decisions are all given in analytically neat closed form. Second, we observe that the optimal decisions differ between Strategies 1 and 2 even

5.3

Basic Models

95

Table 5.4 Optimal trade-in decisions without emission abatement Trade-in rebate Reimbursement New product demand Trade-in demand Wholesale price Retailing price

Optimal decisions in Strategy 1 p1t = ½3ðα - θÞ þ v=4 p1r = ðα þ v - θÞ=2 q1n = ½α - ðcn þ te0 Þ=4 q1t = ½θ þ v - ðcn þ te0 Þ=4 w1n = ½α þ ðcn þ te0 Þ=2 p1n = ½3α þ ðcn þ te0 Þ=4

Optimal decisions in Strategy 2 p2t = ðα þ v - θÞ=2 N/A q2n = ½2α - ðcn þ te0 Þ - ðv þ θÞ=6 q2t = ½2ðv þ θÞ - α - ðcn þ te0 Þ=6 w2n = ½α þ ðcn þ te0 Þ=2 p2n = ½4α þ ðcn þ te0 Þ þ ðv þ θÞ=6

though the wholesale price is identical.8 More comparisons will be reported in the subsequent analyses.

5.3.2

Models with GT

In this section, we set up two other models in which GT is used. Following existing research such as Liu et al. (2012), Ji et al. (2017), and Xu et al. (2017), we assume that the cost of using GT exhibits a quadratic form: λ(ei)2/2 (i = 3, 4), where λ measures the marginal emission abatement cost and ei is the emission abatement level. The quadratic cost function means that the cost is convex in the abatement level, and achieving an excellent level of emission reduction is much more expensive than achieving a good level. To show the robustness of our findings with respect to the cost function, we test cases with a linear or exponential cost function in Sect. 6.1.

R-Collect Scheme with GT (Strategy 3) In Strategy 3, the decision-making process is similar to Strategy 1, except that the manufacturer makes an additional decision on the emission abatement level. This is similar to the case for Apple’s iPhone 11 Pro, in which a GT using biobased plastic is employed in manufacturing processes and trade-in of iPhones is collected by retailers. The retailer’s decision problem is formulated as follows:

8 With reference to real-world practices, we assume that all optimal decisions are interior points and they are positive.

5 Does Implementing Trade-In and Green Technology Together Benefit. . .

96

= q3n ðp3n - w3n Þ þ q3t ðp3n - w3n þ p3r - p3t Þ

max 3R ðq3n , q3t Þ

s:t:

ð5:5Þ

p3n = α - q3n , ðp3n - p3t Þ = θ - q3t :

Here, we assume that customers’ demands are not affected by the GT. Similar to Krass et al. (2013), we first focus on this situation in the main part and consider consumers’ environmental awareness in which the demand accelerates when GT is used in the extension. We show that our main results still hold when consumers’ demand is affected by the GT (see the extension in Sect. 6.3). With the response of the retailer, the manufacturer’s optimization problem can be formulated as follows: max

= q3n ðw3n - cn Þ þ q3t ðv - p3r þ w3n - cn Þ - t ðe0 - e3 Þ

3M ðw3n , p3r , e3 Þ

 q3n þ q3t - λðe3 Þ2 =2:

ð5:6Þ

M-Collect Scheme with GT (Strategy 4) Likewise, the decision-making process of Strategy 4 is similar to Strategy 2, with the exception that the manufacturer decides the emission abatement level. This case appears in HP, in which its trade-in program is based on the “manufacturer-collect” mode and HP also invests in GT, focusing on using renewable energy to manufacture electronic products. The retailer’s optimization problem is formulated as follows: max

= ðq4n þ q4t Þðp4n - w4n Þ

4R ðq4n Þ

ð5:7Þ

s:t:p4n = α - q4n : With the retailer’s response, the optimization problem of the manufacturer is formulated as follows:

5.4

Comparisons and Analysis

97

Table 5.5 Optimal trade-in decisions with emission abatement Optimal decisions in Strategy 3 when t2 < 2λ Trade-in rebate

p3t =

Emission abatement level Reimbursement

e3 =

New product demand Trade-in demand

½3ðα - θÞþv 4 tðαþvþθ - 2cn - 2te0 Þ 2ð2λ - t 2 Þ

p3r = q3n = q3t =

αþv - θ 2

Optimal decisions in Strategy 4 when t2 < 3λ p4t = e4 =

αþv - θ 2 t ðαþvþθ - 2cn - 2te0 Þ 2ð3λ - t2 Þ

N/A

ð4λ - t2 Þαþt2 ðθþvÞ - 4λðcn þte0 Þ 8ð2λ - t2 Þ

 q4n =

αð4λ - t2 Þ - 2λðcn þte0 Þ - ð2λ - t2 ÞðvþθÞ 4ð3λ - t2 Þ

αt 2 þðvþθÞð4λ - t 2 Þ - 4λðcn þte0 Þ 8ð2λ - t 2 Þ

q4t =

αðt 2 - 2λÞþð4λ - t 2 ÞðvþθÞ - 2λðcn þte0 Þ 4ð3λ - t 2 Þ

Wholesale price

w3n =

αð4λ - 3t 2 Þ - t 2 ðθþvÞþ4λðcn þte0 Þ 4ð2λ - t2 Þ

w4n =

3αð2λ - t2 Þ - t2 ðvþθÞþ6λðcn þte0 Þ 4ð3λ - t 2 Þ

Retailing price

 = p3n

αð12λ - 7t2 Þ - t 2 ðθþvÞþ4λðcn þte0 Þ 8ð2λ - t 2 Þ

p4n =

αð8λ - 3t 2 Þþ2λðcn þte0 Þþð2λ - t 2 ÞðvþθÞ 4ð3λ - t2 Þ

max

= q4n ðw4n - cn Þ þ q4t ðv þ w4n - cn - p4t Þ - t ðe0 - e4 Þ

4M ðw4n , q4t , e4 Þ

 q4n þ q4t - λðe4 Þ2 =2:

ð5:8Þ

Optimizing the manufacturer’s profit functions in (6) and (8) under the respective supply chain gaming structure, we obtain the following theorem. Theorem 2 The equilibrium results for Strategies 3 and 4 are summarized in Table 5.5. Theorem 2 illustrates that the carbon tax rate has no impact on the trade-in rebate and the corresponding reimbursement. For trade-in consumers, the price they pay for a new product is pin - pit (i = 3, 4), and the impact of the carbon tax is reflected in the new product price; the trade-in rebate only reflects the residual value of used products. On the other hand, during the process in which the returned products are shipped back, nothing related to manufacturing happens. As a result, the value of the tax does not affect the reimbursement.

5.4

Comparisons and Analysis

In this section, we explore the optimal pricing decisions and the corresponding impacts among the four strategies. We assume that t2 < 2λ, which is equivalent to the case when λ > t2/2 (i.e., λ is sufficiently large). This assumption reflects a common situation in practice and avoids having the optimal decisions go to the boundary (i.e., the optimal decisions exist in the “interior”), and the closed-form results are valid.

98

5.4.1

5

Does Implementing Trade-In and Green Technology Together Benefit. . .

Pricing Properties

By comparing the trade-in rebates and product retail prices, we obtain the following proposition. Proposition 1 Denote pit as the extra price that trade-in consumers need to pay, i.e., pin - pit (i = 1, 2, 3, 4), and let t =

λ½2ðvþθÞ - α - ðcn þte0 Þ ½ðvþθÞ - ðcn þte0 Þ , t =

λ½2α - ðcn þte0 Þ - ðvþθÞ ½α - ðcn þte0 Þ

; then: (1) If α > θ + v, then p1t > p2t and p3t > p4t ; otherwise, p1t < p2t and p3t < p4t . (2) p1n < p2n , p3n < p4n , and p1t < p2t ,p3t < p4t . (3) If t < t (t < t), then p4n > p1n (p4t > p1t ); if t > t (t > t), then p1n > p4n (p1t > p4t ). First, Proposition 1 illustrates that the R-collect scheme may generate either higher or lower trade-in rebates than the M-collect scheme. Second, both the new product retail price and the extra price that trade-in consumers need to pay are lower in the R-collect scheme. Third, there exists a threshold such that when the tax rate is smaller (larger), the prices in Strategy 4 would be higher (lower) than that in Strategy 1. The results indicate that although a higher rebate may be offered in the M-collect scheme, both groups of consumers (i.e., the new product purchasing consumers and the trade-in consumers) pay higher prices in this scheme. In addition, using GT does not always create benefits for consumers. For better illustrations, we conduct a numerical example for new product retail prices. Following the model setting and the respective real-world physical meanings, we set the parameters as follows: α = 105, v = 10, cn = 5, e0 = 10, θ = 95, λ = 50, then for t 2 [0, 9.9], Fig. 5.1 shows the relationship among the prices. For the trade-in rebate, the condition α < θ + v indicates a high residual value, with which a higher trade-in demand improves profit. Thus, the manufacturer prefers improving the rebate to attract more trade-in consumers. Otherwise, if α > θ + v, the manufacturer will not be well motivated to collect more. However, the retailer can improve his profit by implementing the trade-in program; thus, the rebate would be improved by the retailer to attract more trade-in consumers. Compared with the M-collect scheme, a proportion of the benefit from trade-in is extracted by the retailer in the R-collect scheme. To enhance his own profit, the manufacturer would like to increase demand; thus, the prices become lower in the R-collect scheme. Between Strategies 1 and 4, the impact of GT is weak with a small tax rate, and then the production scale is larger with the R-collect scheme, thus leading to lower prices. However, when the tax rate exceeds a certain threshold, the emission tax increases significantly if GT is not used. As a result, the production scale reduces considerably in Strategy 1, thus leading to higher prices in Strategy 4. Our results indicate that regardless of whether the GT is used, the trade-in program benefits consumers more in the R-collect scheme than in the M-collect scheme. In other words, compared with implementing trade-in alone by the

5.4 Comparisons and Analysis 95

99

* p1n * p2n * p3n * p4n

90

85

80

75

70

t 0

2

4

6

8

10

Fig. 5.1 The new product retail prices in the four strategies

manufacturer, cooperating with the retailer to implement trade-in in a supply chain improves consumers’ benefit. As we can observe in practice, consumers of Samsung are encouraged to return used products to offline retailers or cooperators; Apple implements trade-in through retail stores. However, using the GT is not always beneficial. Particularly, if the emission tax rate becomes sufficiently large, consumers benefit more in the R-collect scheme without GT than in the M-collect scheme with GT.

5.4.2

Impacts of the Carbon Tax and the Emission Abatement Cost

By conducting sensitivity analyses of the emission abatement levels and product retail prices, we explore the impacts of the carbon tax rate and the coefficient of the emission abatement cost. The results are summarized below. Proposition 2 The following results hold: (1) In all strategies, the new product retail price increases with the carbon tax rate, i.e., ∂pin =∂t > 0 (i = 1, 2, 3, 4); in Strategies 3 and 4, the new product retail price increases with the coefficient of the emission abatement cost, i.e., ∂pin =∂λ > 0 (i = 3, 4). (2) In Strategies 3 and 4, the emission abatement level increases with the carbon tax rate, i.e., ∂ei =∂t > 0 (i = 3, 4).9 9

Note that ei only exists in Strategies 3 and 4 where the GT is used.

100

5

Does Implementing Trade-In and Green Technology Together Benefit. . .

Proposition 2 reveals intuitive results that both a larger tax rate and a larger coefficient of emission abatement cost lead to higher new product retail prices, and a larger tax rate induces a higher emission abatement level. The logic behind this is that the emission tax increases with a larger tax rate, and the emission abatement level decreases as it requires a higher cost when the coefficient increases. To avoid paying more emission taxes, the manufacturer reduces the production scale to lower total emissions. As a result, the price increases. Likewise, when the emission tax increases with a larger tax rate, to reduce the total emissions, more effort can be devoted to reducing the emission intensity, which improves the emission abatement level. Our results indicate that when the tax rate increases, improving the product price would be more beneficial. For instance, due to the value-added tax, the ThinkPad Tablets (16GB Wi-Fi) were sold in Hong Kong at 3998 HK$ but at 5999 on JD. COM.10 In addition, devoting more effort to emission abatement (if the GT is used) could also be effective. In our model, the emission-related costs include the carbon tax and the emission abatement cost. Although using the GT causes emission abatement costs, the emission tax is reduced; thus, part of the loss can be compensated.

5.4.3

Environmental Performance

By comparing the total emissions11 of the four strategies, we obtain the following important proposition on environmental performance. Proposition 3 The following results hold: E1 > E 2 and E3 > E4 ; _

_

_

(1) If t < t , then E 1 > E3 (E 2 > E4 ); if t > t , then E 1 < E3 (E 2 < E4 ), where t = _ λðΦ - 2e0 t Þ=e0 ð2λ - t 2 Þ (t = 3λðΦ - 2e0 t Þ=2e0 ð3λ - t 2 Þ ) for the R-collect scheme (M-collect scheme). ^ ^ ^ (2) If t < t , then E1 > E 4 ; if t > t , then E 1 < E4 , where t = e0 3λ2 þ t 4 =λð6te0 - ΦÞ. Proposition 3 shows three aspects of comparisons: (1) the total emissions in the M-collect scheme are less than those in the R-collect scheme regardless of whether the GT is used; (2) for each scheme, fewer (more) total emissions are generated when the GT is used with a tax rate smaller (larger) than a threshold; and (3) there also exists a threshold that for a smaller (larger) tax rate, fewer (more) emissions are generated in Strategy 4 than in Strategy 1. For better illustration, we give another

10

https://news.qq.com/a/20120306/000132.htm We define the total emissions as the production emission intensity multiplying the production quantity. 11

5.4

Comparisons and Analysis

101

500

E3* E1* E4* E2*

400

300

200

100

0

t 0

2

4

6

8

10

Fig. 5.2 The total emissions of the four strategies

numerical example. With the same set of parameters above, the total emissions of the four strategies are shown below. Figure 5.2 illustrates the results in Proposition 3. Recall that the production scale is larger in the R-collect scheme than in the M-collect scheme either when the GT is used or not; thus, more emissions are generated in the R-collect scheme. For each scheme, the production scale remains large with a small tax rate even if GT is not used. Thus, more emissions are generated. However, if the tax rate becomes very large, the production scale will decrease considerably if GT is not used. Fewer emissions are hence generated. For this reason, with a quite large tax rate (e.g., ^ t > t ), the emissions become even lower in Strategy 1 than in Strategy 4. Interestingly, the results above suggest that the M-collect scheme outperforms the R-collect scheme in terms of environmental protection, even though consumers favor the R-collect scheme as the prices are lower. Contrary to this finding, in Miao et al. (2017), the R-collect scheme is shown to be more environmentally efficient. The difference is driven by the presence of GT in our paper because the R-collect scheme induces a higher emission abatement level, the production scale then becomes larger, and hence, more emissions are generated. Our results also indicate that implementing trade-in together with the GT does not always benefit the environment. When the tax rate becomes very large, using the GT may lead to more emissions. Therefore, when the government aims to achieve better environmental protection by raising the tax rate, the GT may not be suitable to be continually used regardless of who implements the trade-in program.

102

5.4.4

5

Does Implementing Trade-In and Green Technology Together Benefit. . .

Economic Performance

To analyze the performance and “priority” of the strategies, in this part, we explore the economic performance of each strategy in terms of supply chain profit. Because the theoretical comparison of the profits is difficult to make, a numerical study is used here. With the same set of parameters as before, we show the supply chain profits in Fig. 5.3. Observation 1 There exists a threshold t for the emission tax rate such that Π3 > Π1 > Π4 > Π2 if t < t and Π3 > Π4 > Π1 > Π2 if t > t. Figure 5.3 shows that Strategy 3 (2) creates the highest (lowest) economic benefit. In particular, the R-collect scheme together with GT generates more economic gains. In addition, given a small (large) emission tax rate, Strategy 4 creates a lower (higher) supply chain profit than Strategy 1. Within each trade-in scheme, when the GT is used, the manufacturer enlarges the production scale. Although it incurs an emission abatement cost, the carbon tax is reduced, which implies that the supply chain obtains a higher profit. However, having GT does not always create more profit. When the tax rate is smaller than t, the supply chain profit under Strategy 1 is higher than that under Strategy 4. Previously, we demonstrated that the market demand in the R-collect scheme is higher than that in the M-collect scheme. With a small tax rate, the GT would not create a substantial benefit, as the original emission tax is not heavy. Owing to the larger demands in the R-collect scheme, Strategy 1 creates a higher profit. In contrast, when the tax becomes sufficiently large, the production scale diminishes considerably. Thus, only a small gap exists between consumers’ demands in the two strategies. Meanwhile, using the GT effectively lowers the total emissions. Consequently, Strategy 4 becomes more profitable than Strategy 1. In line with Miao et al. (2017), our results indicate that compared with the M-collect scheme, implementing trade-in in the R-collect scheme generates more Fig. 5.3 The supply chain profits of the four strategies

4000

P*3 P*4 P1* P*2

3500 3000 2500 2000 1500

1000 500 0

t 0

2

4

6

8

10

5.5

Government Policy

103

economic gains (i.e., Π3 > Π4 , and Π1 > Π2 ). As we can observe in practice, the R-collect scheme is chosen by firms such as Apple, Huawei, and Samsung, and used products are collected by retailers or the online platforms they cooperate with. Interestingly, using the GT in each scheme is economically beneficial (i.e., Π3 > Π1 , and Π4 > Π2 ), while this is not the case within different schemes. When the tax rate is small enough, compared with the M-collect scheme with GT, implementing trade-in in the R-collect scheme without GT creates a higher profit. Moreover, considering that the GT may not benefit the environment, when the tax rate is set to be very large for better environmental protection, some “economic sacrifices” are needed; thus, the GT is not supposed to be advocated. Our finding is consistent with Savaskan et al. (2004) but contrary to Miao et al. (2017) or Feng et al. (2019). Savaskan et al. (2004) demonstrate that more supply chain profits can be brought by the R-collect scheme, while Feng et al. (2019) and Miao et al. (2017) show that the M-collect scheme improves supply chain profits. In the context of Feng et al. (2019), when the manufacturer autonomously decides the trade-in rebate, the system nearly becomes centralized, and hence, the supply chain profit is improved. In Miao et al. (2017), the government subsidy for consumers is modeled, which accelerates the trade-in demand. Under the respective circumstances, the manufacturer would use his power to control the wholesaling and collection, which helps improve both his own and the supply chain profits. In contrast, in our model, the retailer has the power to determine the trade-in rebate, which strikes a balance between new product retailing and used product collection. By expanding the whole market demand, a higher supply chain profit is achieved.

5.5

Government Policy

In this section, by modeling social welfare, we explore the government’s policy in balancing environmental protection, supply chain profit, and consumer benefits by imposing carbon tax and subsidy measures. Following the existing research (e.g., Krass et al., 2013; He et al., 2017; Zheng et al., 2020), we formulate social welfare as follows: SW i = Πi þ Sit þ Sin - τE i ,

ði = 1, 2, 3, 4Þ,

ð5:9Þ

where the coefficient τ measures the degree of environmental awareness of the government, which translates the emissions into monetary units; and Sit (Sin ) is the surplus of trade-in consumers (new product purchasing consumers), which is defined as follows:

104

5

Does Implementing Trade-In and Green Technology Together Benefit. . .

5000

SW3* SW4* SW1* SW2*

4000

3000

2000

1000

0

t 0

2

4

6

8

10

Fig. 5.4 Social welfare with the increase of the carbon tax rate

qit

Sit =

qin

θ -x- pin -pit dx,

Sin =

0

α-x-pin dx , ði=1,2,3,4Þ, ð5:10Þ 0

As the analytical results of the comparison are difficult to obtain, we also use a numerical study to learn the social welfare in the four strategies. Assuming τ = 0.05, with the same set of parameters, we show the social welfare in Fig. 5.4. Observation 2 There exists a threshold t for the emission tax rate such that ~

SW 3 > SW 1 > SW 4 > SW 2 if t < t and SW 3 > SW 4 > SW 1 > SW 2 if t > t. ~

~

Figure 5.4 shows that Strategy 3 (2) creates the highest (lowest) social welfare. When the tax rate is smaller (larger) than a threshold t , the social welfare under ~

Strategy 1 is higher (lower) than that under Strategy 4. This is mainly because with a small carbon tax rate, the consumer surplus in Strategy 1 is higher than that in Strategy 4, and when the tax rate becomes larger, the GT improves the consumer surplus. As a result, Strategy 4 creates a higher level of social welfare. From the observed relationships, we interestingly show that having GT does not always benefit the whole society. If the tax rate is small enough, Strategy 4 is inferior to Strategy 1. If the government makes decisions from the social welfare perspective, Strategy 3 has the top priority, as it creates the most social welfare and supply chain profit. However, maximizing social welfare may not always be the sole purpose. Facing severe environmental pollution, sacrificing a proportion of social welfare to protect the environment may become necessary. For instance, 36 enterprises stopped

5.5

Government Policy

105

Table 5.6 The advocated strategy and corresponding subsidies Carbon tax rate _

t< t _

^

t t

Advocated strategy Strategy 3 Strategy 4 Strategy 4

Ssc 0 Π3 - Π4 Π3 - Π4

SN 0 p3n - p4n p3n - p4n

ST 0 p3t - p4t p3t - p4t

Decision purpose Better SW Better EP Better EP

Strategy 4 Strategy 1

Π3 - Π4 Π3 - Π1

p3n - p4n p1n - p3n

p3t - p4t p1t - p3t

Better SW Better EP

manufacturing activities in February 2014 in Beijing during haze weather.12 Combining the environmental and social welfare performances, we suggest the following policies from the government perspective. Proposition 4 (the optimal “carrot-and-stick” policy): Denoted by Ssc, SN, and ST, the subsidies for the supply chain, the new product purchasing consumers, and the trade-in consumers, respectively, the carbon tax setting and subsidizing policies _ for the government can be listed in Table 5.6 ( t = λðΦ - 2e0 t Þ=e0 ð2λ - t 2 Þ , SW, social welfare; EP, environmental protection). First, in the case of light pollution, the prior policy is to set a carbon tax rate _ _ smaller than t and advocate Strategy 3 (see Fig. 5.2 for fewer emissions when t < t and Fig. 5.4 for the highest level of social welfare). If the government aims to achieve better environmental protection, then Strategy 4 should be advocated (see _ Fig. 5.2 for the lowest emissions when t < t ). Second, if the environment needs more _ protection, then setting a carbon tax larger than t and advocating Strategy 4 is the proper action (see Figs. 5.2 and 5.4 for fewer emissions from Strategy 4 than Strategy 1 but a higher level of social welfare). Third, if the environment needs ^ urgent protection, then setting the carbon tax larger than t is the choice. If the government pursues better social welfare, Strategy 4 should still be advocated; otherwise, if further environmental protection is needed, Strategy 1 should be advocated (see Figs. 5.2 and 5.4, the emissions can be further mitigated in Strategy 1, but the social welfare is not largely reduced). Corresponding to these polices, Fig. 5.3 reveals that the supply chain profit gets hurt and the prices may be raised if Strategy 3 is not advocated. As a result, supply chain members or consumers may be reluctant to follow the government’s policy, which conflicts with the goal of attaining environmental sustainability. To motivate cooperation, subsidies can be offered. Specifically, when advocating Strategy 4, the supply chain should be subsidized with Π3 - Π4 , and the two groups of consumers should be subsidized with p3n - p4n and p3t - p4t for each purchase. If Strategy 1 is advocated, the supply chain and the two groups of consumers should be subsidized with Π3 - Π1 , p1n - p3n , and p1t - p3t , respectively. In the literature, such as Webster and Mitra (2007), Ma et al. (2013), and Zhang and Zhang (2018), a subsidy/tax policy is proposed for social welfare maximization, 12

http://www.chinanews.com/gn/2014/02-22/5869903.shtml

5 Does Implementing Trade-In and Green Technology Together Benefit. . .

106

in which only the firm is involved. Comparatively, in our research, the proposed “carrot-and-stick” policy is customized and powerful. According to the urgent levels of environmental protection, we propose corresponding policies that include emission taxes and subsidies for both the supply chain and consumers (i.e., not just the firm).

5.6

Extension: Consumers’ Environmental Awareness

We now explore the supply chain decisions to check the robustness of our results when considering consumers’ environmental awareness, i.e., consumers would like to pay more for greener products when GT is used. Following Xu et al. (2017) and Ji et al. (2017), inverse demand functions are set as follows: pin = α - qin þ ξei and ðpin - pit Þ = θ - qit þ ξei for new and trade-in consumers, respectively. The parameter ξ represents the strength of consumers’ environmental awareness. The decisionmaking problems in Strategies 3 and 4 can be formulated as follows. (1) R-Collect Scheme with GT (Strategy 3) In this strategy, the retailer’s decision problem is formulated as follows: max 3R = q3n ðp3n - w3n Þ þ q3t ðp3n - w3n þ p3r - p3t Þ ðq3n , q3t Þ s:t:

p3n = α - q3n þ ξe3 ,

ð5:21Þ

ðp3n - p3t Þ = θ - q3t þ ξe3 :

Maximizing the profit function, the best response of the retailer can be given as q3n = ðα þ ξe3 - w3n Þ=2, and q3t = ðθ þ ξe3 - w3n þ p3r Þ=2. With the retailer’s response, the manufacturer’s decision problem is given below: max 3M = q3n ðw3n - cn Þ þ q3t ðv - p3r þ w3n - cn Þ - t ðe0 - e3 Þ ðw3n , p3r , e3 Þ  q3n þ q3t - λðe3 Þ2 =2: (2) M-Collect Scheme with GT (Strategy 4) In this strategy, the retailer’s decision problem is formulated as follows:

ð5:22Þ

5.6

Extension: Consumers’ Environmental Awareness

107

Table 5.7 Optimal decisions in Strategy 3 considering consumers’ environmental awareness Optimal supply chain decisions when 2λ > (ξ + t)2 3ðα - θÞþv 4 ðtþξÞ½αþvþθ - 2ðcn þte0 Þ 2½2λ - ðξþt Þ2 

Trade-in rebate

p3t =

Emission abatement level

e3 =

Reimbursement

p3r =

New product demand

q3n =

Trade-in demand

 = q3t

Wholesale price

w3n

Retailing price

p3n =

=

αþv - θ 2 α½4λ - ðξþt Þ2 þðvþθÞðtþξÞ2 - 4λðcn þte0 Þ 8½2λ - ðξþtÞ2 

αðtþξÞ2 þðvþθÞ½4λ - ðtþξÞ2  - 4λðcn þte0 Þ 8½2λ - ðξþt Þ2 

α½4λ - ðtþξÞðξþ3t ÞþðvþθÞðξ - tÞðtþξÞþ4ðcn þte0 Þ½λ - ξðtþξÞ 4½2λ - ðξþtÞ2  α½12λ - ðtþξÞð3ξþ7tÞþðtþξÞðvþθÞð3ξ - t Þþ4ðcn þte0 Þ½λ - 2ξðtþξÞ 8½2λ - ðξþt Þ2 

max 4R = ðq4n þ q4t Þðp4n - w4n Þ ðq4n Þ s:t:p4n = α - q4n þ ξe4 :

ð5:23Þ

Maximizing the profit function, the best response of the retailer can be given as q4n = ðα þ ξe4 - w4n - q4t Þ=2. With the retailer’s response, the manufacturer’s decision problem is formulated as follows: q4n ðw4n - cn Þ þ q4t ðv þ w4n - cn - p4t Þ - t ðe0 - e4 Þ q4n þ q4t

max 4M = - λðe4 Þ2 =2 ðw4n , q4t , e4 Þ

s:t:ðp4n - p4t Þ = θ - q4t þ ξe4 : ð5:24Þ Solving the profit-maximizing problem in each strategy, we obtain Theorem 3. Theorem 3 The equilibrium results in Strategies 3 and 4 when considering consumers’ environmental awareness are summarized in Tables 5.7 and 5.8. Theorem 3 shows similar results as Theorem 2. Based on the derived results, we next explore the relationships among the optimal prices and supply chain emissions and discuss the properties of the optimal pricing and emission abatement levels. The results are summarized in Proposition 5. ^

Proposition 5 Denote pit as the extra price that trade-in consumers need to pay, i.e., pin - pit (i = 3, 4); then: p p p p ^ ^ (1) When 3 λ < 2 2t, then p3n < p4n , and p3t < p4t ; when 3 λ > 2 2t, then there ^ ^ exists a unique ξ (ξ) at which p3n = p4n (p3t = p4t ), and if ξ < ξ (ξ < ξ), p3n < p4n

108

5

Does Implementing Trade-In and Green Technology Together Benefit. . .

Table 5.8 Optimal decisions in Strategy 4 considering consumers’ environmental awareness Optimal supply chain decisions when 3λ > (ξ + t)2 ðαþv - θÞ 2 ðtþξÞ½ðαþvþθÞ - 2ðcn þte0 Þ 2½3λ - ðξþt Þ2 

Trade-in rebate

p4t =

Emission abatement level

e4 =

New product demand

q4n =

α½4λ - ðtþξÞ2  - ðvþθÞ½2λ - ðtþξÞ2  - 2λðcn þte0 Þ 4½3λ - ðξþtÞ2 

ðvþθÞ½4λ - ðξþtÞ

2

 - α½2λ - ðξþtÞ2  - 2λðcn þte0 Þ

Trade-in demand

q4t =

Wholesale price

w4n =

α½6λ - ðtþξÞðξþ3tÞþðvþθÞðξ - t ÞðtþξÞþ2ðcn þte0 Þ½3λ - 2ξðtþξÞ 4½3λ - ðξþt Þ2 

Retailing price

p4n =

α½8λ - ðtþξÞðξþ3tÞþðvþθÞ½2λþðtþξÞðξ - tÞþ2ðcn þte0 Þ½λ - 2ξðtþξÞ 4½3λ - ðξþtÞ2 

4½3λ - ðξþtÞ2 

p p ^ ^ (p3t < p4t ); otherwise, when ξ < ξ < 2λ - t (ξ < ξ < 2λ - t ), p3n > p4n ^ ^ (p3t > p4t ). ^ (2) If t < t (t < t ), then p1n < p4n (p1t < p4t ); otherwise, if t > t (t > t ), then p1n > p4n (p1t

_

_

> p4t ), where

t= t=

_

^

2λ þ ξ2 ½ðv þ θÞ - ðcn þ te0 Þ - ½α - ðcn þ te0 Þ½λ - 2ξðt þ ξÞ ½ðv þ θÞ - ðcn þ te0 Þ

.

λ þ ξ2 ½α - ðcn þ te0 Þ þ λ½α - ðv þ θÞ þ 2ξðt þ ξÞ½ðv þ θÞ - ðcn þ te0 Þ ½α - ðcn þ te0 Þ

Recall that in Proposition 1, we have shown that when consumers’ demand is not affected by the GT, the prices are lower in Strategy 3 than in Strategy 4, i.e., p3n < p4n , and p3t < p4t . In contrast, Proposition 5 reveals that depending on the strength of consumers’ environmental awareness, the prices in Strategy 3 may become higher than those in p Strategy p 4. Note that the condition 3 λ < 2 2t implies high emission abatement levels in Strategies 3 and 4 because when λ is small, the demand in Strategy 3 is lifted to a larger p extent p as the emission abatement level is higher. When λ becomes large (3 λ > 2 2t ), less effort is devoted to emission abatement in both strategies. Under this circumstance, if consumers’ environmental awareness is weak (ξ < ξ), the GT cannot bring too much benefit. Then, raising the prices helps compensate for the cost of emission abatement. In contrast, with strong environmental awareness, the demand can still be well enhanced, although the emission abatement level is low. Hence, the GT well benefits the manufacturer in the M-collect scheme, and a higher profit can be obtained by further increasing the demand. Thus, the prices are lowered in Strategy 4. The results suggest that for costly GT, consumers’ environmental awareness becomes a key determinant in shaping pricing strategies. In particular, if consumers strongly prefer greener products, lowering the prices for both new and trade-in consumers can be more profitable.

5.6

Extension: Consumers’ Environmental Awareness

109

Proposition 6 In Strategies 3 and 4, the following results hold: (1) When ξ(t + ξ)2 + λ(ξ - t) < 0 (ξ(ξ + t)2 + λ(2ξ - t) < 0), ∂p3n =∂t < 0 (∂p4n =∂t < 0); otherwise, ∂p3n =∂t > 0 (∂p4n =∂t > 0). (2) When 3ξ > t (5ξ > t), ∂p3n =∂λ < 0 (∂p4n =∂λ < 0 ); otherwise, ∂p3n =∂λ > 0 (∂p4n =∂λ > 0). (3) When λ(3ξ + t) < t(ξ + t)2 (λ(5ξ + 2t) < t(ξ + t)2), ∂p3n =∂ξ < 0 (∂p4n =∂ξ < 0); otherwise, ∂p3n =∂ξ > 0 (∂p4n =∂ξ > 0). ^ (4) When e0 < e0 (e0 < e0 ), ∂e3 =∂t > 0 (∂e4 =∂t > 0 ); otherwise, ∂e3 =∂t < 0 ½ðαþvþθÞ - 2ðcn þte0 Þ½2λþðtþξÞ2  (∂e4 =∂t < 0 , ), where e0 = 2ðtþξÞ½2λ - ðξþt Þ2  ½ðαþvþθÞ - 2ðcn þte0 Þ½3λþðtþξÞ2  ^ e0 = . 2ðtþξÞ½3λ - ðξþt Þ2  Recall that in Proposition 2, the new product retail prices are shown to increase with the emission tax rate and the coefficient of emission abatement cost. However, when consumers are environmentally conscious, Proposition 6 shows that prices are piecewise monotonic with respect to the tax rate, the cost coefficient, and the strength of consumers’ environmental awareness. The emission abatement levels are also piecewise monotonically related to the emission tax. The condition ξ(t + ξ)2 + λ(ξ - t) < 0 indicates the case with a low level of consumers’ environmental awareness. Then, a higher emission tax results because when the tax rate increases, the price can be lowered to increase consumers’ demand, which helps mitigate the loss. In contrast, when consumers’ environmental awareness level is high, raising prices could improve profit. However, note that for the case with a high level of consumers’ environmental awareness, if the lower emission abatement level is caused by a higher cost, then consumers’ demand decreases sharply. In this situation, lowering the price helps slow down the decrease. Therefore, the prices decrease when 3ξ > t (5ξ > t) and increase otherwise. Given a small cost (λ < t(ξ + t)2/(3ξ + t)), a high emission abatement level is induced. Hence, as consumers’ environmental awareness level increases, demand is lifted. In this situation, lowering the price better captures the benefit brought by demand acceleration driven by higher consumers’ environmental awareness. Otherwise, with a large cost (λ > t(ξ + t)2/(3ξ + t)), the emission abatement level drops, and hence, market demand cannot be well enhanced. Then, with stronger environmental awareness, raising prices captures more profit. In addition, with a small initial emission intensity, the emission tax would not be heavy even if the tax rate increases. In this situation, devoting more effort to emission abatement improves consumers’ demand and hence creates a higher profit. In contrast, when the initial emission intensity is large, the emission tax increases heavily if the tax rate becomes larger. Hence, although emission abatement enhances demand, it is dominated by the increased emission tax and the cost of using the GT. Consequently, less effort is devoted to emission abatement. The results above reveal a mutual influence among the emission abatement cost, the emission tax, and consumers’ environmental awareness in impacting the pricing

110

5

Does Implementing Trade-In and Green Technology Together Benefit. . .

700

Eˆ 3*

Eˆ 4* Eˆ1* Eˆ 2*

600 500 400 300 200

100

t 0

0

1

2

3

4

5

6

7

Fig. 5.5 The total emissions when considering consumers’ environmental awareness

strategies. Demand acceleration driven by consumers’ environmental awareness plays a key role. In particular, prices should be lowered to enhance the acceleration when consumers’ demand is significantly reduced indirectly by large emission abatement costs or when the acceleration is not strong enough. Proposition 7 Suppose that t satisfies 2λ 2λ - ξ þ t ^

3λ - ξ þ t

^

^

2

=

ξþ t

^

2

-λ 

2

; then: 



E3 > E4 : 

(1) If t < λ[(α + v + θ) - 2(cn + te0)]/{e0[2λ - (ξ + t)2]} - ξ, then E 1 > E 3 ;  otherwise, E1 < E 3 .  (2) If t < 3λ[(α + v + θ) - 2(cn + te0)]/{2e0[3λ - (ξ + t)2]} - ξ, then E2 > E 4 ;  otherwise, E2 < E 4 .   (3) If t < t , then E 1 > E4 ; otherwise, E1 < E 4 . ^

Proposition 7 shows similar results as Proposition 3, which demonstrates that the comparative relationship among the supply chain emissions would not be affected by consumers’ environmental awareness. To visualize the effect, we present a numerical example (parameters: α = 105, v = 10, cn = 5, e0 = 14, θ = 95, λ = 50, ξ = 2, for t 2 [0, 7]). Figure 5.5 shows the results. As we can see from Fig. 5.5, the relationships among the emissions in the four strategies are similar to what we have shown in Fig. 5.2. We now proceed to compare

5.7

Conclusion

111

4000

* 3

* 4

3500

* 1 * 2

3000 2500 2000 1500 1000

500

t 0

1

2

3

4

5

Fig. 5.6 The supply chain profits when considering consumers’ environmental awareness

the profits and social welfare of the supply chains through numerical analyses. With the same set of parameters above, for t 2 [0, 5], we obtain Figs. 5.6 and 5.7. From Figs. 5.6 and 5.7, we observe similar results as what we have found from Figs. 5.3 and 5.4, which uncover that the relationships among supply chain profits and social welfare are not affected by consumers’ environmental awareness. Therefore, the optimal “carrot-and-stick” policy we summarize in Proposition 4 continues to hold when the GT promotes consumers’ demand.

5.7 5.7.1

Conclusion Concluding Remarks and Managerial Insights

This chapter explores whether implementing the trade-in program with the use of GT is always beneficial to the environment. Four strategies are comprehensively modeled, compared, and discussed. Meanwhile, from the government’s perspective, the four strategies are analyzed with respect to social welfare. Then, we discuss how to use the measures of the carbon tax rate and subsidies to balance the interests of the supply chain and consumers when the government pursues better environmental protection. Extensions are examined to show the robustness of the findings. Our main findings are listed as follows:

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5

Does Implementing Trade-In and Green Technology Together Benefit. . .

4500

SWˆ3*

4000

SWˆ4*

SWˆ1* SWˆ2*

3500 3000 2500 2000 1500 1000 500

t 0

1

2

3

4

5

Fig. 5.7 Social welfare when considering consumers’ environmental awareness

R-collect versus M-collect Compared with the M-collect scheme, the R-collect scheme creates higher levels of economic benefit and social welfare. However, more emissions are generated in the R-collect scheme, either when the GT is used or not. This shows the clear trade-off between these two schemes. Impacts of GT In each collection scheme, using GT in a trade-in system increases the supply chain’s profit and social welfare. However, surprisingly, GT does not necessarily protect the environment. When the carbon tax is relatively large, more emissions would be generated by having GT. Within different collection schemes, the GT does not always benefit the whole society. For a relatively small carbon tax, social welfare can be lower in the R-collect scheme with GT than in the M-collect scheme without GT. Thus, when implementing trade-in, having GT may do more harm than good to the environment and social welfare. This is counterintuitive, and it brings important insight to companies implementing trade-in. Impacts of carbon tax Together with the GT, the carbon tax determines the new product retail price but has no impact on the trade-in rebate. If the GT has no impact on consumer demand, a larger tax rate leads to higher product prices (emission abatement effort). Otherwise, if the GT enhances demand, a larger tax rate may lead to either higher or lower prices (emission abatement effort). All supply chain emissions, profits, and social welfare decrease with the carbon tax rate. These findings highlight one critical insight: conventional wisdom may indicate that imposing a carbon tax is good for society. However, the real-world situation is far more complex because in terms of social welfare, it actually decreases with the carbon tax rate when the trade-in program is implemented. Consumers’ environmental awareness In the extended model, we have examined the robustness of the findings when the GT affects consumers’ demand. We show

Appendix

113

that when consumers’ demand can be enhanced by the GT, similar relationships among the supply chain profits, total emissions, and social welfare as the ones in our basic models are derived. Thus, the findings summarized above are robust. Our results unveil the following managerial insights: To implement the trade-in program, the R-collect scheme with GT is usually preferred by both the consumers and the supply chain, as well as from the social welfare perspective. As is observed in practice, many firms, such as Apple or Samsung, choose to implement trade-in together with retailers. However, in either the R-collect or M-collect scheme, the environmental performance might be worse off by implementing GT, as more emissions can be generated. If the environment needs urgent protection such that a large emission tax rate needs to be set by the government, more environmentally efficient strategies, including the M-collect scheme with GT or the R-collect scheme without GT, should be advocated. To compensate for the loss suffered by the supply chain and consumers, subsidies can be offered by the government to both the supply chain and consumers. This turns out to be a wise action. As we can observe in practice, consumers are subsidized when trading household electrical appliances in different regions; enterprises that manufacture electrical cars and consumers purchasing these cars are both subsidized by the government.

5.7.2

Future Research

Our study can be extended in a few ways in the future. First, the optimal trade-in decisions under the case with the emission regulation of cap-and-trade would be an area that deserves deep exploration. The significance and priority of different regulations may also be discussed. Second, the model describing the practice that firms collect their competitors’ products in their trade-in programs can be developed to extract novel managerial insights for the case with trade-in competition. Third, extending the model to a multiperiod planning horizon would also be meaningful but analytically challenging. Fourth, some real practices of government policies on trade-ins from different parts of the world can be investigated and compared. Last but not least, it will also be interesting to explore whether disruptive technologies, such as blockchain (Choi et al., 2020), may play a role in trade-in operations and how they may help to enhance environmental sustainability.

Appendix Proof of Theorem 1 With the optimal response of the retailer that q1n = α - w1n2 - q1t , and q1t = θ - ( p1n - p1t), the manufacturer’s profit is rewritten as 1 1M = 2 ½ðα þ θ - 2w1n þ p1r Þðw1n - cn - te0 Þ þ ðθ - w1n þ p1r Þðv - p1r Þ. Then, solving the first-order conditions of the profit functions

∂ 1M ∂w1n

= - 4w1n þ

5 Does Implementing Trade-In and Green Technology Together Benefit. . .

114

∂ 1M = 2w1n þ v - θ - ðcn þ te0 Þ - 2p1r = ∂p1r αþðcn þte0 Þ , p1r = αþv2- θ ; thus, q1n = α - ðc4n þte0 Þ, 0 gives the optimal solutions: w1n = 2 q1t = θþv - ð4cn þte0 Þ, p1n = 3αþðc4n þte0 Þ, p1t = 3ðα -4θÞþv. The proving process for Strategy

2ðcn þ te0 Þ þ α þ θ - v þ 2p1r = 0 and

2 is the same. We hence omit it here. Proof of Theorem 2 Based on the demand function, the retailer’s profit function (5) can be rewritten as the following maximization problem max 3R = ðq3n þ q3t Þðα - q3n - w3n Þ þ q3t ðp3r þ θ - q3t - α þ q3n Þ. The best ðq3n , q3t Þ response of the retailer can be obtained by maximizing this function as 3n Þ 3r Þ q3n = α -2w3n , q3t = θ - w3n2 þp3r , then p3n = ðαþw , and p3t = ðα - θþp . 2 2 With the retailer’s response, the profit function of manufacturer (6) can be rewritten as the following maximization problem: 2 max 3M = ðαþθ - 2w3n þp3r Þ2½w3n - ðcn þte0 Þþte þ ðv - p3r Þðθ2- w3n þp3r Þ - λ ðe23 Þ , then the ðw3n , p3r , e3 Þ first-order derivatives are derived as follows: ∂ 3M ðv - p3r Þ α þ θ - 2w3n þ p3r = - ½w3n - ðcn þ te0 Þ þ te3  2 2 ∂w3n ∂ 3M ðα þ θ - 2w3n þ p3r Þ : =t - λe3 2 ∂e3 ∂ 3M ½w - ðcn þ te0 Þ þ te3  ðθ - w3n þ p3r Þ ðv - p3r Þ = 3n þ 2 2 2 ∂p3r We find that when 2λ - t2, the Hessian matrix is negative definite, and the firstαð4λ - 3t 2 Þ - t 2 ðθþvÞþ4λðcn þte0 Þ order condition ensures the equilibrium results as w3n = , 4ð2λ - t 2 Þ

e3 =

t ½ðαþvþθÞ - 2ðcn þte0 Þ  p3r 2ð2λ - t 2 Þ

have p3t = demand

3ðα - θÞþv 4

ðαþw3n Þ αþv - θ 3r Þ and p3t = ðα - θþp , we 2 . Next, from p3n = 2 2 2 2 αð12λ - 7t Þ - t ðθþvÞþ4λðcn þte0 Þ . Additionally, based on the 8ð2λ - t 2 Þ

=

p3n =

we have ð4λ - t2 Þαþt2 ðθþvÞ - 4λðcn þte0 Þ = = . 8ð2λ - t 2 Þ The steps of the proof for the supply chain (in which the manufacturer implements trade-in) are similar to the proof above. Thus, we omit the detailed proof here.

q3t

function,

αt 2 þðvþθÞð4λ - t 2 Þ - 4λðcn þte0 Þ  ,q3n 8ð2λ - t 2 Þ

Proof of Proposition 1 Between Strategies 3 and 4, the gap of the trade-in rebates is      = α - ð4θþvÞ. Then, if α > θ + v, p3t > p4t ; otherwise, if α < θ + v, p3t < p4t . p3t - p4t Between Strategies 3 and 4, the gap in the new product retail prices is ð4λ2 - 5λt2 þt4 Þ½α - ðθþvÞ - 4λ2 ½ðθþvÞ - ðcn þte0 Þ - p4n = . 8ð2λ - t2 Þð3λ - t 2 Þ Let h(t) = (4λ2 - 5λt2 + t4), then h′(t) = - 2t(5λ - 2t2). Thus, h(t) < 4λ2. On the other hand, if α - (θ + v) > (θ + v) - (cn + te0), then α + (θ + v) > 3(θ + v) (cn + te0), which requires 3(θ + v) - (cn + te0) ≤ 2(cn + te0) because α + (θ + v) > 2 p3n

Appendix

115

(cn + te0) holds. However, since (θ + v) > (cn + te0), we know that 3(θ + v) (cn + te0) ≤ 2(cn + te0) does not hold. If α - (θ + v) < (θ + v) - (cn + te0), then α + (θ + v) < 3(θ + v) - (cn + te0), which requires 2(cn + te0) < 3(θ + v) - (cn + te0). Since (θ + v) > (cn + te0), we know that the condition 2(cn + te0) < 3(θ + v) (cn + te0) holds. Therefore, we have the following result: (4λ2 - 5λt2 + t4)[α (θ + v)] < 4λ2[(θ + v) - (cn + te0)], which implies p3n < p4n . Combining the optimal return rebate in the two models, the prices that a consumer involved in the trade-in program should pay are denoted as p3n - p3t and p4n - p4t , respectively. Then, p3n - p3t - p4n - p4t - ð4λ - t 2 Þðλ - t 2 Þ½α - ðθþvÞ - 4λ2 ½α - ðcn þte0 Þ = . Note that since θ + v > cn + te0 and 8ð2λ - t 2 Þð3λ - t 2 Þ 2 2 (4λ - t )(λ - t ) decreases with t, we have α - (θ + v) < α - (cn + te0) and (4λ - t2)(λ - t2) < 4λ2. Thus, |(4λ - t2)(λ - t2)[α - (θ + v)]| < 4λ2[α - (cn + te0)], which gives p3n - p3t < p4n - p4t . The corresponding proofs for Strategies 1 and 2 are easy to obtain by a similar process. We thus omit the details here. λ½α - ðvþθÞ - ðλ - t 2 Þ½ðvþθÞ - ðcn þte0 Þ Between Strategies 1 and 4, p1n - p4n = , which is 4ð3λ - t 2 Þ λ½α - ðcn þte0 Þ - ð2λ - t 2 Þ½ðvþθÞ - ðcn þte0 Þ . Therefore, if the same as 4ð3λ - t 2 Þ t> if t
p4n , and p2n > p1n > p4n > p3n ; otherwise,

λ½2ðvþθÞ - α - ðcn þte0 Þ ½ðvþθÞ - ðcn þte0 Þ ,

λ½2α - ðcn þte0 Þ - ðvþθÞ , ½α - ðcn þte0 Þ

we can prove that if t > and if t
p4n > p1n > p3n . Similarly,

λ½2α - ðcn þte0 Þ - ðvþθÞ , ½α - ðcn þte0 Þ

then p1t > p4t and p2t > p1t > p4t > p3t;

then p1t < p4t , p2t > p4t > p1t > p3t .

Proof of Proposition 2 From Table 5.1, it is easy to find that 1 and 2. We focus on the proof for Strategies 3 and 4 here. In Strategy 3, observe that

∂p3n ∂t

=

λ½e0 t 2 - tΦþ2λe0  2ð2λ - t 2 Þ2

∂pin ∂t

> 0 in Strategies

, where Φ = α + v + θ - 2cn. Let

g(t) = t e0 - tΦ + 2λe0. Note that α > (cn + te0) and θ > (cn + te0); thus, we have g′(t) = 2te0 - Φ < 0. Thus, maxg(t) = g(0) = 2λe0 and ming(t)= p p p ∂p g 2λ = 2λ 2 2λe0 - Φ = 0. Therefore, g(t) > 0, and ∂t3n > 0. 2

have

∂e3 ∂t

t 2 Φþ2λΦ - 8λte0 . Let 2ð2λ - t 2 Þ2 0 4λ f ðt Þ = 2ðΦt - 4λe0 Þ = 2t Φ - t e0 < 2t

Similarly, note that Since min f ðt Þ = f

p

=

f(t) = Φt2 - 8λte0 + 2λΦ; then, we p Φ - 2 2λe0 = 0. Thus,f ′(t) < 0.

p ∂e 2λ = 4λ Φ - 2 2λe0 = 0, we have f(t) > 0, and ∂t3 > 0.

we addition, have 2 2 2 ½12αþ4ðcn þte0 Þð2λ - t Þ - 2½αð12λ - 7t Þ - t ðθþvÞþ4λðcn þte0 Þ In

simplified as

∂p3n ∂λ

=

8ð2λ - t 2 Þ2 t ½αþðθþvÞ - 2ðcn þte0 Þ ; 4ð2λ - t 2 Þ2 2

that

∂p3n ∂λ

=

for Strategy 3, which can be

thus, we obtain

∂p3n ∂λ

> 0.

The same results can be derived for Strategy 4, and the proof is similar. We thus omit the details here.

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Does Implementing Trade-In and Green Technology Together Benefit. . .

Proof of Proposition 3 Between Strategies 1 and 2, E1 = e0 ðΦ - 2te0 Þ ; 6

e0 ðΦ - 2te0 Þ 4

and E 2 =

thus, E 1 - E2 > 0.

Between Strategies 3 and 4, with the optimal solutions, we have ðΦ - 2te0 Þð4e0 λ2 - λtΦÞ ðΦ - 2te0 Þð6e0 λ2 - λtΦÞ = , E 4 = . Therefore, 4ð2λ - t 2 Þ2 4ð3λ - t 2 Þ2 2 2 4 2 λ ð Φ 2te Þ 2e 6λ t tΦ 5λ 2t Þ ð Þ 0 ½ 0ð . E 3 - E 4 = 4ð2λ - t 2 Þ2 ð3λ - t 2 Þ2 E 3

Define the function k(t) = 2e0(6λ2 - t4) - tΦ(5λ - 2t2); then, we have k′(t)p= 0 0 2λ . 8t e0 + 6Φt2 - 5λΦ, and k″(t) = p - 12t(2e00t - Φ) 0>p0. Thus, maxpk ðt Þ = k Note that 2te0 = Φ when t = 2λ, max k ðt Þ = k 2λ = - 2λp2λe0 < 0. Thus, k′(t) < 0. pAgain, given that 2te0 = Φ when t = 2λ, we have min k ðt Þ = k 2λ = 0. Therefore, E 3 - E4 > 0. 2 ðΦ - 2te0 Þð4e0 λ2 - λtΦÞ e0 ðΦ - 2te0 Þð2λ - t 2 Þ , Between Strategies 1 and 3, E 1 - E3 = 4ð2λ - t 2 Þ2 4ð2λ - t 2 Þ2 2 t ðΦ - 2te0 Þ½e0 t ð2λ - t Þ - λðΦ - 2e0 t Þ which can be simplified as . Therefore, when 4ð2λ - t 2 Þ2 3

t < λeð0Φð2λ--2et02tÞÞ, we have E 1 - E3 < 0, while when t > λeð0Φð2λ--2et02tÞÞ, we have E 1 - E 3 > 0. Similarly, we can demonstrate that E2 - E4 2 t ðΦ - 2te0 Þ½2te0 ð3λ - t Þ - 3λðΦ - 2e0 t Þ ðΦ - 2e0 t Þ   = . Thus, if t < 3λ 2e0 ð3λ - t 2 Þ , then E 2 - E 4 < 0; and if 12ð3λ - t 2 Þ2 t>

3λðΦ - 2e0 t Þ 2e0 ð3λ - t 2 Þ ,

then E 2 - E 4 > 0.

e0 ðΦ - 2te0 Þð3λ - t 2 Þ ðΦ - 2te0 Þð6e0 λ2 - λtΦÞ Similarly, E 1 - E 4 = , which can be sim2 2 4ð3λ - t Þ 4ð3λ - t 2 Þ2 ðΦ - 2te0 Þ½e0 ð3λ2 þt 4 Þ - t ð6λte0 - λΦÞ e0 ð3λ2 þt 4 Þ plified as . Therefore, when t < 2 2 ð6λte0 - λΦÞ, we have 4ð3λ - t Þ 2 4 e 3λ þt ð Þ 0 E 1 - E 4 > 0; when t > ð6λte0 - λΦÞ, we have E 1 - E4 < 0. 2

Proof of Theorem 3 The detailed proving process of Theorem 5 is similar to that of the former theorems, and we omit the proof here. Proof of Proposition 5 Based on the optimal results, the gap between p3n and p4n can be derived as ½α - ðvþθÞ½4λ2 þðtþξÞ4 - λðtþξÞðξþ5t Þ - ½ðvþθÞ - ðcn þte0 Þ½4λ2 - 8λξðtþξÞ  = p3n - p4n : 8½2λ - ðξþt Þ2 ½3λ - ðξþt Þ2  Denote

the

numerator

as

Γ;

then,

we

have

∂Γ ∂ξ

= ½α - ðv þ θÞ 

4ðt þ ξÞ3 - 2λðξ þ 3t Þ +8λ(t + 2ξ)[(v + θ) - (cn + te0)]. Then, if 4(t + ξ)3 > 2λ(ξ + 3t), then 8λ(t + 2ξ) - [4(t + ξ)3 - 2λ(ξ + 3t)] > 4(ξ + t)2ξ + 2λ(ξ + 3t) > 0; otherwise, if 4 (t + ξ)3 < 2λ(ξ + 3t), then 8λ(t + 2ξ) - [2λ(ξ + 3t) - 4(t + ξ)3] > 2λ(t + 7ξ) + 4 (t + ξ)3 > 0. Recall that [α - (v + θ)] < [(v + θ) - (cn + te0)]; thus, we have ∂Γ > 0. ∂ξ p p p   Therefore, max p3n - p4np = 2λ pλ 3 λ - 2 2t ½α þ ðv þ θÞ - 2ðcn þ te0 Þ when p ξ = 2λ - t. p Hence,pif 3 λ < 2 2t, max p3n - p4n < 0 ; thus, p3n < p4n . Otherwise, if 3 λ > 2 2t, max p3n - p4n > 0. Recall that when ξ = 0,

Appendix

117

ξ at which p3n = p4n , and if ξ < ξ, min p3n - p4n < 0; thus, there exists p a unique    p3n < p4n ; otherwise, when ξ < ξ < 2λ - t,p3n > p4n . ^ ^ Similar results can be obtained for p3t and p4t in the same proving process; thus, we omit the detailed proof. For Strategies 1 and 4, the gap between p1n and p4n can be derived as Þ - ðcn þte0 Þ½2λþðtþξÞðξ - t Þ , then p1n > p4n p1n - p4n = ½α - ðcn þte0 Þ½λ - 2ξðtþξÞ4 -3λ½ð-vþθ if ½ ðξþtÞ2  [α - (cn + te0)][λ - 2ξ(t + ξ)] > [(v + θ) - (cn + te0)][(2λ + ξ2) - t2]; otherwise, ½ðvþθÞ - ðcn þte0 Þð2λþξ2 Þ - ½α - ðcn þte0 Þ½λ - 2ξðtþξÞ p1n < p4n . Therefore, if t > , p1n > p4n ; ½ðvþθÞ - ðcn þte0 Þ ^

otherwise, p1n < p4n . Similar results can be obtained for p1t and p4t in a similar proving process; thus, we omit the detailed proof. Proof of Proposition 6 For Strategies 3 and 4, we have the following results: 2 ∂p3n ½α þ ðv þ θÞ - 2ðcn þ te0 Þ ξðt þ ξÞ þ λðξ - t Þ = 2 ∂t 2 2λ - ðξ þ t Þ2

∂p3n ðt þ ξÞðt - 3ξÞ½α þ ðv þ θÞ - 2ðcn þ te0 Þ = 2 ∂λ 4 2λ - ðξ þ t Þ2

,

2 ∂p3n ½ðα þ v þ θÞ - 2ðcn þ te0 Þ λð3ξ þ t Þ - t ðξ þ t Þ = 2 ∂ξ 2 2λ - ðξ þ t Þ2 2 ∂p4n ½α þ ðv þ θÞ - 2ðcn þ te0 Þ ξðξ þ t Þ þ λð2ξ - t Þ = 2 ∂t 2 3λ - ðξ þ t Þ2

∂p4n ðt þ ξÞðt - 5ξÞ½α þ ðv þ θÞ - 2ðcn þ te0 Þ = 2 ∂λ 4 3λ - ðξ þ t Þ2

:

2 ∂p4n ½ðα þ v þ θÞ - 2ðcn þ te0 Þ λð5ξ þ 2t Þ - t ðξ þ t Þ = 2 ∂ξ 2 3λ - ðξ þ t Þ2

Therefore, we can conclude that: (1) When ξ(t + ξ)2 + λ(ξ - t) > 0, ∂p3n =∂t > 0; otherwise, ∂p3n =∂t < 0. Similarly, ξ(ξ + t)2 + λ(2ξ - t) > 0, ∂p4n =∂t > 0; otherwise, ∂p4n =∂t < 0. (2) When t > 3ξ, ∂p3n =∂λ > 0 ; otherwise, ∂p3n =∂λ < 0, and when t > 5ξ, ∂p4n =∂λ > 0; otherwise, ∂p4n =∂λ < 0. (3) When λ(3ξ + t) > t(ξ + t)2, ∂p3n =∂ξ > 0; otherwise, ∂p3n =∂ξ < 0, and when λ(5ξ + 2t) > t(ξ + t)2, ∂p4n =∂ξ > 0; otherwise, ∂p4n =∂ξ < 0.

5 Does Implementing Trade-In and Green Technology Together Benefit. . .

118

In addition, for the optimal emission abatement level, we have that: 2 2 ∂e3 ½ðα þ v þ θÞ - 2ðcn þ te0 Þ 2λ þ ðt þ ξÞ - 2e0 ðt þ ξÞ 2λ - ðξ þ t Þ , = 2 ∂t 2λ - ðξ þ t Þ2 2 2 ∂e4 ½ðα þ v þ θÞ - 2ðcn þ te0 Þ 3λ þ ðt þ ξÞ - 2e0 ðt þ ξÞ 3λ - ðξ þ t Þ : = 2 ∂t 3λ - ðξ þ t Þ2

Therefore, when e0
0 ; other-

Proof of Proposition 7 Based on the optimal results, the total demands in Strategies Þ - 2ðcn þte0 Þ 3 and 4 can be given as q3n þ q3t = λ½αþ2ðvþθ and q4n þ q4t = ½2λ - ðξþtÞ2    λ½αþðvþθÞ - 2ðcn þte0 Þ . Thus, E 3 - E4 = e0 - e3 q3n þ q3t - e0 - e4 q4n þ q4t , 2½3λ - ðξþt Þ2  which can be simplified as ðtþξÞ½5λ - 2ðξþt Þ2 ½ðαþvþθÞ - 2ðcn þte0 Þ λ2 ½ðαþvþθÞ - 2ðcn þte0 Þ e0 . Therefore, if 2½2λ - ðξþt Þ2 ½3λ - ðξþt Þ2  2½3λ - ðξþt Þ2 ½2λ - ðξþt Þ2      ðtþξÞ½5λ - 2ðξþt Þ2 ½ðαþvþθÞ - 2ðcn þte0 Þ , E 3 > E4 ; otherwise, E3 < E 4 . Note that e0 > 2½2λ - ðξþt Þ2 ½3λ - ðξþt Þ2  ðtþξÞ½5λ - 2ðξþt Þ2 ½ðαþvþθÞ - 2ðcn þte0 Þ Because e0 > max e3 , e4 , = e3 þ e4 . 2½2λ - ðξþt Þ2 ½3λ - ðξþt Þ2  max e3 , e4 < e0 < e3 þ e4 does not hold; thus, E 3 < E 4 does not hold. Thus, E 3 > E 4 . Similarly, the gap between the optimal emissions of strategies 1 (2) and 3 (4) can ^ 3 = ðt þ ξÞ ½ðα þ v þ θÞ - 2ðcn þ te0 Þ fλ - e0 be derived as follows: E 1 - E ðξ þ t Þ½2λ

- ðξþt Þ2 g

ðt þ ξÞ½ðα þ v þ θÞ - 2ðcn þ te0 Þf3λ ½ðαþ v þ θÞ -

4½2λ - ðξþt Þ2  E 2 - E^ 4 = ½3λ - ðξþtÞ2 g 2ðcn þ te0 Þ - 2e0 ðξ þ t Þ 12 3λ - ðξþtÞ2 ½   Þ - 2ðcn þte0 Þ  (t < 3λ½ðαþvþθ > E ξ), E 2 1 3 2e0 ½3λ - ðξþt Þ  2

λ½ðαþvþθÞ - 2ðcn þte0 Þ e0 ½2λ - ðξþt Þ2     E1 < E 3 (E 2 < E 4 ).

2:, therefore, when t <  (E2 > E 4 );

otherwise,

-ξ

Additionally, the gap between the optimal emissions of strategies 1 and 4 can be  e0 ½3λ - ðξþt Þ2 ½λ - ðξþt Þ2 þλðtþξÞ½ðαþvþθÞ - 2ðcn þte0 Þ derived as follows: E1 - E4 =  2½3λ - ðξþt Þ2   ½ðαþvþθÞ - 2ðcn þte0 Þ : Then, if λ > (ξ + t)2, E 1 > E4 ; otherwise, if λ < (ξ + t)2, then 2½3λ - ðξþt Þ2    ^ ^ ^ Þ½ðαþvþθÞ - 2ðcn þte0 Þ E 1 > E 4 if e0 < e 0 , and E 1 < E 4 if e0 > e 0 with e 0 = λðtþξ . Recall ½3λ - ðξþtÞ2 ½ðξþtÞ2 - λ ^    that e0 > max e3 , e4 , by comparing e3 and e 0 , we have

References

119

½7λλ - 6λðξþtÞ2 þðξþtÞ4  , of which the numerator decreases with (ξ + t). Thus, ½ðξþtÞ2 - λ½3λ - ðξþtÞ2  2 4 min{7λλ - 6λ(ξ + t) + (ξ + t) } = - λ2 and max{7λλ - 6λ(ξ + t)2 + (ξ + t)4} = 2λ2, p which indicates that there exists a unique tax t that when λ < ðξ þ t Þ < ξ þ t , ^ ^ p  ^ ^ e0 > e 0 and E1 > E 4 ; otherwise, when λ < ξ þ t < ðξ þ t Þ, e0 < e0 and ^

e3 - e 0 = e3





^



E 1 < E 4 . Consequently, when t < t , E 1 > E4 ; and when t < t,E 1 < E4 . ^

^

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Chapter 6

Coordination of a Supply Chain with an Online Platform Considering Green Technology in the Blockchain Era

6.1 6.1.1

Introduction Background and Motivation

With the rapid development of the platform economy, an increasing number of manufacturers sell their products through traditional retailers and online platforms (Tan & Carrillo, 2017; Shen et al., 2019). For instance, electronic equipment manufacturers, such as Apple and Huawei, sell their products not only through their offline retail stores but also through online platforms such as JD.com or Tmall.com. Generally, online platforms operate in two modes, i.e., marketplace mode and reselling mode (Tian et al., 2018; Shen et al., 2019). In the marketplace mode, manufacturers sell their products directly to consumers but pay a commission for their online sales to the platforms. In practice, Tmall.com, which is the largest B2C online platform in China (Wang & Li, 2020; Lin, 2014), takes a 2–5% commission rate for products depending on industries. With the reselling mode, the platforms purchase products from the manufacturers with a wholesale price and then sell these products to consumers at a retail price (Hagiu & Wright, 2015; Shen et al., 2019). For instance, Haier sells its products to JD.com at a wholesale price, and JD.com further sells them to consumers at a retail price. In this mode, the platforms have the power to determine the retail price. As can be observed in practice, online platforms such as Amazon.com and JD.com mainly operate in reselling mode. These online platforms usually buy products from manufacturers and further sell them on their platforms. In addition, compared with the traditional offline channel, online platforms have the inherent feature “the network effect” (Shen et al., 2019; Yi et al., 2019; Xu et al., 2020), which endows manufacturers with the ability to enlarge the potential market demand, as there are no longer temporal and spatial constraints for purchasing on online platforms. Additionally, to follow the trend of omnichannel and avoid conflicts between offline and online channels, an increasing number of © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Dou et al., Operations Management for Environmental Sustainability, SpringerBriefs in Operations Management, https://doi.org/10.1007/978-3-031-37600-9_6

123

124

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Coordination of a Supply Chain with an Online Platform Considering. . .

manufacturers implement the same retail price on offline channels and online platforms (Gao & Su, 2017; Zhou et al., 2018; Xu et al., 2020). For instance, Uniqlo, Peacebird, and Semir sell their products through offline channels and online platforms with the same retail price. Other than online sales, the products’ property plays another key role in determining their popularity. Currently, with increasing concern about environmental protection attached to society as a whole, “greener” products are increasingly preferred by consumers (Xu et al., 2017; Ji et al., 2017b). Catering with this preference, green technologies are adopted by many modern manufacturers to provide eco-friendly products. For instance, Apple uses green technologies (i.e., renewable energy and biobased plastic recycling) to manufacture the iPhone 11 Pro.1 Similarly, recyclable and biological materials are widely used in Huawei products, which helped Huawei reduce 612 tons of carbon emissions in 2018.2 These green actions attract more consumers to buy their products. For instance, from a report of Canalys for China smartphone shipments, Huawei ranks first, with a market share of 38.5%.3 When the manufacturers adopt green technology, the platforms with marketplace mode can earn more profits since the manufacturers sell more products through the platforms, and the platforms with reselling mode can obtain more profits by selling more products. Recently, blockchain technology has drawn increasing attention in research about supply chains (Chang et al., 2020; Pournader et al., 2020; Manupati et al., 2020; Dubey et al., 2020; Yoon et al., 2020), among which some consider the technology’s enhancement of consumers’ trust in the green or sustainable supply chain (Dutta et al., 2020; Cai et al., 2021) since consumers require access to verify the green level of the products (Kouhizadeh et al., 2021). In other words, blockchain technology is beneficial to sustainability certifications (Kouhizadeh et al., 2021). Let us consider a common example. When a consumer buys products from a manufacturer and is told of the green level of the products, he/she may doubt the accuracy of the green level, which further induces this consumer not to buy the products. However, after using blockchain technology, the data of the whole production process are recorded, and the data cannot be changed arbitrarily (Chod et al., 2018, 2019, 2020). Therefore, the application of blockchain technology helps consumers understand the authenticity of green information, which can increase the possibility for consumers to buy green products (Choi, 2019). We know that manufacturers and retailers cannot be coordinated via wholesale price contracts in a single channel due to double marginalization. When manufacturers sell their products through traditional retailers and online platforms, it involves the platforms’ modes and the network effect. In addition, manufacturers adopt green technology to gain more market share. These actions can directly affect manufacturers’ production decisions, which further affects the coordination of manufacturers

1

https://www.apple.com/environment/pdf/products/iphone/iPhone_11_Pro_PER_sept2019.pdf https://www.huawei.com/cn/about-huawei/sustainability/environment-protect/green_pipeline 3 https://new.qq.com/omn/20200130/20200130A02GRP00.html 2

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Introduction

125

and retailers. In other words, whether manufacturers and retailers can be coordinated is affected by the platforms’ modes, the network effect, and the use of green technology.

6.1.2

Research Questions and Major Findings

From the above context, we consider a manufacturer who adopts green technology in the blockchain era and sells its products through a retail channel and an online platform. The platform can operate in marketplace mode or reselling mode. The network effect is considered to reflect the power of the platform to enlarge the potential market size. The problems of operational decisions and supply chain coordination have some special features. One is that the online platform’s modes and the network effect can directly affect operational decisions and supply chain coordination. The other is that green technology in the blockchain era plays a vital role in the manufacturer’s operational decisions, which further affects supply chain coordination. To the best of our knowledge, there is no research discussing supply chain coordination with marketplace mode and reselling mode after considering green technology in the blockchain era. Our work establishes analytical models to investigate the following important research questions: 1. How do the platform’s operational modes and the network effect affect the manufacturer’s optimal decisions and profits? 2. How do the platform’s operational modes and the network effect affect supply chain coordination? More specifically, is there any possibility for supply chain members to obtain “Pareto improvement” for their profits? 3. What are the effects of blockchain technology on the profits of the manufacturer and platform? Can blockchain technology induce supply chain coordination? To address the above questions, we first explore the optimal operational decisions with the two modes. Then, we discuss the coordination problem of the supply chain with the two modes and extend our model by considering the coordination problem of the manufacturer, the retailer, and the platform. Finally, based on the sales data of a food manufacturing company, numerical studies are conducted to show the properties of the production quantities, the abatement level, and the coordination of the supply chain. The key findings of this chapter can be summarized as follows. (1) The increase in the network coefficient improves the abatement level and benefits the manufacturer and the platform. (2) If the network coefficient is high, the decentralized supply chain with the reselling mode brings a higher abatement level than the centralized supply chain. (3) If the network coefficient is low, the supply chain with the two modes can be coordinated. The manufacturer and the retailer can reach a “win–win” with a two-part tariff agreement after coordination. (4) The manufacturer, the platform, and the retailer can be coordinated in the marketplace mode if the network coefficient is low and cannot be coordinated in the reselling mode. (5) With the two

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6 Coordination of a Supply Chain with an Online Platform Considering. . .

modes, blockchain technology helps the products become greener and brings more profits for the manufacturer and the platform. Additionally, blockchain technology induces supply chain coordination.

6.1.3

Contribution Statement and Paper’s Structure

To the best of our knowledge, this chapter is the first work to investigate the supply chain coordination problem with marketplace mode and reselling mode considering green technology in the blockchain era. Specifically, the key role of the network effect is considered to analyze its impact on optimal operational decisions and supply chain coordination. Our research uncovers the effect of the platform’s mode, the network coefficient, and blockchain technology on the abatement level, the profits of the manufacturer and the platform, and the supply chain coordination. The remainder of this chapter is organized as follows. Section 6.2 presents a review of the related literature. Section 6.3 formulates the research problem. Section 6.4 presents the models and solutions with marketplace mode and reselling mode, respectively. Section 6.5 explores supply chain coordination with the two modes. Section 6.6 summarizes and concludes the paper. All the proofs are provided in the Appendix.

6.2

Literature Review

This chapter is related to studies on the selection of online platforms’ modes, the emission abatement decisions of a dual-channel supply chain, and the coordination of a dual-channel supply chain.

6.2.1

The Selection of Online Platform Modes

Many studies pay attention to the emerging field of online platforms and discuss the selection of their operational modes. For instance, Jiang et al. (2011) build models to explain online platform retailing. Specifically, they take Amazon.com as an example to explain the marketplace mode and reselling mode. Similarly, Abhishek et al. (2016) use a stylized theoretical model to explore when online retailers should use the marketplace mode instead of the reselling mode, and the marketplace mode is proven to be more efficient and leads to lower retail prices. Hagiu and Wright (2015) model the intermediaries’ choice of being a marketplace or as a reseller, and the control over a noncontractible decision variable such as a marketing activity is shown to be the determinant for the switch between marketplace mode and reselling mode. Tan and Carrillo (2017) build a model of vertically differentiated products to

6.2

Literature Review

127

compare the marketplace mode with the reselling mode. They show that the marketplace mode can generate more profits if the upstream publisher has control over the retail price. Tian et al. (2018) discuss an online retailer’s choice among resellers, online marketplaces, or both. They examine how the order-fulfilment cost and upstream competition determine the mode configuration choice. More recently, Yan et al. (2019) examine whether the manufacturer and “e-tailer” should agree to introduce a marketplace mode. They interestingly show that the marketplace mode should be introduced under both a low and a high degree of upstream sales inefficiency. Shen et al. (2019) explore the optimal production and pricing decisions with marketplace mode and reselling mode. Two cases are modeled, where one is that they just negotiate the revenue-sharing rate, and the other is that they negotiate both the revenue-sharing rate and the slotting fee. They show that the second case can lead to a win–win result, and the benefit of the slotting fee for the manufacturer and the platform retailer depends on the demand substitution effect between the online and offline retailing channels. Our work contributes to the above studies in that we consider green technology and focus on supply chain coordination after considering the network effect. Our work is closely related to Shen et al. (2019), who also considers the network effect. We differ from their paper in two aspects. One is that we consider green technology in the blockchain era, which can directly affect the manufacturer’s operational decisions and supply chain coordination. The other is that we mainly discuss the effect of online modes on supply chain coordination.

6.2.2

Emission Abatement Decision of a Dual-Channel Supply Chain

Many studies explore the emission abatement decision in a single supply chain, such as Krass et al. (2013); Toptal et al. (2014); Dong et al. (2016); Xu et al. (2017) and Qin et al. (2020). Here, we mainly review the emission abatement decision of a dualchannel supply chain. Ji et al. (2017a) study emission reduction behaviors, where the behaviors can be performed by a retailer or together with a manufacturer. The joint emission abatement strategy is proven to be more profitable. Ji et al. (2017b) further examine consumers’ low-carbon preferences in an O2O retail supply chain under cap-and-trade regulation. They find that consumers’ low-carbon preference induces the manufacturer and the retailer to increase the low-carbon investment. Considering carbon emission constraints, Yang et al. (2018) analyze a manufacturer’s emission reduction decisions and channel selection. They show that the manufacturer should sell its products only through a single online channel if consumers prefer online shopping. Liu and Ke (2021) explore how emission regulation affects an “e-tailer’s” choice between marketplace mode and reselling mode. Specifically, the manufacturer’s investment strategy for emission abatement is taken into account. They find

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6 Coordination of a Supply Chain with an Online Platform Considering. . .

that if the commission rate is low and the unit carbon emissions are moderate, the marketplace mode is preferred. It can be observed from the above studies that the abatement level has recently attracted much attention. The above studies mainly consider an online channel, which can be seen as a manufacturer’s own website. However, different from their work, we focus on how the online retailing mode (i.e., marketplace mode, reselling mode) and the network effect shape emission abatement decisions, thus leading to different greenness levels of products. Specifically, we consider green technology in the blockchain era. Some important findings are obtained in our work.

6.2.3

Coordination of a Dual-Channel Supply Chain

The coordination of a dual-channel supply chain has drawn increasing attention in recent years. Chen et al. (2012) find that the dual-channel supply channel can be coordinated with the manufacturer’s contract with a wholesale price and a price for the direct channel. Ryan et al. (2012) explore whether a retailer should choose to sell with marketplace mode when he already has an online selling website. The optimal decisions for the retailer and marketplace firm, as well as the system equilibrium, are analyzed. Zhang et al. (2015) discuss the coordination issue of a dual-channel supply chain in situations of demand or cost disruption; a contract with a wholesale price, a direct channel’s price, and a lump sum fee is utilized to coordinate the supply chain. Shang and Yang (2015) take risk preferences and negotiating power into account when characterizing Pareto-optimal contracts for two- and three-stage dual-channel supply chains. Saha et al. (2016) study the coordination of closed-loop supply chains with retailer selling and direct selling forward channels and three modes of collection in the reverse channel. Li et al. (2016) consider a dual-channel supply chain consisting of a risk-neutral supplier and a risk-averse retailer, where the supplier opens an “e-channel.” They present an improved risk-sharing contract to coordinate the supply chain and ensure that both members achieve a “win–win” outcome. David and Adida (2015) find that if a supplier operates both a direct channel and sells through differentiated retailers, the contracts coordinating a single “e-channel” supply chain fail to coordinate the dual-channel supply chain. Then, they propose a linear quantity discount contract and demonstrate its ability to perfectly coordinate the dual-channel supply chain. Tan et al. (2016) discuss the marketplace mode and compare it with the reselling mode. They find that the marketplace mode can coordinate the competing retailers by dividing the coordinated profits into a pre-negotiated revenue-sharing proportion. Zheng et al. (2017) examine the effect of forward channel competition and power structure on dual-channel closed-loop supply chains, and modified two-part tariff contracts are designed to coordinate supply chains under different channel power structures. Xu et al. (2018) explore the optimal decisions and coordination in a dual-channel supply chain considering low-carbon preferences and channel substitution. An improved revenue-sharing contract is proposed to effectively coordinate the supply chain. By modeling both

6.3

Problem Formulation

129

Table 6.1 The difference between our work and most related studies Paper Tian et al. (2018) Shen et al. (2019) Yan et al. (2019) Liu and Ke (2021) Ji et al. (2017a) Tan et al. (2016) Our paper

Green technology

Network effect √

√ √ √

√

Platform mode √ √ √ √ √ √

Blockchain

√

noncooperative and cooperative games, Jabarzare and Rasti-Barzoki (2020) discuss pricing and quality level decisions in a dual-supply chain comprising a manufacturer and a packaging company. Wang et al. (2020) address the supply chain coordination and contracting issue for competitive dual sales channels. They propose a two-way revenue sharing contract to solve the coordination failure with the subsidy-only contract. In our research, we also explore the coordination problem of a dual-channel supply chain. However, we discuss how the online platform retailing modes affect the coordination of the manufacturer and the retailer, and we also try to determine whether the manufacturer, retailer, and platform can be coordinated altogether. Additionally, we explicitly examine the impact of the online platform’s network effect on supply chain coordination. Sections 6.2.1–6.2.3 show that our research problems are important but are not explored. Table 6.1 presents the difference between our work and the most related studies.

6.3

Problem Formulation

We consider a stylized supply chain composed of a manufacturer and a retailer. In such a supply chain, the manufacturer sells its products through a retail channel and an online platform. The decision process is modeled as a Stackelberg game where the manufacturer is the leader, and the retailer and the platform are the followers. For the retail channel, the retailer orders the products from the manufacturer with a wholesale price wr and then sells them to the market with a retail price p. For the online platform with marketplace mode, the platform takes a commission rate ϕ for the manufacturer’s online sales, and with reselling mode, the platform orders the products from the manufacturer with a wholesale price wp and then sells them to consumers with a retail price p. To follow the trend of omnichannel and avoid the conflict of the offline and online channels, the manufacturer implements the same retail price on the two channels. This is also considered by an increasing number of studies, such as Ji et al. (2017b), Gao and Su (2017), and Zhou et al. (2018). Since consumers have environmental awareness, they are willing to pay more for green

130

6 Coordination of a Supply Chain with an Online Platform Considering. . .

products (Liu et al., 2012; Xu et al., 2017; Ji et al., 2017b). To protect the environment and raise market competitiveness, the manufacturer adopts green technology to reduce the carbon emissions of a unit product and uses blockchain technology to record the data of the abatement level (Kouhizadeh et al., 2021). Consumers can buy this kind of green product through the retail channel and the platform. Following the studies of Ji et al. (2017b) and Shen et al. (2019), the demands faced by the retailer and platform are linear functions of the retail price and the green degree of the products. Consequently, the demand functions in the two channels are as follows: Dr = a - γp þ ð1 þ τb Þτg e:

ð6:1Þ

Dp = ð1 þ ρÞa - γp þ ð1 þ τb Þτg e:

ð6:2Þ

where a is the potential demand of the retail channel and ρ > 0 is the network coefficient (Shen et al., 2019; Yi et al., 2019; Xu et al., 2020), which means that the manufacturer has a larger potential demand in the online platform; e is the green degree of the product (i.e., abatement level); γ is the sensitivity to the retail price; τg is the consumers’ environmental awareness level for the green technology; and τb is the improvement of the consumers’ environmental awareness level when the manufacturer uses blockchain technology (Dutta et al., 2020; Choi, 2019). Without loss of generality, we assume that the production cost of the manufacturer and the use of blockchain technology are normalized to zero. If the manufacturer adopts the abatement level e, it involves a cost he2, where h is the cost coefficient of the green degree. Such a quadratic-type function is commonly used in previous studies (Xu et al., 2017; Ji et al., 2017b; Li et al., 2018). In addition, to ensure that the profit functions in the following models are jointly concave on the decision variables, we assume that h > [(1 + τb)τg]2(2 - ϕ)/(2γ). Actually, this assumption can also avoid trivial discussion. A similar assumption can be found in Wang et al. (2016) and Ji et al. (2017b).

6.4

Optimal Operational Decisions

In this section, we discuss the optimal decisions of the manufacturer and the retailer in the decentralized supply chain with marketplace mode and reselling mode, respectively.

6.4.1

Marketplace Mode

In the marketplace mode, the manufacturer charges the retailer a wholesale price wM - r. We denote ΠM - r and ΠM - m as the profits of the retailer and the

6.4

Optimal Operational Decisions

131

manufacturer with marketplace mode, respectively. Then, we can obtain their profits as follows: ΠM - r = ðpM - wM - r ÞDr : ΠM - m = wM - r Dr þ

ð6:3Þ

ð1 - ϕÞpM Dp - he2M :

ð6:4Þ

Then, we derive the retailer’s response function as follows: pM = [a + wM + eM(1 + τb)τg]/(2γ). It is obvious that there is a one-to-one relationship between the retail price and the wholesale price. Substituting pM into Eq. (6.4), we can further obtain ΠM - m as follows:

rγ

ΠM - m =

2γwM - r a - wM - r γ þ eM 1 þ τb τg þ 1 - ϕ a þ wM - r γ þ eM 1 þ τb τg a þ 2aρ - wM - r γ þ eM 1 þ τb τg 4γ - he2M :

ð6:5Þ To solve Eq. (6.5), we can obtain the following theorem. Theorem 1 The optimal decisions with marketplace mode are as follows: (1) If 0 < ρ
eM :  dðec M - eM Þ dρ

< 0: If ρ ≥

If 0 < ρ
0:

Corollary 1 shows that the abatement level in the centralized supply chain is larger than that in the decentralized supply chain. The main reason is that the centralized situation eliminates double marginalization, which indicates relatively high marginal profit. In addition, we find that the optimal abatement level in the decentralized supply chain is closer to that in the centralized supply chain with the increase in the low network coefficient. In addition, it is far away that in the centralized supply chain with the increase in the high network coefficient. This indicates that there is a network coefficient that makes the abatement levels in the two situations closest to each other.

Reselling Mode In the centralized supply chain, we can obtain the profit of the centralized supply chain as follows: 2

ΠcR = pcR Dr þ wcR - p Dp - h ecR :

ð6:10Þ

From Sect. 6.4.2, we know the platform’s response function wcR - p = 2pcR γ - ð1 þ ρÞa - ecR ð1 þ τb Þτg =γ: Then, we have the following theorem. Theorem 4 The optimal decisions with the reselling mode in the centralized supply chain are as follows: ec R = qc R-r =

a½ð1þτb Þτg  3hγ - ½ð1þτb Þτg 

2hγa - 3hγ - ½ð1þτb Þτg  2 3hγ - ½ð1þτb Þτg 

2

4hγa2 - ρ2 a2 3hγ - ½ð1þτb Þτg  4γ 3hγ - ½ð1þτb Þτg 

ρa 3hγ - ½ð1þτb Þτg 

2

pc R =

2 ,

2

2

ρa

,

þ4hγa

2γ 3hγ - ½ð1þτb Þτg 

qc R-p =

2

,

wc R-p =

2hγaþ 3hγ - ½ð1þτb Þτg  2 3hγ - ½ð1þτb Þτg 

2

2

ah 2 3hγ - ½ð1þτb Þτg 

ρa

,

,

Πc R =

2

:

Theorem 4 presents some important findings. First, the abatement level and the wholesale price to the platform are independent of the network coefficient. This result is surprising. This indicates that the manufacturer should keep the abatement level and the wholesale price to the platform constant. Second, the retail price and online demand are increasing in the network coefficient, while offline demand is

6.5

Supply Chain Coordination

135

decreasing in the network coefficient. Finally, we interestingly find that the total profit of the supply chain is decreasing in the network coefficient. We know that with the increase in the network coefficient, the online channel encroaches on the demand of the offline channel. Moreover, the retail price increases with the network coefficient, and the wholesale price to the platform remains unchanged. This indicates that the manufacturer obtains relatively less profit from the online channel. Therefore, the total profit is decreasing in the network coefficient. In addition, the optimal abatement level and the optimal total profit are increasing in τb. Therefore, using blockchain technology can increase the abatement level and enhance the total profit. Corollary 2 (1) If 0 < ρ < 5hr/{3hr - [(1 + τb)τg]2}, then eR < ec R ; (2) if ρ ≥ 5hr/ {3hr - [(1 + τb)τg]2}, theneR > ec : R Corollary 2 presents an interesting finding. It is intuitive that the abatement level in the centralized situation is larger than that in the decentralized situation. However, the opposite finding emerges if the network coefficient is large. The abatement level in the decentralized supply chain is increasing in the network coefficient, while the abatement level in the centralized supply chain remains constant. Thus, the abatement level in the centralized supply chain is less than that in the decentralized supply chain if the network coefficient is large. Comparing Corollary 1 and Corollary 2, we find that whether the centralized supply chain has advantages in the abatement level depends on the platform’s operational modes and the network coefficient.

6.5.2

Supply Chain Coordination via Marketplace Mode

In this subsection, we design a wholesale price wcM to try to achieve supply chain coordination. Then, we have the following theorem. Theorem 5 If 0 < ρ ≤ coordinated;

2hγ ð2 - ϕÞ ð1 - ϕÞ 2hγ - 2½ð1þτb Þτg  þϕ½ð1þτb Þτg 

when

2

, the supply chain can be

wcM = aρð1 - ϕÞ=½γ ð2 - ϕÞ;

2hγ ð2 - ϕÞ ð1 - ϕÞ 2hγ - 2½ð1þτb Þτg  þϕ½ð1þτb Þτg  2

2

2

if

ρ>

, the supply chain cannot be coordinated.

Theorem 5 interestingly shows that a wholesale price contract can coordinate the supply chain if the network coefficient is low. In the traditional supply chain, a wholesale price contract cannot coordinate the supply chain (Cachon & Kök, 2010; Xu et al., 2017). It is worth noting that a wholesale price contract cannot coordinate the supply chain if there is no network coefficient. From Theorem 1, we can easily verify that the value of pM - wM is decreasing in the network coefficient. Thus, the increase in the network coefficient weakens the double marginalization. Hence, a wholesale price contract can coordinate the supply chain. If the network coefficient is large, the manufacturer will not sell its products through the offline channel, which leads to non-coordination. From Theorem 5, we know that the threshold of the

136

6 Coordination of a Supply Chain with an Online Platform Considering. . .

network coefficient is increasing in τb. This indicates that the conditions for the supply chain coordination are more relaxed with an increase in τb. Thus, blockchain technology can induce supply chain coordination. In addition, the wholesale price after coordination via the marketplace mode is independent of τb., which means that using blockchain technology has no effect on the wholesale price after coordination. Theorem 5 also shows that the manufacturer’s profit is sacrificed while the retailer’s profit is enhanced after supply chain coordination. To achieve a “win– win” for the profits of the manufacturer and the retailer, we try to combine the optimal decisions after supply chain coordination with a two-part tariff agreement, which is similar to Chen et al. (2012), Xu et al. (2017), and Bai et al. (2017). Under this agreement, the manufacturer charges a lump sum fee for the loss of profit after supply chain coordination. We assume the manufacturer charges the retailer a lump sum fee T. We define two thresholds for the lump fee as follows: 2

2

TM =

4a2 h 2hγ ð2 - ϕ - ρ þ ρϕÞ þ ρ ð1 þ τb Þτg ð2 - ϕÞð1 - ϕÞ 2

ð2 - ϕÞ2 4hγ - ð1 þ τb Þτg ð2 - ϕÞ

2

2

TM =

8a2 h 2hγ ð2 - ϕ - ρ þ ρϕÞ þ ρ ð1 þ τb Þτg ð2 - ϕÞð1 - ϕÞ 2

4hγ - ð1 þ τb Þτg ð2 - ϕÞ

,

2

4hγ ð3 - ϕÞ - ð1 þ τb Þτg ð2 - ϕÞ2

2

2

2

2hγ ð5 - 2ϕÞ - ð1 þ τb Þτg ð2 - ϕÞ2 2

4hγ ð3 - ϕÞ - ð1 þ τb Þτg ð2 - ϕÞ2

2

ð2 - ϕÞ2

:

Then, we obtain the following corollary. Corollary 3 If 0 < ρ ≤

2hγ ð2 - ϕÞ ð1 - ϕÞ 2hγ - 2½ð1þτb Þτg  þϕ½ð1þτb Þτg  2

2

,

there is an interval

T M , T M for the lump sum fee to achieve a “win–win” for the profits of the manufacturer and the retailer.

6.5.3

Supply Chain Coordination via the Reselling Mode

Theorem 6 If 0 < ρ < 2hγ/{3hγ - [(1 + τb)τg]2}, then the supply chain can be 2 ρa 3hγ - ½ð1þτb Þτg  þhγa coordinated; when wcR = ; if ρ ≥ 2hγ/{3hγ - [(1 + τb)τg]2}, 2 γ 3hγ - ½ð1þτb Þτg  then the supply chain cannot be coordinated. Theorem 6 shows similar results to Theorem 5. From Theorems 5 and 6, we find that a wholesale price contract can coordinate the supply chain if the network coefficient is low, and this result is independent of the platform’s operational modes. In addition, the wholesale price after coordination via the reselling mode is increasing in τb, which indicates that using blockchain technology increases the wholesale price after coordination. By comparing the manufacturer’s and the retailer’s profits after supply chain coordination and those in Theorem 2 (1), we find that the manufacturer’s profit is reduced while the retailer’s profit is increased. Then, we try to combine the results

6.5

Supply Chain Coordination

137

with a two-part tariff agreement. We define two thresholds for the lump fee as follows:

TR =

TR =

a2 h 2hγ - 3hγρ þ ρ ð1 þ τb Þτg 4 4hγ - ð1 þ τb Þτg

2

2

2

3hγ - ð1 þ τb Þτg

a2 h 7hγ - 2 ð1 þ τb Þτg

2

2

2

,

2hγ - 3hγρ þ ρ ð1 þ τb Þτg 2

4 12h2 γ 2 - 7hγ ð1 þ τb Þτg

þ ð1 þ τb Þτg

4

2

2

2

:

Then, we find the following corollary. Corollary 4 If 0 < ρ < 2hγ/{3hγ - [(1 + τb)τg]2}, there is an interval T R , T R for the lump sum fee to achieve a “win–win” for the profits of the manufacturer and the retailer. Corollary 4 shows that the manufacturer and the retailer can achieve Pareto improvement in terms of profits after supply chain coordination. It is easy to verify that the value of T R - T R is decreasing in the network coefficient. Hence, with the increase in the network coefficient, the advantage of the two-part tariff agreement is increasingly weaker. Now, we explore whether the manufacturer and the platform can cooperate to achieve coordination when the manufacturer only sells its products through an online platform (i.e., the network coefficient is high). In the centralized situation, the total profit of the manufacturer and the platform is as follows: 2

ΠcT = pcS Dp - h ecS :

ð6:10Þ

Following the same process in proving Theorem 1, we can obtain the optimal 2 , retail price and the abatement level as: pc S = 2ahð1 þ ρÞ= 4hγ - ð1 þ τ b Þτg ec S = a ð1 þ τb Þτg ð1 þ ρÞ= 4hγ - ð1 þ τb Þτg

2

: To achieve the coordination of

the manufacturer and the platform, it needs ϕ = 0. Hence, if ρ > 2hγ(2 - ϕ)/{(1 ϕ){2hγ - 2[(1 + τb)τg]2 + ϕ[(1 + τb)τg]2}}, the manufacturer and the platform cannot achieve coordination. From Sect. 6.4.2, we know the platform’s response function as follows: wR - p = {2pRγ - (1 + ρ)a - eR[(1 + τb)τg]}/γ. After submitting pc S = 2ahð1 þ ρÞ= 4hγ - ð1 þ τb Þτg ð1 þ ρÞ= 4hγ - ð1 þ τb Þτg

2

2

and

ec S = a ð1 þ τb Þτg 

into the response function, we have wR

- p

= 0.

Hence, if ρ ≥ 2hγ/{3hγ - [(1 + τb)τg] }, the manufacturer and the platform cannot achieve coordination. 2

138

6

Coordination of a Supply Chain with an Online Platform Considering. . .

From the above analyses, we know that both the marketplace mode and reselling mode cannot coordinate the manufacturer and the platform if the network coefficient is high.

6.6

Conclusion

In this chapter, we investigate the coordination problem of a supply chain consisting of a retailer and a manufacturer who sells its products through a retail channel and an online platform. We consider two modes of the platform (i.e., marketplace mode and reselling mode), and the network effect is considered to reflect the power of the platform to enlarge the potential market size. Green technology in the blockchain era is also considered. First, we investigate the optimal production quantities and the abatement level with marketplace mode and reselling mode, respectively. Second, we discuss the coordination problem of the manufacturer and the retailer. The effect of blockchain technology on supply chain coordination and the profits of the manufacturer and the platform are also analyzed. Finally, we extend our studies by considering the coordination of the manufacturer, the retailer, and the platform. A set of numerical studies based on real data are conducted to illustrate our findings. By investigating the optimal operational decisions with the two modes, we have the following findings. (1) With the increase in the network coefficient, the online channel can encroach on offline demand, although the two channels have the same retail price. (2) The optimal abatement level is increasing in the network coefficient. (3) The increase in the network coefficient strengthens the double marginalization. (4) The increase in the network coefficient benefits the manufacturer and the platform but damages the retailer’s profit. By discussing the coordination of the manufacturer and the retailer with the two modes, we obtain the following findings. (5) Under the marketplace mode, the optimal abatement level in the centralized supply chain is larger than that in the decentralized supply chain. The difference is decreasing (increasing) in the low (high) network coefficient. (6) With the reselling mode, (a) the abatement level in the centralized supply chain is independent of the network coefficient; (b) the optimal total profit of the supply chain is decreasing in the network coefficient; and (c) the abatement level in the centralized supply chain is larger (less) than that in the decentralized supply chain if the network coefficient is low (high). If the network coefficient is low, then (7) both marketplace mode and reselling mode can coordinate the supply chain. Combining the results with a two-part tariff agreement can achieve a “win–win” for the profits of the manufacturer and the retailer. If the network coefficient is high, (8) the supply chain cannot be coordinated, and it is also true for the coordination of the manufacturer and the platform. To extend the model by considering the coordination of the manufacturer, the retailer, and the platform, (9) in marketplace mode, the three members can be coordinated if the network coefficient is low, while in reselling mode, the three members cannot be coordinated.

Appendix

139

Some managerial insights can be derived from this chapter. (1) The manufacturer should support the platform to increase the network coefficient. Using blockchain technology benefits the manufacturer and the platform. (2) With the marketplace mode, the centralized supply chain can help the products become “greener,” while with the reselling mode, the decentralized situation can help the products become “greener” if the network coefficient is high. (3) The coordination of the supply chain can be coordinated if the network coefficient is low, which is independent of the platform’s modes. (4) Blockchain technology can help products become greener and bring more profits for the manufacturer and the platform. In addition, blockchain technology can induce supply chain coordination. Several limitations exist in our work, and some of them may be possible directions for further research. First, in this chapter, we assume the manufacturer is the leader and the retailer and the platform are the followers. Considering the platform as the leader is also an interesting direction. Second, the discussion of the optimal decisions with multiple periods may obtain some new findings. Finally, the application of other technologies, such as machine learning and AI technology, should be considered in the model to explore the optimal operational decisions and analyze the supply chain coordination.

Appendix Proof of Theorem 1 Case 1. 0 < ρ
[(1 + τb)τg]2(2 - ϕ)2/[4γ(3 - ϕ)]. We can easily verify that |H| > 0. To let ∂ΠM - m/∂wM - r = 0 and ∂ΠM - m/∂eM = 0, we have 2 2 2aρð1 - ϕÞ hγþ½ð1þτb Þτg  þ2hγað4 - ϕÞ 4hγaþρað1 - ϕÞ 4hγþϕ½ð1þτb Þτg  pM = and wM - r = : 2 2 2 2 γ 4hγ ð3 - ϕÞ - ½ð1þτb Þτg  ð2 - ϕÞ γ 4hγ ð3 - ϕÞ - ½ð1þτb Þτg  ð2 - ϕÞ Now, we compare pM andwM - r : pM - wM - r =

=a

2aρð1 - ϕÞ hγ þ ð1 þ τb Þτg

2

þ 2ahγ ð4 - ϕÞ 2

γ 4hγ ð3 - ϕÞ - ð1 þ τb Þτg ð2 - ϕÞ2

hγ ð4 - 2ϕÞ - ρð1 - ϕÞ 2hγ - 2 ð1 þ τb Þτg

We

2

þ ϕ ð1 þ τb Þτg

2

γ 4hγ ð3 - ϕÞ - ð1 þ τb Þτg ð2 - ϕÞ2

know,

>

h

[(1

+

2hγ ð2 - ϕÞ

-

τb)τg]2(2

4hγa þ ρað1 - ϕÞ 4hγ þ ϕ ð1 þ τb Þτg

2

2

γ 4hγ ð3 - ϕÞ - ð1 þ τb Þτg ð2 - ϕÞ2 2

:

-

ϕ)/(2γ)

and

0 wM - r :

ð1 - ϕÞ 2hγ - 2½ð1þτb Þτg  þϕ½ð1þτb Þτg  2hγ ð2 - ϕÞ 2

Case 2. ρ ≥

2

ð1 - ϕÞ 2hγ - 2½ð1þτb Þτg  þϕ½ð1þτb Þτg  pM ≤ wM - r : That is to say, the manufacturer 2

2

We have does not sell its products through the retailer. Then, we obtain the manufacturer’s profit as follows: ΠM - m = ð1 - ϕÞpM Dp - he2M :

ð6:11Þ

The first partial derivatives of ΠM - m with respect to pM and eM are derived as follows: ∂ΠM - m/∂pM = (1 - ϕ){a - 2pMγ + aρ + eM[(1 + τb)τg]}, ∂ΠM - m/∂eM = 2heM + (1 - ϕ)[(1 + τb)τg]pM. The second partial derivatives of ΠM - m with respect to pM and eM are derived as follows: 2 2 2 2 ∂ ΠM - m =∂p2M = - 2γ ð1 - ϕÞ, ∂ ΠM - m =∂e2M = - 2h, ∂∂pΠM∂e-Mm = ∂∂eΠMM∂p- m = M M ð1 þ τb Þτg ð1 - ϕÞ: The Hessian matrix of ΠM - m is as follows: H=

- 2γ ð1 - ϕÞ ð1 þ τb Þτg ð1 - ϕÞ

ð1 þ τb Þτg ð1 - ϕÞ - 2h

Then, |H| = 4hγ - [(1 + τb)τg]2(1 - ϕ). We know h > [(1 + τb)τg]2(1 - ϕ)/(4h). We can easily verify that |H| > 0. Let ∂ΠM - m/∂pM = 0 and ∂ΠM - m/∂eM = 0, we

Appendix

141

have pM = obtain

2ahð1þρÞ

and eM =

4hγ - ½ð1þτb Þτg  ð1 - ϕÞ that qM - r 2

andΠM - m =

2

a hð1þρÞ ð1 - ϕÞ 2

4hγ - ½ð1þτb Þτg  ð1 - ϕÞ 2

a½ð1þτb Þτg ð1þρÞð1 - ϕÞ

= 0,

4hγ - ½ð1þτb Þτg  ð1 - ϕÞ qM - p 2

: Then, we can further =

2ahγ ð1þρÞ 4hγ - ½ð1þτb Þτg  ð1 - ϕÞ 2

,

:

Proof of Theorem 2 Case 1. 0 < ρ < 2hγ/{3hγ - [(1 + τb)τg]2} We know that the retailer’s response function is wR - r = {2pRγ - a eR[(1 + τb)τg]}/γ, and the platform’s response function is wR - p = {2pRγ (1 + ρ)a - eR[(1 + τb)τg]}/γ. Since there is a one-to-one relationship between wR - r (wR - p) and pR, we explore the optimal retail price and abatement level after substituting them into Eq. (6.8). We can have ∂ΠR - m/∂pR = - 8pRγ + 3a(2 + ρ) + 6eR[(1 + τb)τg], ∂ΠR - m =∂eR = 2 - 6pR γ ½ð1þτb Þτg þ2a½ð1þτb Þτg ð2þρÞþ2eR hγþ2½ð1þτb Þτg  : γ The second partial derivatives of ΠR - m with respect to pR and eR are derived as follows: 2 2 2 ∂ ΠR - m =∂e2R = - 2 hγ þ 2 ð1 þ τb Þτg =γ, ∂ ΠR - m =∂p2R = - 8γ, 2

∂ ΠR - m ∂pR ∂eR

=

2

∂ ΠR - m ∂eR ∂pR

= 6 ð1 þ τb Þτg : The Hessian matrix of ΠR - m is as follows:

H=

Then, jH j =

2

- 8γ

6 ð1 þ τb Þτg - 2 hγ þ 2 ð1 þ τb Þτg

6 ð1 þ τb Þτg 2

∂ ΠR - m ∂ ΠR - m ∂p2R ∂e2R

-

2

2

∂ ΠR - m ∂ ΠR - m ∂pR ∂eR ∂eR ∂pR

2

=γ

= 4 4hγ - ð1 þ τb Þτg

2

> 0: To

let ∂ΠR - m/∂pR = 0 and ∂ΠR - m/∂eR = 0,, we obtain the optimal decisions shown in Theorem 2 (2). It is easy to verify that pR > wR - p : Now, we compare pR andwR - r : pR

- wR - r

=a

=

3ahð2 þ ρÞ 2 4hγ - ð1 þ τb Þτg

2hr - 3hr - ð1 þ τb Þτg 2γ 4hγ - ð1 þ τb Þτg

2

2

ρ

2

-

ρa 4hγ - ð1 þ τb Þτg

2

þ 2hγað2 þ ρÞ

2γ 4hγ - ð1 þ τb Þτg

2

:

We know that h > [(1 + τb)τg]2/(3γ) and 0 < ρ < 2hr/{3hr - [(1 + τb)τg]2}. Then, we havepR > wR - r : Case 2. ρ ≥ 2hγ/{3hγ - [(1 + τb)τg]2} We have pR < wR - r : That is to say, the manufacturer does not sell its products through the retailer. Then, we obtain the manufacturer’s profit as follows:

142

6

Coordination of a Supply Chain with an Online Platform Considering. . .

ΠR - m = wR - p Dp - he2R :

ð6:12Þ

We know that the platform’s response function is wR - p = {2pRγ - (1 + ρ)a eR[(1 + τb)τg]}/γ. Since there is a one-to-one relationship between wR - p and pR, we explore the optimal retail price and abatement level after substituting them into Eq. (6.8). We can have ∂ΠR - m =∂pR = - 4pR γ þ 3að1 þ ρÞ þ 3eR ð1 þ τb Þτg , ð1 þ τb Þτg ½3pR γ - 2að1 þ ρÞ - 2eR hγ þ ð1 þ τb Þτg

∂ΠR - m =∂eR =

2

γ

:

The second partial derivatives of ΠR - m with respect to pR and eR are derived as follows: 2 2 2 ∂ ΠR - m =∂e2R = - 2 hγ þ ð1 þ τb Þτg =γ, ∂ ΠR - m =∂p2R = - 4γ, 2

∂ ΠR - m ∂pR ∂eR

=

2

∂ ΠR - m ∂eR ∂pR

= 3 ð1 þ τb Þτg : The Hessian matrix of ΠR - m is as follows:

Then, jH j = let ∂ΠR

2

3 ð1 þ τb Þτg 2

∂ ΠR - m ∂ ΠR - m ∂p2R ∂e2R

- m/∂pR

3 ð1 þ τb Þτg

- 4γ

H=

-

= 0 and ∂ΠR

2

- 2ðhγ þ τ2 Þ=γ 2

∂ ΠR - m ∂ ΠR - m ∂pR ∂eR ∂eR ∂pR - m/∂eR

= 0, we can have pR =

a½ð1þτb Þτg ð1þρÞ

qR - p = 2ahγð1þρÞ 2 2 , 8hγ - ½ð1þτb Þτg  8hγ - ½ð1þτb Þτg  a2 hð1þρÞ2 4a2 h2 γ ð1þρÞ2  : 2 , ΠR - p = 2 2 8hγ - ½ð1þτb Þτg  8hγ - ½ð1þτb Þτg 

eR =

= 8hγ - ð1 þ τb Þτg

, wR - p =

> 0: To

6ahð1þρÞ 8hγ - ½ð1þτb Þτg 

4ahð1þρÞ 8hγ - ½ð1þτb Þτg 

2

2

2

,

, ΠR - m =

Proof of Theorem 3 The first partial derivatives of ΠcM with respect to pcM and ecM are derived as follows: ∂ΠcM =∂pcM = a½2 þ ρ - ð1 þ ρÞϕ - ð2 - ϕÞ 2pcM γ - ecM ð1 þ τb Þτg , ∂ΠcM =∂ecM = - 2hecM þ pcM ð1 þ τb Þτg ð2 - ϕÞ: The second partial derivatives of ΠcM with respect to pcM and ecM are derived as follows: 2

∂ ΠcM =∂ pcM

2

2

= - 2γ ð2 - ϕÞ, ∂ ΠcM =∂ ecM

ð1 þ τb Þτg ð2 - ϕÞ: The Hessian matrix of H=

- 2γ ð2 - ϕÞ ð1 þ τb Þτg ð2 - ϕÞ

ΠcM

2

= - 2h,

2

∂ ΠcM ∂pcM ∂ecM

is as follows:

ð1 þ τb Þτg ð2 - ϕÞ - 2h

=

2

∂ ΠcM ∂ecM ∂pcM

=

Appendix

143

Then, |H| = 4hγ(2 - ϕ) - [(1 + τb)τg]2(2 - ϕ)2. We know h > [(1 + τb)τg]2(2 ϕ)/(4γ). We can easily verify that |H| > 0. To let ∂ΠcM =∂pcM = 0 and ∂ΠcM =∂ecM = 0, , we obtain the optimal decisions shown in Theorem 3. 2hγ ð2 - ϕÞ

Proof of Corollary 1 Case 1. 0 < ρ < From Theorem 1, we know eM = 5, we know ec M =  ec M - eM =

ð1 - ϕÞ 2hγ - 2½ð1þτb Þτg  þϕ½ð1þτb Þτg  2

a½ð1þτb Þτg ½ð2 - ϕÞ2 þρð4 - ϕÞð1 - ϕÞ 2

:

Then, we can verify that

4hγ - ½ð1þτb Þτg  ð2 - ϕÞ a½ð1þτb Þτg ½ð2 - ϕÞþð1 - ϕÞρ a½ð1þτb Þτg ½ð2 - ϕÞ2 þρð4 - ϕÞð1 - ϕÞ

-

4hγ - ½ð1þτb Þτg  ð2 - ϕÞ 2

:

: From Theorem

4hγ ð3 - ϕÞ - ½ð1þτb Þτg  ð2 - ϕÞ2 a½ð1þτb Þτg ½ð2 - ϕÞþð1 - ϕÞρ 2

2

4hγ ð3 - ϕÞ - ½ð1þτb Þτg  ð2 - ϕÞ2 2

2a½ð1þτb Þτg  2hγ ½2 - ð1 - ϕÞρ - ϕÞþρ½ð1þτb Þτg  ð2 - ϕÞð1 - ϕÞ

, which can

2

be simplified as

4hγ - ½ð1þτb Þτg  ð2 - ϕÞ 2

4hγ ð3 - ϕÞ - ½ð1þτb Þτg  ð2 - ϕÞ2 + ρ[(1 + τb)τg]2(2 - ϕ)(1 2

:

Let f(ρ) = 2hγ[2 - (1 - ϕ)ρ - ϕ)] - ϕ). It is obvious  e is determined by the sign of f(ρ). To simplify f(ρ), we have that the sign of ec M M f(ρ) = 2hγ(2 - ϕ) - {2hγ - [(1 + τb)τg]2(2 - ϕ)}(1 - ϕ)ρ. Since h > [(1 + τb)τg]2(2 2hγ ð2 - ϕÞ , it is easy to verify that ϕ)/(2γ) and 0 < ρ < 2 2 ð1 - ϕÞ 2hγ - 2½ð1þτb Þτg  þϕ½ð1þτb Þτg   dðec M - eM Þ  < 0: f(ρ) > 0. Thus, ec M > eM : In addition, we can verify that dρ Case 2. ρ >

2hγ ð2 - ϕÞ

ð1 - ϕÞ 2hγ - 2½ð1þτb Þτg  þϕ½ð1þτb Þτg  2

From Theorem 1, we know eM = ec M =

a½ð1þτb Þτg ½ð2 - ϕÞþð1 - ϕÞρ 4hγ - ½ð1þτb Þτg  ð2 - ϕÞ 2

2

:

a½ð1þτb Þτg ð1þρÞð1 - ϕÞ 4hγ - ½ð1þτb Þτg  ð1 - ϕÞ 2

: From Theorem 5, we know

: We can verify that a[(1 + τb)τg][(2 - ϕ) + (1 - ϕ)ρ]

>a[(1 + τb)τg](1 + ρ)(1 - ϕ) and {4hγ - [(1 + τb)τg]2(2 - ϕ)} < {4hγ  In addition, we can verify that [(1 + τb)τg]2(1 - ϕ)}. Hence, ec M > eM : c  d ð eM - eM Þ > 0: dρ Proof of Theorem 4 Following the same process in proving Theorem 3, we can obtain the optimal decisions shown in Theorem 4. Proof of Corollary 2 Following the same process in proving Corollary 1, we can obtain the optimal decisions shown in Corollary 2. Proof of Theorem 5 From Eq. (6.3), we can obtain the retailer’s response function p = {a + wγ + e[(1 + τb)τg]}/(2γ). From Theorem 3, we have ec M = a½ð1þτb Þτg ½ð2 - ϕÞþð1 - ϕÞρ 4hγ - ½ð1þτb Þτg  ð2 - ϕÞ 2

, pc M =

2ah½2þρð1 - ϕÞ - ϕ 4hγ - ½ð1þτb Þτg  ð2 - ϕÞ ð2 - ϕÞ 2

into the response function, we can obtain wcM = supply chain. Comparing 0 w ; M M

that if if ρ>

6 Coordination of a Supply Chain with an Online Platform Considering. . .

144

2hγ ð2 - ϕÞ ð1 - ϕÞ 2hγ - 2½ð1þτb Þτg  þϕ½ð1þτb Þτg  2

, the manufacturer sells its products only through

2

the online platform. That is to say, the supply chain cannot be coordinated. Proof of Corollary 3 From Theorem 5, we know the manufacturer’s profit is 4 2 a2 4h2 γ 2 ½2ρð3 - ϕÞð2 - ϕÞþð2 - ϕÞ2 þρ2 ð1 - ϕÞ2 ð1 - ϕÞ - ρ2 ½ð1þτb Þτg  ð2 - 3ϕþϕ2 Þ Πc = 2 M -m 2 γ 4hγ - ½ð1þτb Þτg  ð2 - ϕÞ ð2 - ϕÞ2 2 hγ ½ð1þτb Þτg  ð2 - ϕÞ½ρ2 ð2 - 3ϕþϕ3 Þ - 2ρð4 - ϕÞð2 - ϕÞð1 - ϕÞ - ð2 - ϕÞ3 g and the retailer’s profit 2 2 γ 4hγ - ½ð1þτb Þτg  ð2 - ϕÞ ð2 - ϕÞ2 a2 2hγ ð2 - ρþρϕ - ϕÞþρ½ð1þτb Þτg  ð2 - ϕÞð1 - ϕÞ 2

is

Πc M -r

know

=

2

γ 4hγ - ½ð1þτb Þτg  ð2 - ϕÞ 2

the

2

: From Theorem 1 (1), we

ð2 - ϕÞ2

manufacturer’s

profit

a2 hγ ½ð2 - ϕÞ2 þ2ρð4 - ϕÞð1 - ϕÞþρ2 ð1 - ϕÞ2 þρ2 ½ð1þτb Þτg  ð1 - ϕÞ2 g

ΠM - m =

is

2

γ 4hγ ð3 - ϕÞ - ½ð1þτb Þτg  ð2 - ϕÞ2 2

ΠM - r =

a2 2hγ ð2 - ρþρϕ - ϕÞþρ½ð1þτb Þτg  ð2 - ϕÞð1 - ϕÞ 2

γ 4hγ ð3 - ϕÞ - ½ð1þτb Þτg  ð2 - ϕÞ2 2

2

, and the retailer’s profit is

2

: To achieve a “win–win” for the

 profits of the manufacturer and the retailer, it needs Πc M - m þ T > ΠM - m and c   c c  ΠM - r - T > ΠM - r : Then, we have ΠM - m - ΠM - m < T < ΠM - r - ΠM - r :

Let have-

T M = ΠM - m - Πc M - m,

and

 T M = Πc M - r - ΠM - r ,

2

TM =

4ha2 2hγ ð2 - ϕ - ρ þ ρϕÞ þ ρ ð1 þ τb Þτg ð2 - ϕÞð1 - ϕÞ 2

ð2 - ϕÞ2 4hγ - ð1 þ τb Þτg ð2 - ϕÞ

2

2

,

2

8a2 h 2hγ ð2 - ϕ - ρ þ ρϕÞ þ ρ ð1 þ τb Þτg ð2 - ϕÞð1 - ϕÞ 4hγ - ð1 þ τb Þτg ð2 - ϕÞ

2

4hγ ð3 - ϕÞ - ð1 þ τb Þτg ð2 - ϕÞ2 2

TM =

we

2

2

2

2hγ ð5 - 2ϕÞ - ð1 þ τb Þτg ð2 - ϕÞ2 2

4hγ ð3 - ϕÞ - ð1 þ τb Þτg ð2 - ϕÞ2

2

ð2 - ϕÞ2

:

Therefore, we can obtain the results shown in Corollary 3. Proof of Theorem 6 From Sect. 6.4.1, we can obtain the retailer’s response function a½ð1þτb Þτg  p = {a + wγ + e[(1 + τb)τg]}/(2γ). From Theorem 6, we have ec R = 3hγ - ð1þτ Þτ 2 , ½ b g 2 3hγ - ½ð1þτb Þτg  ρaþ4hγa : After submitting them into the response function, we pc 2 R = 2γ 3hγ - ½ð1þτb Þτg  2 2 ρa 3hγ - ½ð1þτb Þτg  þhγa 2hγa - ρa 3hγ - ½ð1þτb Þτg  c : Then pc : w = can obtain wcR = 2 2 R R 2γ 3hγ - ½ð1þτb Þτg  γ 3hγ - ½ð1þτb Þτg  Therefore, if 0 < ρ < 2hγ/{3hγ - [(1 + τb)τg]2}, then the supply chain can be 2 ρa 3hγ - ½ð1þτb Þτg  þhγa coordinated when wcR = ; if ρ ≥ 2hγ/{3hγ - [(1 + τb)τg]2}, 2 γ 3hγ - ½ð1þτb Þτg  then the supply chain cannot be coordinated. Proof of Corollary 4 From Theorem 6, we know the manufacturer’s profit is 2 4 a2 h2 γ 2 ð4þ6ρ - 9ρ2 Þ - 2hγ ½ð1þτb Þτg  ð1þρ - 3ρ2 Þ - ρ2 ½ð1þτb Þτg  Πc = , and the retailer’s 2 R-m 2 2γ 3hγ - ½ð1þτb Þτg 

Appendix

145

profit is Πc R-r =

a2 2hγ - 3hγρþρ½ð1þτb Þτg  4γ 3hγ - ½ð1þτb Þτg 

manufacturer’s profit is ΠR - m = profit is ΠR - r =

2

2

: From Theorem 2 (1), we know the

2

2

a2 hγ ð4þ4ρ - 7ρ2 Þþ2ρ2 ½ð1þτb Þτg 

2

4γ 4hγ - ½ð1þτb Þτg 

a2 2hγ - 3hγρþρ½ð1þτb Þτg  4γ 4hγ - ½ð1þτb Þτg 

2

2

, and the retailer’s

2

2

: To achieve “win–win” for the profits of

2

 c the manufacturer and the retailer, it needs Πc R - m þ T > ΠR - m and ΠR - r - T > c  ΠR - r : Then, we have ΠR - m - Πc R - m < T < ΠR - r - ΠR - r : To let T R =

ΠR - m - Πc R - m , we have T R =

a2 h 2hγ - 3hγρþρ½ð1þτb Þτg  4 4hγ - ½ð1þτb Þτg 

 let T R = Πc R - r - ΠR - r , and have T R =

2

2

2

3hγ - ½ð1þτb Þτg 

2

a2 h 7hγ - 2½ð1þτb Þτg 

2

: Similarly, we

2hγ - 3hγρþρ½ð1þτb Þτg 

2

4 12h2 γ 2 - 7hγ ½ð1þτb Þτg  þ½ð1þτb Þτg  2

4

2

2

:

2

Thus, we can obtain the results shown in Corollary 4. Proof of Theorem 7 Following the same process in proving Theorem 3, we can obtain the optimal decisions shown in Theorem 7. Proof

of

Theorem

8 (1)

2hγ ð2 - ϕÞ ð1 - ϕÞ 2hγ - 2½ð1þτb Þτg  þϕ½ð1þτb Þτg  pcT = a þ wcT γ þ ecT ð1 þ τb Þτg 2

2

With

marketplace

mode,

0

ð1 - ϕÞ 2hγ - 2½ð1þτb Þτg  þϕ½ð1þτb Þτg  2

2hγ

hγ - ½ð1þτb Þτg  2

2

: We can verify that

c : Hence, pc T > wT :

½ð1þτb Þτg  ð2 - ϕÞ 2

Case 3: h ≥

γ

In this situation, we can similarly obtain that ρT = 2hγ ð2 - ϕÞ ð1 - ϕÞ 2hγ - 2½ð1þτb Þτg  þϕ½ð1þτb Þτg  c thenpc T < wT : 2

2

2hγ hγ - ½ð1þτb Þτg 

2


wT ; if ρ > ρT,

146

6

Similarly, if ρ >

Coordination of a Supply Chain with an Online Platform Considering. . . 2hγ ð2 - ϕÞ ð1 - ϕÞ 2hγ - 2½ð1þτb Þτg  þϕ½ð1þτb Þτg  2

2

,

the manufacturer, the

retailer, and the platform cannot be coordinated. (2) With the reselling mode, we follow the same process in proving Theorem 8 (1), and we find that the manufacturer, the retailer, and the platform cannot achieve coordination.

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