Operations Research and Analytics in Latin America: Proceedings of ASOCIO/IISE Region 16 Joint Conference 2022 (Lecture Notes in Operations Research) 3031288696, 9783031288692

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Lecture Notes in Operations Research

Jairo R. Montoya-Torres William J. Guerrero David L. Cortés-Murcia   Editors

Operations Research and Analytics in Latin America Proceedings of ASOCIO/IISE Region 16 Joint Conference 2022

Lecture Notes in Operations Research Editorial Board Ana Paula Barbosa-Povoa, University of Lisbon, Lisboa, Portugal Adiel Teixeira de Almeida , Federal University of Pernambuco, Recife, Brazil Noah Gans, The Wharton School, University of Pennsylvania, Philadelphia, USA Jatinder N. D. Gupta, University of Alabama in Huntsville, Huntsville, USA Gregory R. Heim, Mays Business School, Texas A&M University, College Station, USA Guowei Hua, Beijing Jiaotong University, Beijing, China Alf Kimms, University of Duisburg-Essen, Duisburg, Germany Xiang Li, Beijing University of Chemical Technology, Beijing, China Hatem Masri, University of Bahrain, Sakhir, Bahrain Stefan Nickel, Karlsruhe Institute of Technology, Karlsruhe, Germany Robin Qiu, Pennsylvania State University, Malvern, USA Ravi Shankar, Indian Institute of Technology, New Delhi, India Roman Slowi´nski, Pozna´n University of Technology, Poznan, Poland Christopher S. Tang, Anderson School, University of California Los Angeles, Los Angeles, USA Yuzhe Wu, Zhejiang University, Hangzhou, China Joe Zhu, Foisie Business School, Worcester Polytechnic Institute, Worcester, USA Constantin Zopounidis, Technical University of Crete, Chania, Greece

Lecture Notes in Operations Research is an interdisciplinary book series which provides a platform for the cutting-edge research and developments in both operations research and operations management field. The purview of this series is global, encompassing all nations and areas of the world. It comprises for instance, mathematical optimization, mathematical modeling, statistical analysis, queueing theory and other stochastic-process models, Markov decision processes, econometric methods, data envelopment analysis, decision analysis, supply chain management, transportation logistics, process design, operations strategy, facilities planning, production planning and inventory control. LNOR publishes edited conference proceedings, contributed volumes that present firsthand information on the latest research results and pioneering innovations as well as new perspectives on classical fields. The target audience of LNOR consists of students, researchers as well as industry professionals.

Jairo R. Montoya-Torres · William J. Guerrero · David L. Cortés-Murcia Editors

Operations Research and Analytics in Latin America Proceedings of ASOCIO/IISE Region 16 Joint Conference 2022

Editors Jairo R. Montoya-Torres School of Engineering Universidad de La Sabana Chia, Colombia

William J. Guerrero School of Engineering Universidad de La Sabana Chia, Cundinamarca, Colombia

David L. Cortés-Murcia School of Engineering Universidad de La Sabana Chia, Colombia

ISSN 2731-040X ISSN 2731-0418 (electronic) Lecture Notes in Operations Research ISBN 978-3-031-28869-2 ISBN 978-3-031-28870-8 (eBook) https://doi.org/10.1007/978-3-031-28870-8 © 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

Committees

Conference Organizing Committee William J. Guerrero, Universidad de La Sabana Luz Helena Mancera, Universidad de La Sabana Jairo R. Montoya-Torers, Universidad de La Sabana David L. Cortés-Murcia, Universidad de La Sabana Juan Sebastián Sánchez-Gómez, Universidad Sergio Arboleda IISE Chapter #782 Universidad de La Sabana, Colombia IISE Chapter #712 Universidad Sergio Arboleda, Colombia IISE Chapter #988 Universidad de Los Andes, Colombia

Administrative Support Laura Gómez Universidad de La Sabana, Chía

Academic Committee Jairo R. Montoya-Torres, Universidad de La Sabana, Colombia—Co-Chair William J. Guerrero, Universidad de La Sabana, Colombia—Co-Chair Luz Helena Mancera, Universidad de La Sabana, Colombia—Co-Chair Juan Sebastián Sánchez-Gómez, Universidad Sergio Arboleda, Colombia—CoChair Sepideh Abolghasem, Universidad de los Andes, Colombia—Co-Chair David L. Cortés, Universidad de La Sabana, Colombia—Co-Chair Edgar Alfonso, Université Jean Monnet de Saint-Etienne, France

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Johanna Amaya, Pennsilvania State University, USA Julio Brito, Universidad de La Laguna, Spain Victor Cantillo, Universidad del Norte, Colombia Fabián Castaño, Frubana, Colombia Nicolás Clavijo, Universidad de Porto, Portugal Jairo Coronado, Universidad de la Costa, Colombia David Barrera, Universidad Javeriana Bogotá, Colombia Carlos A. Franco, Universidad del Rosario, Colombia Ricardo Gatica, Pontificia Universidad Católica de Valparaíso, Chile Guisselle García, Universidad del Norte, Colombia Rosa González, Universidad de los Andes, Santiago, Chile Eliana M. González, Universidad Javeriana Bogotá, Colombia Elena Valentina Gutiérrez, Universidad del Valle, Colombia Edgar Gutiérrez-Franco, MIT Center for Transportation and Logistics, USA Andrés Felipe Gutiérrez, Frubana, Colombia Nilson Herazo-Padilla, Universidad del Rosario, Colombia Juan Jaramillo, Adelphi University, NY, USA José-Fernando Jiménez, Université de Savoie Mont Blanc, France Adriana Leiras, PUC Rio, Brazil Andrés López, Universidad del Norte, Colombia Eduyn López, Universidad Distrital Francisco José de Caldas, Colombia Antonio Martínez, University of Southampton, UK Pablo Andrés Amaya Duque, Universidad de Antioquia, Colombia Andrés Medaglia, Universidad de los Andes, Colombia Christopher Mejía, MIT Center for Transportation and Logistics, USA Gonzalo Mejía, Universidad de La Sabana, Colombia Carlos Montoya, Universidad Javeriana Bogotá, Colombia Carlos A. Moreno-Camacho, Ecole des Ponts ParisTech, France Javier Neira, Universidad Politécnica de Valencia, Spain Miguel Ortega Mier, Universidad Politécnica de Madrid, Spain Camilo Ortiz, HEC Montréal, Canada Andrés Felipe Osorio, Universidad ICESI, Colombia Carlos L. Quintero-Araújo, Universidad de La Sabana, Colombia Juan Sebastián Sánchez-Gómez, Universidad Sergio Arboleda, Colombia Luis Alfredo Paipa, Universidad de La Sabana, Colombia Andrea Pirabán, Universidad de la Costa, Colombia Daniel Prato, Logyca, Colombia Catalina Ramírez, Universidad de los Andes, Colombia Diana Ramírez, Rensselaer Polytechnic Institute, USA María Isabel Restrepo, IMT Atlantique, France Lorena Reyes-Rubiano, Otto-von-Guericke University Magdeburg, Germany Reinaldo Rivera, Universidad del Valle, Colombia Diana Rodríguez Coca, Oklahoma State University, USA Ruben Ruíz, Universidad Politécnica de Valencia, Spain José Luis Ruíz, Universidad de La Sabana, Colombia

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Alfonso Sarmiento, Universidad de La Sabana, Colombia Angélica Sarmiento, Escuela Colombiana de Ingeniería Julio Garavito, Colombia Carlos Mario Socarras, Smart BP Elyn Solano-Charris, Universidad de La Sabana, Colombia Carlos Suárez, Universidad San Francisco de Quito, Ecuador Rafael Tordecilla, Universitat Oberta de Catalunya, Spain Andrés Felipe Torres, Universidad de los Andes, Colombia Carlos A. Vega-Mejía, Universidad de La Sabana, Colombia Nubia Velasco, Universidad de los Andes, Colombia Mario C. Vélez, Universidad EAFIT, Colombia Juan Guillermo Villegas, Universidad de Antioquia, Colombia

Preface

This volume gathers a selection of full peer-reviewed papers presented at the 2022 Joint Congress of ASOCIO and IISE Region 16. ASOCIO is the Colombia Society for Operations Research (http://asociocolombia.org/site/), while IISE Region 16 is the Regional Chapter of the Institute of Industrial and Systems Engineering (IISE) for Latin America and the Caribbean (https://www.iise.org/details.aspx?id=40187). ASOCIO was founded in October 2014 and its congress has taken place continuously since then hosted by different universities: Universidad de La Sabana, Chia, Colombia (July 2015), Universidad EAFIT, Medellin (August 2017), Universidad Industrial de Santander UIS in Bucaramanga (September 2019). This is the fourth edition of the congress, taking place again at Universidad de La Sabana. Attendance for each version of the ASOCIO congress include mostly university faculty and doctoral and master students, working in the fields of operations research, analytics, applied mathematics, computer sciences, and artificial intelligence. ASOCIO was recognized as a member of the International Federation of Operational Research Societies (IFORS), and by the Latin-Ibero-American Association of Operations Research (ALIO). IISE Region 16 (Latin America and the Caribbean) is a regional chapter of the Institute of Industrial and Systems Engineering, USA (https://www.iise.org/). The regional congress takes place annually organized by different universities belonging to the chapter. This is the 19th edition of the IISE Region 16 congress. Attendance includes undergraduate and postgraduate students, industrial and systems engineering professionals and university faculty, related to the different subfields of the industrial engineering (industrial management, production and operations, quality management, logistics and supply chain, operations research, ergonomics, lean manufacturing, finance, etc.). For this joint version of 2022, a set of different academic, professional, and networking activities took place, outlined next, plus two panels with experts and one networking event. A total of 124 contributions were received: 91 abstracts and 33 full papers; 122 were accepted after peer-review, and 103 were duly presented at the conference venue. All contributions were evaluated by external reviewers. Only full papers were considered for inclusion in this volume. Full papers followed a ix

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double-step review process based on scientific merit. The academic program included keynote conferences given by recognized scholars in the field: • Professor Ana Paula Barbosa-Povoa, Universidade de Lisboa, Portugal, • Professor Ruben Ruiz, currently Principal Applied Scientist at Amazon Web Services, Elastic Compute Cloud (EC2) team, • Dr. Christopher Mejia-Argueta, Research Scientist and Director of the MIT SCALE Network—Latin America, Director of the MIT Graduate Certificate in Logistics and SCM (GCLOG) program, and Founder & Director of the MIT Food and Retail Operations Lab at MIT Center for Transportation and Logistics, Massachusetts Institute of Technology, Cambridge, USA • Professor Andrés Medaglia, Full Professor and Director of the Research Center on Optimization and Applied Probability (COPA) at Universidad de los Andes, in Bogotá, Colombia, and • Luis Alejandro Ángel, dean of the School of Industrial Engineering at Universidad Sergio Arboleda, in Bogotá, Colombia. Several tutorials were also organized as part of the academic program: • “Predictive analytics for cancer management”, by David Barrera, Pontificia Universidad Javeriana, Bogotá, Colombia, • “Circular Economy and Operations Research”, by Prof. Juan Guillermo Villegas and Dr. Pablo Andrés Maya, Universidad de Antioquia, Medellín, Colombia, • “How can Operations Research support decision-making in sustainable procurement and distribution?”, by Dr. Gonzalo Mejía, Universidad de La Sabana, Chía, Colombia, • “Operations Research in Humanitarian Logistics”, by Prof. Victor Cantillo, Universidad del Norte, Barranquilla, Colombia, • “Publishing in Sustainability Analytics and Modeling”, by Prof. Elise MillerHooks, Professor and Bill & Eleanor Hazel Chair in Infrastructure Engineering, George Mason University, Fairfax, USA, and Editor-in-Chief of the journal Sustainability Analytics and Modeling, published by Elsevier and IFORS (International Federation of Operations Research Societies), • “Simulation using Flexim”, by representatives of this company, and • “Leadership in Production”, by Diana Ramírez, production engineer working within the manufacturing sector. The book contains a total of 17 full papers selected from the conference submissions, plus one invited paper, and is structured in four parts that correspond to a general view of the technical sessions of the program. They include papers describing results of the research addressing the development and applications of Analytics and Operations Research methods to a variety of complex problems, including modeling, algorithmic developments, and real-life applications. These subjects are treated in the book’s Part 1: Modeling, Optimization, Analytics, and Artificial Intelligence; Part 2: Applications in Production, Logistics, and Supply Chain Management; Part 3: Applications in Humanitarian and Health Logistics; and Part 4: Sustainability Modeling and Analytics.

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All these issues have been studied throughout the years in the different version of both ASOCIO and IISE Region 16 congress series. We do expect to see further developments within the Latin America research community. We think that students at both graduate and undergraduate levels, researchers, and engineers will find this volume useful for the study of analytics and operations research. Last, but not least, we want to thank the support of and the help of many people from the university chapters of the IISE at the three universities that jointly organized this conference: Universidad de La Sabana, Universidad Sergio Arboleda and Universidad de los Andes. We also want to thank ICETEX (Instituto Colombiano de Crédito y Estudios Técnicos en el Exterior), for their economic support through the Colombia Scholarship Program for Visiting Faculty 2022 that allowed the participation of the three international plenary speakers. Chia, Colombia September 2022

Jairo R. Montoya-Torres William J. Guerrero David L. Cortés-Murcia

Contents

An Overview of Operations Research/Management Science in Latin America . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Juan G. Villegas, Jairo R. Montoya-Torres, and William J. Guerrero

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Modeling, Optimization, Analytics, and Artificial Intelligence Collaborative Versus Non-collaborative Bus School Routing . . . . . . . . . . . Luz Helena Mancera, Julián Andrés Hincapié-Urrego, Jairo R. Montoya-Torres, Danna Valentina Ubaque-Hernández, Natalia Andrea Orrego-Oviedo, and Angie Natalia Montaña-Gil Method for Assigning Break Times in Predefined Shifts for Call Center Teleoperators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kevin Felipe Jaimes Vanegas, Sergio Andres Villamizar Lozano, and Raúl Fabián Roldán Nariño Financial Risk Analysis for a Specialized Dairy Farm Project and Impacts of Government Interest Rate Subsidies . . . . . . . . . . . . . . . . . . Juan Antonio Martinez Becerra and Kathleen Salazar-Serna Brand Positioning Analysis for the Automotive Lubricants Industry Using Perceptual Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Juan Sebastián Gil Castro, Juan Diego González, Julián David González, Andrés Felipe Martínez, Nicolás Rodríguez, Edward Steven Rojas, Juan Diego Román, and Karen Dayane Santana

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Applications in Production, Logistics, and Supply Chain Management Comparison of Nawaz-Enscore-Ham Algorithm and Local Search Operator in Flowshop Scheduling with Learning Effects . . . . . . . . . . . . . . Yenny Alexandra Paredes-Astudillo, Jairo R. Montoya-Torres, and Valérie Botta-Genoulaz

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Methodology for Integrating Variables for a Transdisciplinary Productivity Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gisela Patricia Monsalve Fonnegra

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Mathematical Models for Scheduling Electric Vertical Take-Off and Landing (eVTOL) Vehicles at Urban Air Mobility Vertiports . . . . . . 101 Julián Alberto Espejo-Díaz, Edgar Alfonso-Lizarazo, and Jairo R. Montoya-Torres Inter-cities Model Proposal for Potato’s Last Mile Logistics: Case Study in Bogotá, Colombia and Cochabamba, Bolivia . . . . . . . . . . . . . . . . . 113 Camilo Ernesto Bejarano Cubillos, Juan David Chavarrio Rojas, Valentina Gama Gutiérrez, Loredana Angélica Orellana Delgadillo, Paola Andrea Ospina Baracaldo, María Alejandra Rojas Trigo, Agatha Clarice da Silva-Ovando, and Gonzalo Mejía Applications in Humanitarian and Health Logistics Road Prioritization for the Reconstruction of an Area Affected by a Disaster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Lorena S. Reyes-Rubiano and Elyn Solano-Charris Heuristic Method for the Emergency Water Delivery Problem with Deprivation Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Nicolás Giedelmann-L, William J. Guerrero, and Elyn L. Solano Charris A Simulation Approach to Analyze the Operational Response Plans in an Emergency Department Under the COVID-19 Pandemic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 David Mora-Meza, Julián Alberto Espejo-Díaz, and William J. Guerrero Formulation of a Logistics Roadmap for the Health Sector in Colombia Through a Maturity Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 H. Herrera and D. Prato Predicting Medicine Administration Times in the Inpatient Ward Using Data Analytics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 Cristian Andrey Jaimez Olarte and William J. Guerrero Modeling Vaccine Allocations in Rural Areas in Central Regions from Colombia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Sthefania Ardila Benitez, Ana Carolina García Hoyos, María Paula Losada Porras, Alejandra Milena Castellanos Guarnizo, and Gonzalo Mejía

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Sustainability Modeling and Analytics Feasibility Study and Multivariate Analysis of a Sustainable Housing Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Isabel García, Kathleen Salazar-Serna, and Juan Pablo Melo Perspectives of Operational Research for Modeling and Analysis of Agricultural Production Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 Nestor E. Caicedo Solano, Guisselle A. García Llinás, and Jairo R. Montoya-Torres Informal Recycling of Venezuelan Migrants in Bogotá . . . . . . . . . . . . . . . . 215 Juan Sebastián Sánchez-Gómez and Oscar David Maturana Fiallo Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

About the Editors

Jairo R. Montoya-Torres is Full Professor and currently director of the doctoral program in Engineering and director of the doctoral program in Logistics and Supply Chain Management at the School of Engineering, Universidad de La Sabana, Chia, Colombia. He holds a Ph.D. in industrial engineering from Ecole des Mines de Saint-Etienne, France and Université Jean Monnet, France, and the Accreditation for Research Supervision (“Habilitation à Diriger des Recherches” HDR) in logistics and operations research from the Institut National des Sciences Appliquées (INSA) de Lyon and Université Claude Bernard Lyon, France. His research interests include sustainability and collaborative decision-making in scheduling, vehicle routing, supply chain design and urban logistics, using advanced optimization, simulation, and hybrid techniques. He is founder member of the Colombian Operations Research Society (ASOCIO) and was also its president and vice-president. e-mail: [email protected] William J. Guerrero holds a Ph.D. in Systems Optimization and Reliability from Université de Technologie de Troyes (France) and Ph.D. in Engineering from Universidad de los Andes (Colombia). He also holds degrees in Industrial Engineer and a master’s in industrial engineering with major in Operations Research. He has experience in supply chain and research projects. His research interests involve combinatorial optimization and heuristics for humanitarian and hospital logistics and supply chain and the vehicle routing problem and its extensions. He also has experience in the European projects under the H2020 research and innovation programme entitled ePICenter for developing disruptive technologies for global supply chains (http://epi centerproject.eu). e-mail: [email protected] David L. Cortés-Murcia received his B.Sc. and M.Sc. in Industrial Engineering from Escuela Colombiana de Ingeniería Julio Garavito (Colombia) and his Ph.D. in Optimization and Systems Reliability from Université de Technologie de Troyes (France). He was a Postdoctoral Fellow within the Research Group in Logistics Systems of the School of Engineering at Universidad de La Sabana, Colombia, xvii

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where his work focused on the analysis of disruptive technologies for global supply chains within the EU-H2020 funded project ePICenter (http://epicenterproject.eu). His research interests include studies in sustainable logistics, routing with electric vehicles, optimization and simulation, as well as supply chain design, green logistics and applied operations research. He is currently Senior Data Scientist at Chiper, a start-up company focusing on B2B one-stop shop in Latin America.

An Overview of Operations Research/ Management Science in Latin America Juan G. Villegas , Jairo R. Montoya-Torres , and William J. Guerrero

Abstract This paper presents an analysis of research articles published in the field of Operations Research and Management Science (OR/MS) by Latin American researchers. The objective is to examine the historical evolution of research in the field and to examine the current state of OR/MS studies in Latin America. The analysis is based on data available on the Web of Science databases. This study provides a general picture of studies in the field, by analyzing the findings through the most productive countries, the most influential authors, and the network of collaborations, among other indicators. The study reveals that OR/MS publications having at least one author from a country in Latin America have steadily increased over time. Expert Systems with Applications and the European Journal of Operational Research are their preferred journals for publication. This study also concludes that Brazilian researchers and institutions dominate the production of OR/MS knowledge with more than half of the documents published in the region, and four other counties (Mexico, Chile, Colombia, and Argentina) account for the remaining document to surpass the 90% threshold. Keywords Operations research · Management science · Bibliometrics · Latin America

J. G. Villegas (B) ALIADO—Analytics and Research for Decision Making, Department of Industrial Engineering, Universidad de Antioquia, Calle 67 No. 53-108, 050010 Medellín, Colombia e-mail: [email protected] J. R. Montoya-Torres · W. J. Guerrero School of Engineering, Universidad de La Sabana, Km 7 Autopista Norte de Bogotá, 250001 Chía, D.C., Colombia e-mail: [email protected] W. J. Guerrero e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. R. Montoya-Torres et al. (eds.), Operations Research and Analytics in Latin America, Lecture Notes in Operations Research, https://doi.org/10.1007/978-3-031-28870-8_1

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1 Introduction The origins of OR/MS as a discipline can be dated back to the decade of 1950’s with the establishment of the Operations Research Society of America (ORSA) in 1952, the Operational Research Society (ORS) of the United Kingdom in 1953, and the Institute of Management Sciences (TIMS) in 1953. As pointed out in [1], “these associations have promoted some classical journals in the field that have become the key instruments to disseminate new research contributions”. The creation in 1959 of the International Federation of Operational Research Societies (IFORS) constituted a world entity focused on the development and application of OR/MS with a rapid grow incorporating OR societies from a wide range of countries. In Latin America (shortly, Latam), OR/MS societies are grouped in the LatinIbero-American Association of Operations Research (ALIO) [2], which also includes the societies from Spain (SEIO) and Portugal (APDIO). ALIO is also part of IFORS. Currently, ALIO member societies are: the Argentine Society of Informatics (SADIO), the Brazilian Society for Operational Research (SOBRAPO), the Chilean Institute of Operations Research (ICHIO), the Colombian Association of Operational Research (ASOCIO), the Cuban Society of Mathematics and Computing (SCMC), the (Spanish) Society for Statistics and Operations Research (SEIO), the Ecuadorian Society of Mathematics (SEDEM), the Peruvian Society for Operations and Systems Research (SOPIOS), the Mexican Society of Operations Research (SMIO), the Portuguese Association of Operational Research (APDIO), and the Uruguayan Association of Informatics and Operations Research (AUDIIO). Up to date, the practice of OR/MS has experienced a substantial increase thanks to the development of new algorithms and computer capacity. Several research papers analyzing the evolution and positioning of OR/MS in various regions of the world have been published, Merigó and Yang [1] present a bibliometric study providing a picture of the evolution of the research in the field. The Web of Science (WoS) database was used to identify leading journals, most cited papers and influential authors worldwide. More recently, Liao et al. [3] provided a bibliometric study of highly cited papers in the field between 2008 and 2017. These authors also identified leading journals, as well as leading countries and universities/research institutions. Following a qualitative approach, an analysis of the state of OR in Africa is also presented [4]. The starting point for this study stands for the efforts of IFORS and EURO (the Association of European Operational Research Societies) to promote OR/MS in Africa. A strategy and action plan are proposed to increase the development, visibility, education, use, and, implementation of OR across Africa. The work of Bilir et al. [5] focuses on the current state of OR/MS research in Europe. These authors also identified the most influential authors and developed bibliometric analyses about leading journals, influential authors, collaboration networks between authors and countries, most productive institutions, and most developed methodologies, and techniques, among others. In the same vein, Chang and Hsieh [6] presented a bibliometric analysis of OR/MS papers by Asian authors for the period between 1968 and 2006.

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Recently, Laengle et al. [7] studied the worldwide contributions to the OR/MS field from an institutional perspective. Using the Web of Science (WoS) database they identified the most productive (CNRS—Centre National de la Recherche Scientifique, France) and influential (MIT—Massachusetts Institute of Technology,) institutions. Dominated by North American, European, and Asian Universities, only two Latin American universities appeared in this study. The Chilean Pontificia Universidad Católica de Chile and the Brazilian Universidade de São Paulo as part of the top 25 institutions contributing the most to the Transportation Research part B and Computational Optimization and Applications journals, respectively. Likewise, Calma et al. [8] analyzed the most studied topics, research methods, and problems investigated in OR/MS from 1952 to 2019. The authors also identified the top contributing countries and authors to the most investigated research problems worldwide. In Latin-America, however, there is not any study of this nature allowing us to see and understand the current state of OR/MS in the region. Therefore, this paper aims at presenting the evolution of OR/MS research in Latin America. The goal is to map the published body of literature on Operations Research and the Management Sciences in the region. Trends in terms of the number of publications per country and per year are identified, as well as the journal in the field where Latin-American authors publish the most. In addition, the most influential authors are also identified both globally and per country. To do so, this paper is organized as follows. Section 2 describes the methodology employed to search and select the set of short-listed papers. The findings of the study are presented in Sect. 3. Concluding remarks are outlined in Sect. 4.

2 Review Methodology We review the literature using a systematic, clear, and reproducible approach, to identify, analyze, and interpret the current body of documents from a methodological point of view [9, 10]. In contrast to narrative reviews, this paper seeks to be explicit in the selection of the studies and use rigorous and reproducible methods of assessment [11, 12]. This paper addresses the following research questions: What has been the evolution over time of OR/MS research in Latin America and which are the most influential countries, journals, institutions, and authors in the region? Thus, to conduct the review and the bibliometric analysis, research articles available in the WoS databases were extracted and analyzed. It is a platform from the company Clarivate Analytics and comprises the Science Citation Index Expanded, the Social Science Citation Index, the Arts and Humanities Citation Index, the Science Citation Index, and the Emerging Science Citation Index. The rationale for choosing WoS is that this platform is made up of a wide collection of bibliographic databases, citations, and references of scientific publications from any discipline of knowledge. It provides bibliographic information and allows us to evaluate and analyze the performance and the scientific quality of research, everything through a single query interface, individually or to several databases simultaneously. Moreover, WoS has

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a specific research area devoted to Operations Research/Management Science (OR/ MS). In the first step, we searched for all research documents in this category, without limiting the publication year or country. The map of Fig. 1 depicts the geographical distribution of OR/MS documents published by Latin-American authors from 1968 to 2022. Likewise, Fig. 2 presents the temporal distribution of the papers produced in the region in this period.

Fig. 1 Geographical distribution of the publications in OR/MS from 1968 to 2022

Fig. 2 Number of publications per year in OR/MS between 1968 and 2022

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Based on the results of this preliminary search, we identified the set of ten most productive Latin American countries, which accounted for 99% of publications (as explained next in Sect. 3). From the temporal point of view, the early 31 years from 1968–1999 account for less than 10% of the publications in the region. By contrast, a clear exponential growth has occurred in the last two decades. Therefore, the bibliometric analyses were carried out on the publication output of these ten countries for the 2000–2022 time interval. The search was carried out on October 14, 2022, using the following search string: WC = (Operations Research and Management Science) AND CU = (“Brazil” OR “Mexico” OR “Chile” OR “Colombia” OR “Argentina” OR “Venezuela” OR “Peru” OR “Ecuador” OR “Uruguay” OR “Cuba”)). To focus on the most influential of the publications, we limited the analysis to articles and book chapters only. We did not exclude any journal from the analysis. However, 20 documents, written in Spanish, French, or Portuguese were excluded. Figure 3 presents the flowchart of the search and analysis process. As it can be seen in this figure, multiple tools have been used in our analysis. Initial search and descriptive analytics leverage mainly on the built-in functionalities of Clarivate Analytics. On the other hand, once the database was extracted from the WoS, several analytics tools has been used, ranging from Microsoft Excel to Python/Pandas, and VOSviewer. A bibliometric analysis is also presented as a tool to quantitatively analyze bibliographic material in a given field [13, 14], by combining science mapping and performance analysis [15]. The former allows understanding how different scientific actors are related to one another through a spatial and graphical representation, while the latter assesses the research performance of countries, universities, departments, or individuals. In the Management Sciences, the bibliometric approach has been widely used to enhance the interpretation of theoretical frameworks in areas such as operations management, information systems, and sustainable management, among others

Fig. 3 Flowchart of the search and analysis process

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[16]. Thus, and from an academic standpoint, mapping the contributions on research in the field of OR/MS in Latin America is indeed important. Therefore, researchers and practitioners can follow the advances and trends in the field, as well as to make decisions and take actions in a more informed way [17].

3 Findings The initial search identified 13,111 documents published until 2022, plus a few more documents with publication dates in 2023. No limitation on publication year was defined but we restricted the search to the ten most productive countries. It is interesting to observe that the first work appeared in 1968, with exponential growth in the decade of the 1980s. Between 1968 and 1999, a total of 950 documents were published (44 between 1968 and 1979, and 906 between 1980 and 1999), corresponding to 7.6% of the total amount of papers, while between 2000 and 2019, a total of 8793 documents were found in the database, corresponding to 70.6% of the total. Finally, 2706 papers (21.7%) have publication date 2021 and 2022 (21.7%). We then carried out a search for publications per country (see Fig. 4). When analyzing the publication outputs, 99% of the total documents were published by authors from Brazil (50.4%), Mexico (18.3%), Chile (13.7%), Colombia (5.5%), Argentina (4.8%), Venezuela (2.1%), Peru (1.6%), Ecuador (1.1%), Uruguay (0.9%), and Cuba (0.8%). Interestingly, with the only exception of Venezuela, these are the Latin-American countries belonging to ALIO (the Latin-Ibero-American Association of OR Societies). Further analysis in this paper is based on this set of the ten most productive countries in Latin America. Therefore, after applying the selection criteria, the search identified 8,546 documents published between 2000 and 2022 by authors from these countries. For journal papers with early access but without a volume assigned yet, we took the early access date to set the publication year.

3.1 Top Journals, Papers, Institutions, and Authors The OR/MS Category of WoS includes 100 journals. By contrast, our database comprises 228 different sources including journals and book series. To analyze the most preferred publication outlets of OR/MS researchers in Latin America we analyze the top 25 publications in our database with respect to total publication (TP) count, total citation (TC) count, and average citation (AC) per document. Table 1 presents this analysis. Additionally, we include the JCR (Journal citation reports) rank, and the JIF (Journal impact factor) quartile the journals in the table. As it can be seen in this table, the topmost preferred journal for Latin-American authors of OR/MS publications is Expert Systems with Applications (ESwA), a non-traditional journal in the field. As a matter of fact, this journal accounts for 13.5% of the papers

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Fig. 4 Number of publications per country

published in the 2000–2022 period. It is followed by the European Journal of Operational Research (EJOR) with 7.2% of the papers, which would be also the second one if the citation count was used for the ranking. The journal with the greatest average citation in the table is the International Journal of Production Economics (IJPE), followed again by EJOR if this metric is used for the ranking. Note also that only three journals in the top 10 according to the JIF appear in this table, namely ESwA, EJOR, and IJPR (the International Journal of Production Research). Likewise, from the eight journals that are usually perceived as the most reputable journals in OR-MS rankings [1] four of them appear in the top 25 of Latin American publications: EJOR, Computers and OR (C&OR), Mathematical Programming (MP), and the Journal of the Operational Research Society (JORS). Interestingly, although highly reputed in the field, none of the INFORMS journals appeared in this table. By contrast, three of the journals in this top 25 are sponsored by other national or international OR/MS societies (EJOR, JORS, and the International Transactions in Operational Research, ITOR). Finally, a regional journal sponsored by a national association (the Brazilian Association of Production Engineering) is in the 9th position of this ranking Brazilian Journal of Operations & Production Management (BJO&PM. This result was, somewhat predictable given the large share that Brazilian authors have in the academic production of OR/MS. Note, however, that this journal does not have a JIF Quartile assigned in JCR. The average citation per paper in the top 25 preferred journals is 16.8, whereas the average citation per paper in all the database is 18.25. The lower average in the most preferred journals is explained mainly by two journals having an AC per document below three (BJO&PM and RAIRO-OR). Therefore, if a weighted average is considered the AC per document raises to 19.9. As a matter of fact, the top 2 journals with uncited papers are ESwA and BJO&PM with 10.5% and 8.0% of the 1142 uncited papers in the databases. As mentioned above, the average citation per paper in the database is 18.25. This is a value comparable to that of European publications [5] even if there are 13.4%

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Table 1 Leading Journals in the WoS OR/MS category for Latam authors Journal name

TP

TC

AC

JIF Quartile

JCR rank

Expert Systems with Applications (ESwA)

1170

27,627

23.6

Q1

8

European Journal of Operational Research (EJOR)

614

18,422

30.0

Q1

17

Computers and Operations Research (C&OR)

415

10,107

24.4

Q1

20

Annals of Operations Research (AOR)

361

5400

15.0

Q2

22

International Journal of Production Economics (IJPE)

281

10,902

38.8

Q1

2

International Journal of Production Research (IJPR)

274

6868

25.1

Q1

6

Journal of Optimization Theory and Applications (JOTA)

263

2598

9.9

Q3

52

International Transactions in Operational Research (ITOR)

245

2413

9.8

Q2

28

Brazilian Journal of Operations and Production Management (BJO&PM)

225

480

2.1

N/A

94

Reliability Engineeringand System Safety (RESS)

197

5682

28.8

Q1

11

Mathematical Programming (MP) 175

5162

29.5

Q2

35

Computational Optimization and Applications (COA)

161

2435

15.1

Q3

59

Journal of The Operational Research Society (JORS)

158

2174

13.8

Q2

36

Optimization (Opt)

155

1355

8.7

Q3

48

Systems and Control Letters (SCL)

153

3545

23.2

Q2

38

International Journal of Systems Science (IJSS)

151

1573

10.4

Q2

40

Journal of Global Optimization (JGO)

146

1497

10.3

Q3

60

Optimization Letters (OL)

132

1139

8.6

Q4

70

Safety Science (SS)

126

2139

17.0

Q1

16

Production Planning and Control (PP&C)

117

2454

21.0

Q1

14

Quality and Reliability Engineering International (QREI)

111

966

8.7

Q2

37

IEEE Systems Journal (IEEESJ)

100

1761

17.6

Q2

23 (continued)

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Table 1 (continued) Journal name

TP

TC

AC

JIF Quartile

JCR rank

Operations Research Letters (ORL)

93

955

10.3

Q4

82

RAIRO-Operations Research (RAIRO-OR)

91

268

2.9

Q3

44

Engineering Optimization (EO)

88

1426

16.2

Q3

45

uncited papers in our database. This result could be explained by the citations received by highly cited papers. Therefore, after identifying the most preferred journals, in the next step in our bibliometric analysis, we turn the analysis to the papers that have received more attention from the scientific community in the field. Table 2 presents the results of this analysis based on the number of citations received by the papers according to the WoS core database. This table presents the top 15 most cited papers for authors with at least one Latam affiliation. Note, however, that the first authors may not be from Latin-American countries. As a matter of fact, these top 15 papers exhibit a large rate of collaboration with academics from other regions (column Intl Colab), since 12/15 papers include authors from other regions. We further explore the collaboration networks in the next section. The papers in Table 2 have citation counts that are an order of magnitude above the average OR/MS paper by Latin-American authors. The most cited paper [18] has more than 150 citations per year, while several other papers in the table have more than 100 citations per year [19–23]. A common feature of four of these highly cited papers is their focus on Industry 4.0, a current hot topic in the research community. Systems resilience ([19]), and a controversial bioinspired metaheuristic [21] are the topics of the two other most highly cited papers. In contrast to Table 1, only one paper published in ESwA appears in the table of highly cited papers, and other important journals in the field appear. Particularly, the journals that have the greatest average citations per paper (in Table 1) contribute with more than one highly cited paper: IJPE(3/15), EJOR (3/15), and MP (2/15). Exceptionally, one book chapter appears in this table [24]. Finally, Table 2 is dominated by review papers (10/15), something that is somewhat expected as this type of papers commonly receive a greater number of citations [25]. Now, we focus the attention on the institutional part of scientific research to identify leading Latin-American institutions in terms of OR/MS publication. We performed this analysis with the help of the Clarivate built-in functions just by filtering the search results by author affiliation and taking the top 25 institution. Table 3 presents the results of this analysis. In this Table, we added the data of the Times Higher Education university ranking (THE-R) [26], and the country of the leading institutions. The Brazilian Universidade de São Paulo is the leading institution in the field according to total publications. Also, the ranking of leading Latin-American institutions is dominated by Brazilian Universities, with seven of them in the top ten and 14 in the top 25. Two Chilean universities (Universidad de

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Table 2 Top 15 highly cited papers in OR/MS coauthored by Latam researchers Rank Title

First author Journal Type

TC Year TC/ (Y) Y

Intl Colab

1

Past, present and future of Liao, YX Industry 4.0-a systematic literature review and research agenda proposal

IJPR

Review 800 2017 160.0 N

2

A review of definitions and Hosseini, S measures of system resilience

RESS

Review 748 2016 124.7 Y

3

Industry 4.0 Frank, AG technologies: Implementation patterns in manufacturing companies

IJPE

Review 708 2019 236.0 Y

4

Mass customization: Literature review and research directions

5

Multi-objective grey wolf Mirjalili, S optimizer: A novel algorithm for multi-criterion optimization

ESwA

Article 661 2016 110.2 Y

6

An interior algorithm for nonlinear optimization that combines line search and trust region steps

Waltz, RA

MP

Article 635 2006 39.7

Y

7

Convergence of descent Attouch, H methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods

MP

Article 625 2013 69.4

Y

8

A review of dynamic vehicle routing problems

Pillac, V

EJOR

Review 619 2013 68.8

Y

9

The expected contribution of Industry 4.0 technologies for industrial performance

Dalenogare, IJPE LS

Review 545 2018 136.3 Y

10

Rescheduling manufacturing systems: A framework of strategies, policies, and methods

Vieira, GE

JSche

Review 522 2003 27.5

Y

11

Ridesharing: The state-of-the-art and future directions

Furuhata, M

TRB

Review 489 2013 54.3

Y

12

Improving PSO-Based Sierra, MR multi-objective optimization using crowding, mutation and epsilon-dominance

EMO

Article 479 2005 28.2

N

Da Silveira, IJPE G

Review 685 2001 32.6

N

(continued)

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Table 2 (continued) Rank Title

First author Journal Type

13

Selecting green suppliers based on GSCM practices: Using fuzzy TOPSIS applied to a Brazilian electronics company

Kannan, D

EJOR

Article 420 2014 52.5

14

Industry 4.0 and the circular economy: a proposed research agenda and original roadmap for sustainable operations

Jabbour, ABLD

AOR

Review 411 2018 102.8 Y

15

Review of recent developments in OR/MS research in disaster operations management

Galindo, G

EJOR

Review 396 2013 44.0

TC Year TC/ (Y) Y

Intl Colab Y

Y

Chile and Pontificia Universidad Católica de Chile) and the Mexican Tecnológico de Monterrey, complete the top ten. According to column THE_R, the most influential universities in the OR/MS field are also leading universities in global rankings, none of the universities in the OR/MS ranking appear in a ranking beyond 100 (the Mexican Universidad Autónoma de Nuevo León—UANL being the one with the lowest ranking). Moreover, all but one university in the top-10 of the ranking appear in Table 3. Interestingly, two national research agencies also appear as leading institutions (the Mexican Cinvestav, and the Argentinian Conicet). Although not reported in the table, three non-Latam institutions appear in the ranking: the French CNRS, (10), the French University consortium UDICE (20), and the Canadian Université de Montréal (23). Their corresponding rankings appear in parenthesis if considered. This result is consistent with the findings in [7], that identified the CNRS as the most productive OR/MS institution and the University of Montreal as an important top player in both productivity and influence in OR/MS. This result reveals strong collaboration networks with these countries that will be analyzed in the following section. Finally, the analysis of the top-most prolific Latin-American OR/MS researchers closes this section. Table 4 also presents the h-index [27], the affiliation of the authors (if an author has multiple affiliations, we use the one of his/her last paper to extract the affiliation) and their country of affiliation. As can be seen in the table, the most prolific authors in the field are Brazilian researchers, the most prolific one being Reinaldo Morabito from the Universidade Federal de São Carlos, and 19 of the top authors come from universities and research institutes in this country. The list is completed by two researchers from Chile (Andrés Weintraub and Vladimir Marianov), two from Venezuela (Jose Emmanuel Ramirez-Marquez and Claudio M. Rocco), and one from Mexico (Leopoldo Eduardo Cárdenas-Barrón) and Colombia (Andrés L. Medaglia). Noteworthy, despite not appearing in other rankings of this

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Table 3 Top 25 most influential institutions in Latin-America in OR/MS Rank institution

TP

% Total

Country

THE_R

1

Universidade de Sao Paulo

631

7.4

Brazil

2

2

Universidad de Chile

482

5.7

Chile

7

3

Universidade Federal do Rio de Janeiro

468

5.5

Brazil

11

4

Universidade Estadual de 441 Campinas

5.2

Brazil

3

5

Universidade Federal Fluminense

314

3.7

Brazil

40

6

Tecnologico de Monterrey

313

3.7

Mexico

5

7

Pontificia Universidad Catolica de Chile

282

3.3

Chile

1

8

Universidade Federal de Minas Gerais

269

3.1

Brazil

9

9

Universidade Federal do Rio Grande do Sul

253

3.0

Brazil

8

10

Universidade Federal de Santa Catarina UFSC

238

2.8

Brazil

6

11

Universidade Federal de Pernambuco

226

2.6

Brazil

37

12

Universidade Estadual Paulista

219

2.6

Brazil

12

13

Consejo Nacional de Investigaciones Cientificas y Tecnicas Conicet

218

2.6

Argentina

NA

14

Universidade Federal de Sao Carlos

216

2.5

Brazil

17

15

Cinvestav Centro de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional

184

2.2

Mexico

NA

16

Instituto Politecnico Nacional Mexico

175

2.0

Mexico

51

17

Universidad Adolfo Ibanez

158

1.8

Chile

59

18

Pontificia Universidade Catolica do Rio de Janeiro

155

1.8

Brazil

10

(continued)

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Table 3 (continued) Rank institution

TP

% Total

Country

THE_R

19

Universidad de Los Andes Colombia

144

1.7

Colombia

13

20

Universidade Federal do Parana

143

1.7

Brazil

20

21

Universidad Autonoma de Nuevo Leon

128

1.5

Mexico

100

22

Pontificia Universidad Catolica de Valparaiso

124

1.5

Chile

38

23

Universidad Tecnica Federico Santa Maria

124

1.5

Chile

49

24

Pontificia Universidade Catolica do Parana

119

1.4

Brazil

39

25

Universidade Federal de Goias

119

1.4

Brazil

41

section, Venezuela contributes with two of the most prolific authors in the OR/MS field in Latam. The top 25 of OR/MS authors of the region include IFORS former presidents (Nelson Maculan and Andrés Weintraub), ALIO former presidents (Celso Ribeiro, Nelson Maculan, and Andrés Weintraub), and Edelman awardees (Andrés Weintraub) as well as IFORS Development Prize awardees (Andrés L. Medaglia). Given the large size of the Brazilian contribution to the OR/MS field, having a per-country view is difficult. Therefore, we complement the results of Table 4 with a short list of the top 5 most prolific authors of the remaining four counties in the region that account for 93% of the documents included in our analysis. Therefore, Table 5 presents the top 5 authors by country of affiliation for Mexico, Chile, Colombia, and Argentina (apart from those already appearing in Table 4).

3.2 Network Analysis: Co-Autorship, Collaboration and Keywords Co-ocurrence As shown in Fig. 1, in the second part of our analysis, we used the text mining software VOSviewers [28] to provide a high-level perspective of the publications in terms of science mapping to identify collaboration networks, co-authorship and cocitation and keywords co-occurrence. VOSviewer charts are Graph-based maps with nodes and edges. In this graph, nodes represent keywords/journals/authors/countries and are shown in circles; the higher the weight of these elements (i.e., its frequency), the bigger the size of the node. Any pair of nodes might have an edge connecting them. These links represent a relation between two elements (e.g., a document where they appear together or a co-citation relationship between journals/authors).

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Table 4 Most prolific authors in the OR/MS filed in Latam (in this table U: University) Rank name

TP

h-index institution

Country

1

Morabito R

87

29

U Federal de Sao Carlos

Brazil

2

Maculan N

85

22

U Federal do Rio de Janeiro

Brazil

3

Cardenas-Barron LE

75

45

Tecnologico de Monterrey

Mexico

4

Martinez JM

71

36

U Estadual de Campinas

Brazil

5

Ribeiro CC

62

29

U Federal Fluminense Brazil

6

Marianov V

59

24

Pontificia U Catolica de Chile

Chile

7

Birgin EG

56

28

U de Sao Paulo

Brazil

8

De Almeida AT

52

5

U Federal de Pernambuco

Brazil

9

Solodov MV

52

30

Inst Matematica Pura & Aplicada

Brazil

10

Uchoa E

51

24

U Federal Fluminense Brazil

11

Weintraub A

49

34

U de Chile

Chile

12

Subramanian A

48

23

U Federal da Paraiba

Brazil

13

Rocco CM

46

25

U Central de Venezuela

Venezuela

14

Ferreira OP

43

20

U Federal de Goias

Brazil

15

Ho LL

40

16

U de Sao Paulo

Brazil

16

Medaglia AL

40

23

U de los Andes

Colombia

17

Svaiter BF

39

38

Inst Matematica Pura & Aplicada

Brazil

18

Cavalcante CAV

38

18

U Federal de Pernambuco

Brazil

19

Saurin TA

37

7

U Federal do Rio Grande do Sul

Brazil

20

Vidal T

37

26

Pontificia U Catolica do Rio de Janeiro

Brazil

21

Ramirez-Marquez JE

36

36

U Central de Venezuela

Venezuela

22

Tortorella GL

36

29

U Federal de Santa Catarina

Brazil

23

Ochi LS

35

22

U Federal Fluminense Brazil

24

Oliveira PR

35

18

U Federal do Rio de Janeiro

Brazil

25

Sagastizabal C

35

26

U Estadual de Campinas

Brazil

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Table 5 Top 5 OR/MS authors for México, Chile, Colombia and Argentina Rank

Mexico

TP

Chile

TP

1

Coello CAC

34

Flores-Bazan, F

33

2

Rios-Mercado RZ

28

Alvarez-Miranda E

27

3

Cavazos-Cadena R

23

Pascual R

27

4

Garcia-Alcaraz JL

20

Cominetti R

23

5

Gonzalez-Velarde JL

20

Maldonado S

23

Rank

Colombia

TP

Argentina

TP

1

Montoya-Torres JR

25

Duran G

26

2

Sanchez-Silva M

19

Marenco J

26

3

Escobar JW

14

Amandi A

13

4

Cantillo V

13

Mendez-Diaz I

11

5

Velasco N

13

Frutos M

10

Initially, Fig. 5 shows the co-authorship network of the top counties in Latin America. The clustering has been generated with a minimum threshold of 100 documents per country. Given this threshold, Cuba and Uruguay do not appear in the figure. As can be seen in the Figure, there are four clusters. A large one grouping together Mexico, Colombia, Venezuela, and Ecuador; with the USA, Spain, The Netherlands, and Germany. The second one groups Chile and Peru with the worldwide leading countries in OR/MS (Canada and France). Finally, two clusters with a single Latam country appear, These last clusters reveal a close relationship between Argentina, England, and Australasian countries (China and Australia), and a non-Spanish speaking relationship between Brazil, Portugal, and Italy. Finally, an analysis of co-occurrence of keywords provided by the authors in the publications is shown in Fig. 6, based on the 98 most frequently used keywords, which have been repeated at least 25 times in the documents in the database. Is this figure there are six clusters and the top 10 keywords are (appearance count in parenthesis): heuristic (225), metaheuristic (223), integer programming (220), scheduling (194), optimization (164), combinatorial optimization (162), genetic algorithm (155), vehicle routing (123), simulation (117), and data envelopment analysis (115). Clearly, in the topics studied by OR/MS researchers in Latin America prevail the study of (meta)heuristics, integer and combinatorial optimization problems, scheduling and vehicle routing problems, and the use of OR techniques like simulation and data envelopment analysis. The six clusters in Fig. 6 groups keywords in the following topics. Cluster 1. Decision support in supply chain and production systems. artificial intelligence, average run length, Brazil, complexity, covid-19, data envelopment analysis, decision support system, efficiency, industry 4.0, innovation, inventory, lean manufacturing, literature review, logistics, Monte Carlo simulation, multiple criteria analysis, optimization, performance, pricing, production, simulation, supply chain, supply chain management, sustainability, uncertainty.

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Fig. 5 Co-authorship network for the most productive OR/MS countries in Latam

Fig. 6 Keyword map of OR/MS papers published by Latam authors from 2000 to 2022

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Cluster 2. Optimization theory. Algorithms, computational complexity, constraint qualifications, convex optimization, game theory, global convergence, global optimization, linear matrix inequalities, linear programming, mathematical programming, multiobjective optimization, nonconvex optimization, nonlinear programming, nonsmooth optimization, optimal control, optimality conditions, packing, stability, stochastic optimization, vector optimization. Cluster 3. Integer programing methods and applications. Benders decomposition, branch-and-bound, branch-and-cut, dynamic programming, facility location, humanitarian logistics, integer linear programming, integer programming, maintenance, makespan, network design, project management, reliability, robust optimization, scheduling, stochastic programming. Cluster 4. Machine learning and data mining. Classification, clustering, constrained optimization, data mining, deep learning, differential evolution, evolutionary algorithms, feature selection, fuzzy logic, genetic algorithm, machine learning, multiobjective optimization, neural networks, particle swarm optimization, support vector machines. Cluster 5. Metaheuristics for transportation and routing. GRASP, heuristic, iterated local search, local search, location, metaheuristic, routing, simulated annealing, tabu search, time windows, transportation, variable neighborhood search, vehicle routing. Cluster 6. Combinatorial optimization methods in production planning. column generation, combinatorial optimization, cutting planes, Lagrangian relaxation, lot sizing, matheuristic, mixed integer linear programming, mixed integer programming, production planning.

4 Conclusions This paper presents, for the first time, a bibliometric and science mapping analysis of Operations research/Management science in Latin America. The analysis was performed on 8546 papers published between 2000 and 2022 and indexed in the Web of Science database. From the results of this study, it is possible to identify some important findings. First, there is a steady increase in the number of documents in the field coauthored by researchers from the region. Second, preferred journals for publication are not necessarily those that are highly recognized internationally e.g. INFORMS journals) and the most preferred journals is ESwA (a no traditional OR/ MS journal). However, other well-known journals in the field (EJOR, C&OR, AOR, IJPE, IJPR, JORS, ITOR, and RESS) also appear in the list of preferred journals, Third, Brazilian researchers and institutions dominate the production of knowledge in this field in the region. They account for more than half of the papers published in the period of analysis. Authors and institutions from four other countries (Mexico, Chile, Colombia, and Argentina) complete most of the picture of OR/MS production in the region. Highly cited papers published by Latin American authors reveal the importance of collaboration networks to gain high visibility of the research conducted in the

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region. Finally, mathematical programming/optimization methods and applications prevail as the topic of interest in the regions over other classical OR/MS problems and methodologies (e.g., decision analysis, game theory, inventory control, etc.) However, important limitations of this study must be recognized, the selection of the indexing database could be changed to include other sources like Scopus and Google Scholar. In addition, this paper only considered publications in journals within the Operations Research / Management Science category, but some authors also publish OR/MS works in journals of other disciplines, such as health care, logistics and operations management, economics, finance, electronics, among others. Likewise, additional analysis like the evaluation of the impact of open access publication, and the application of other text-mining techniques could be performed. These changes could lead to different conclusions.

References 1. Merigó, J., Yang, J.: A bibliometric analysis of operations research and management science. Omega 73, 37–48 (2017) 2. ALIO, “Latino-Ibero-American Association of Operational Research,”. https://alio-online.org. Accessed 29 Nov 2022 3. Liao, H., Tang, M., Li, Z., Lev, B.: Bibliometric analysis for highly cited papers in operations research and management science from 2008 to 2017 based on essential science indicators. Omega 88, 223–236 (2019) 4. Ittmann, H.: The current state of OR in Africa. Oper. Res. Int. J. 21(3), 1793–1825 (2021) 5. Billir, C., Güngör, C., Kökalan, Ö.: Operations research/management science in Europe: a bibliometric overview. Adv. Oper. Res. 2020, 1607637 (2020) 6. Chang, P.L., Hsieh, P.N.: Bibliometric overview of operations research/management science research in Asia. Asia-Pacific J. Oper. Res. 25(2), 217–241 (2008) 7. Laengle, S., Merigó, J.M., Modak, N.M., Yang, J.B.: Bibliometrics in operations research and management science: a university analysis. Ann. Oper. Res. 294(1), 769–813 (2020) 8. Calma, A., Ho, W., Shao, L., Li, H.: Operations research: topics, impact, and trends from 1952–2019. Oper. Res. 69(5), 1487–1508 (2021) 9. Fink, A.: Conducting Research Literature Reviews: From the Internet to paper. SAGE Publications, Thousand Oaks, CA, USA (2019) 10. Badger, D., Nursten, J., Williams, P., Woodward, M.: Should all literature reviews be systematic? Eval. Res. Educ. 14(3–4), 220–230 (2000) 11. Tavares Thomé, A., Scavarda, L., Scavarda, A.: Conducting systematic literature review in operations management. Prod. Plan. Control 27(5), 408–420 (2016) 12. Delbufalo, E.: Outcomes of inter-organizational trust in supply chain relationships: a systematic literature review and a meta-analysis of the empirical evidence. Supply Chain Manag.: Int. J. 17(4), 377–402 (2012) 13. Pritchard, A.: Statistical bibliography or bibliometrics. J. Doc. 25(4), 348–349 (1969) 14. Merigó, J.M., Pedrycz, W., Weber, R., de la Sotta, C.: Fifty years of information sciences: a bibliometric overview. Inf. Sci. 432, 245–268 (2018) 15. Noyons, E., Moed, H., Van Raan, A.: Integrating research performance analysis and science mapping. Scientometrics 46(3), 591–604 (1999) 16. Bensalem, A., Kin, V.: A bibliometric analysis of reverse logistics from 1992 to 2017. Supply Chain Forum: Int. J. 20(1), 15–28 (2019) 17. Gaviria-Marin, M., Merigó, J., Baier-Fuentes, H.: Knowledge management: a global examination based on bibliometric analysis. Technol. Forecast. Soc. Chang. 140, 194–220 (2019)

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18. Liao, Y., Deschamps, F., Loures, E.D.F.R., Ramos, L.F.P.: Past, present and future of Industry 4.0-a systematic literature review and research agenda proposal. Int. J. Prod. Res. 55(12), 3609–3629 (2017) 19. Hosseini, S., Barker, K., Ramirez-Marquez, J.E.: A review of definitions and measures of system resilience. Reliab. Eng. Syst. Saf. 145, 47–61 (2016) 20. Frank, A.G., Dalenogare, L.S., Ayala, N.F.: Industry 4.0 technologies: implementation patterns in manufacturing companies. Int. J. Prod. Econ. 210, 15–26 (2019) 21. Mirjalili, S., Saremi, S., Mirjalili, S.M., Coelho, L.D.S.: Multi-objective grey wolf optimizer: a novel algorithm for multi-criterion optimization. Expert Syst. Appl. 47, 106–119 (2016) 22. Dalenogare, L.S., Benitez, G.B., Ayala, N.F., Frank, A.G.: The expected contribution of Industry 4.0 technologies for industrial performance. Int. J. Prod. Econ. 204, 383–394 (2018) 23. Lopes de Sousa Jabbour, A.B., Jabbour, C.J.C., Godinho Filho, M., Roubaud, D.: Industry 4.0 and the circular economy: a proposed research agenda and original roadmap for sustainable operations. Ann. Oper. Res. 270(1), 73–286 (2018) 24. Sierra, M.R., Coello Coello, C.A.: Improving PSO-based multi-objective optimization using crowding, mutation and ∈-dominance. In: Evolutionary Multi-criterion Optimization, pp. 505– 519. Springer, Berlin (2005) 25. Tahamtan, I., Safipour Afshar, A., Ahamdzadeh, K.: Factors affecting number of citations: a comprehensive review of the literature. Scientometrics 107(3), 1195–1225 (2016) 26. Times Higher Education, “Latin America University Rankings 2022,” Times Higher Education. https://www.timeshighereducation.com/world-university-rankings/2022/latin-ame rica-university-rankings. Accessed 29 Nov 2022 27. Hirsch, J.E., Buela-Casal, G.: The meaning of the h-index. Int. J. Clin. Health Psychol. 14(2), 161–164 (2014) 28. Van Eck, N., Waltman, L.: Software survey: VOS viewer, a computer program for bibliometric mapping. Scientometrics 84(2), 523–538 (2010)

Modeling, Optimization, Analytics, and Artificial Intelligence

Collaborative Versus Non-collaborative Bus School Routing Luz Helena Mancera , Julián Andrés Hincapié-Urrego, Jairo R. Montoya-Torres , Danna Valentina Ubaque-Hernández, Natalia Andrea Orrego-Oviedo, and Angie Natalia Montaña-Gil

Abstract Vehicle congestion in Bogota is high, generating high operating costs and long waiting times for school buses for children. Currently, in Bogota, and in most of Colombian cities, each school owns its own transportation fleet or outsources buses for the exclusive transportation service for its own students. Student pickup in the morning and drop-off in the afternoons can be each one modeled as the well-known bus routing problem, which is a special case of the vehicle routing problem (VRP) with a single depot (the school). This approach of the problem can generate inefficiencies when analyzing schools located nearby within the same area. Therefore, this paper compares the results obtained by applying traditional routing models, where each school picks up its students, with a collaborative transportation scheme, in which students from different schools are assigned to a shared bus fleet. This last approach allows schools in the same area picking up students regardless of the school they belong to. Mathematical models are proposed and solved using a commercial solver. As a result, due to the number of pick-up points for each configuration, the solver was not able to reach the global optimum for any of both “traditional” and “collaborative” routes. Despite this, the collaborative transportation model showed advantages in terms of the total distance traveled by the bus fleet, which decreases by 4.37%. The paper opens opportunities for further exploring the collaboration bus routing problem. L. H. Mancera · J. A. Hincapié-Urrego · J. R. Montoya-Torres (B) · D. V. Ubaque-Hernández · N. A. Orrego-Oviedo · A. N. Montaña-Gil Facultad de Ingeniería, Universidad de La Sabana, km 7 autopista norte de Bogotá, D.C., Chía, Cundinamarca, 250001 Bogotá, Colombia e-mail: [email protected] L. H. Mancera e-mail: [email protected] D. V. Ubaque-Hernández e-mail: [email protected] N. A. Orrego-Oviedo e-mail: [email protected] A. N. Montaña-Gil e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. R. Montoya-Torres et al. (eds.), Operations Research and Analytics in Latin America, Lecture Notes in Operations Research, https://doi.org/10.1007/978-3-031-28870-8_2

23

24

L. H. Mancera et al.

Keywords Bus school routing · Collaboration · Mathematical programming · Case study

1 Introduction The school bus routing problem (SBRP) is an important problem which impacts local schools, transportation companies, public policy makers and millions of families alike. It consists on finding the routes for a set of buses that pick-up students at their homes to drive them to their school. This routing problem has been predominantly studied in the literature from the focus on economic gains through the optimization of cost or time [1, 2], as well as some recent papers focusing on the environmental impact of routing operations [3]. The School Bus Routing Problem (SBRP) belongs to the family of the wellknown Vehicle Routing Problems (VRP) in Operations Research [4]. The VRP is a large family of extensively studied combinatorial optimization problems thanks to their relevance in logistics practice and research. The SBRP was firstly introduced by Newton and Thomas [5], but it has received much less attention in the scientific literature than the different version of the VRP for freight applications. Among the existing solution approaches, there is no dominant approach to deal with the SBRP; most of the solution methods are very problem-specific motivated by school practices and school transport contexts. As pointed out in the review of Ellegood et al. [6], most research about SBRP studies North American contexts, where private schools and large buses are common. This context is different from the Colombian cases, which is the focus of this paper. Similar to the VRP literature, the most common objective functions are minimizing the total distance, bus travel time or student travel time. The literature has witnessed applications of the SBRP in urban [1] or rural settings [7], as well as for single or multiple schools [2, 8–10]. When the objective is to minimize student walking distance (i.e., the distance between students’ homes and the bus stops), the problem is called bus stop location problem [11]. Due to specific characteristics of our problem, we consider that students are picked up at their home address. However, to the best of our knowledge, there is no recent research which considers, directly or indirectly, the social aspect of school bus routing. To fill this gap, this paper proposes the analysis of collaborative strategies between transportation companies in order to reduce the time students spent in-route from their home to the schools. This work follows a case-study research approach to analyze the benefits of implementing collaborative routing between the schools, and hence between transportation companies. Mathematical programming is employed to formalize the routing problem and numerical experiments allows to quantitatively compare the performance of the proposed collaborative approach against the traditional non-collaborative bus routing. The remaining of this paper is organized as follows. Section 2 describes in detail the problem under study taking into consideration the characteristics of the city

Collaborative Versus Non-collaborative Bus School Routing

25

that served as case study. Section 3 presents the solution approach and the mathematical models employed to solve both the non-collaborative and the collaborative scenarios. Section 4 is devoted to describing the experimental setting and the analysis of results. Section 5 presents the conclusions and outlines some opportunities for future research.

2 Problem Description The problem presented in this paper is inspired from a real-life situation existing the city of Bogotá, D.C., Colombia. Bogota is the capital of and the largest city in Colombia. It is the 5th largest city in Latin America and 25th in the world. The population of Bogota is approximately 7.1 million inhabitants [12]. We have selected Bogota as the city under study because its configuration and size allow a complex scenario that can be an example of the behavior of cities with similar characteristics. As a matter of fact, heavy traffic in Bogota is common, generating high operating costs and long travel times for children within the buses. The locations of the selected schools were collected using Google Maps™. As an exemplary benefits of implementing collaboration for school bus routing, this study considers a subset of 4 representative schools located in the north area of Bogota which collecting 1248 students in 827 pick-up points. It is assumed that all the students have the same conditions, so no special restrictions were considered for their pick-up. In order to define the proportion of children requiring pick-up at home (doorto-door transportation), phone interviews were carried out with representatives of the selected schools. The output of these interviews was that 70% of the total students at the schools located in the zone opt for the door-to-door transportation service. Finally, cartesian coordinates will be used to assign the location of the schools and their respective students.

3 Solution Approach This paper aims at evaluating the benefits of implementing collaborative strategies for school student pick-up. The comparison is made at the operational efficiency and effectiveness in terms of transport costs (i.e., travel distance or travel time), the fleet utilization, and the service level in both collaborative and non-collaborative scenarios. The generic global approach, presented in Fig. 1, is composed of the following main phases. The characterization of the schools is first necessary to understand the particularities of each school in terms of location, number and capacity of buses, and number and location of students. Then, the bus routing problems are solved. For the traditional (non-collaborative) scenario, a single-depot vehicle routing problem with bus capacity constraints has to be solved. The collaborative case is solved using a multi-depot capacitated vehicle routing problem, where the depots are defined to be

26

Characterization of Schools School location, number of buses, capacity of buses, number of students, location of students

L. H. Mancera et al. Non-collaborative Scenario Solving a CVRP, optimizing routing costs or times for each school

Non-collaborative Scenario Solving a MDCVRP optimizing global routing costs or times for all the schools

Evaluation and Comparison of Scenarios Analysis of routing decisions, performance evaluation, evaluation of benefits, etc.

Fig. 1 Overview of the solution approach (source own elaboration)

the schools. The assignment of students to the depots is first solved, followed by the routing of buses itself. Details of each scenario are described next.

3.1 Non-collaborative Strategy: Baseline Scenario In the traditional non-collaborative scenario, each school must manage the fleet of buses to pick-up students in the morning and drop them off in the afternoon. The bus routing problem for each school can hence be modeled as a capacitated vehicle routing problem (CVRP) with homogeneous fleet. The schools represent the depots and the students’ homes represent the customers. The objective function to be minimized is defined as the distance traveled by the buses departing from each of the schools and returning to the same school at the end of the tour. The following mathematical model was formulated: Sets i, j : pick up points{1, 2, . . . , n} Parameters Dem i : number of students at pointi Ai : abscissa of location i Oi : ordinate of locationi Di, j : distance between pointsi and j C A P : bus capacity Decision Variables  1 if students at pointiare picked up just before students at point j xi, j = 0 otherwise Q i = Available capacity of bus upon arrival atpoint i

Collaborative Versus Non-collaborative Bus School Routing

27

Objective Function: Subject to: Min f =

N N  

Di, j xi, j

(1)

i=1 j=1 N 

xi, j = 1∀ j

(2)

x j,i = 1∀ j

(3)

i=1;i= j N  j=1;i= j

  Q j ≤ C A P + Dem j − C A P x0, j ∀ j

(4)

  Q j ≥ Q i − Dem i − C A P + C A P xi, j + C A P − Dem j − Dem i x j,i ∀i, j (5) xi, j ∈ {0, 1}∀i, j

(6)

Objective function (1) expresses total transportation distance. Constraints (2) and (3) ensure that entry and exit of the collection point is done only once, except for the school (depot). Constraints (4) and (5) ensure that the capacity of the bus is respected. Finally, binary values of decision variables are ensured by Constraints (6).

3.2 Collaborative Strategy: Proposed Scenario In order to make the comparison with a collaborative transportation scheme, a model was formulated that allows sharing routes between schools. In this way, a bus can pick up students from different schools until it fills its capacity and then go to the schools to drop off the picked-up students. This model generates a list of locations of students from all schools that will be supplied by the routes of a given school, in order to subsequently define the route followed by the buses of each school through a VRP model. The following is the formulation of the assignment model: Sets i : schoolsordepots{1, 2, . . . , m} j : pickuppoints{1, 2, . . . , n} Parameters Dem j : numberofstudentsatpoint j

28

L. H. Mancera et al.

Di, j : distancebetweenschooliandpoint j C A P : buscapacity U : minimumlevelofbusutilization Decision Variables  1if school located at point i is used to pick up students at point j xi, j = 0 otherwise yi = numberofbusesofschooliusedtopickupstudents Objective Function: Subject to: Min f =

N  N 

Di, j xi, j

(7)

i=1 j=1 N 

X i j = 1∀ j

(8)

X i j ≥ 1∀i

(9)

i=1 M  j=1

M Yi ≥ M 

j=1

X i j ∗ Dem j C AP

∀i

X i j Dem j ≥ U ∗ C A P ∗ Yi ∀i

(10)

(11)

j=1

X i j ∈ {0, 1}∀i, j

(12)

Yi ∈ Z∀i

(13)

Objective function (7) seeks to minimize the distance traveled. Constraints (8) ensure that each pick-up point is assigned to only one school. Constraints (9) allow a school to be assigned to more than one pick-up point. Constraints (10) establish the necessary number of school buses to satisfy demand. Constraints (11) guarantee a minimum level of bus utilization. Constraints (12) and (13) set the values of decision variables. As mentioned above, once the pick-up points are assigned to the schools, the optimal route for each school must be found using a VRP model. These models consider the school to which the students are assigned as the depot and include constraints that each student is drop-off at his/her school.

Collaborative Versus Non-collaborative Bus School Routing

29

4 Analysis of Numerical Experiments The first scenario considered in this study was the one in which non-collaborative bus routing is considered. Due to the number of pick-up points for each school, the complexity of the problem was very high making impossible to find the optimal solution in a short computational time and with a low gap from the computed lower bound. Therefore, a computational time of one hour was fixed as the maximum time to find an integer solution. Results show that 60 buses are required to collect 1248 students, and 3548 m were traveled. Table 1 reports these results under this computational time constraint. When implementing the collaborative bus routing strategy with all schools, the total distance traveled increased when using the results obtained to parameterize the VRP models for each school. This is because the assignment model does not consider that each route must go to four schools, which increases the value of the objective function. In order to find a better solution, two allocation models were implemented, one for schools A and D, and another for schools B and C, due to the proximity of these pairs of schools. Additionally, a point distribution constraint was included so that each school was left with a similar number of pick-up points; without this constraint, the solution obtained largely assigns the pick-up points to a single school, which implies greater administrative complexity for the school itself. Models reallocated students according to the distance between the pick-up point and the location of the schools. Following this, 46.15% of the students kept their initial assignment, while 53.8% were reallocated, mostly to school B. Table 2 shown the values of allocated points for each school. Based on this solution, the routing models were implemented for each school, now with the new allocated pick-up points. The lower rows of Table 1 show the results of collaborative school bus routing. This table also presents the benefits, in terms of improvement in traveled distance. Figure 2, 3, 4, 5, 6, 7, 8 and 9 show the routing for each of the schools in both strategies. A comparative analysis with Table 1 Results for the non-collaborative versus collaborative routing strategies School A Non-collaborative bus routing

Collaborative bus routing

School B

School C

School D

Distance (m)

1090

1576

330

551

Required buses

21

26

9

4

Pick-up points

270

368

78

111

Gap

70.86%

70.44%

22.75%

51.47%

Distance (m) (Improvement)

1031 (−5.4%)

669 (−57.5%)

1175 (255.2%)

516 (−6.2%)

Required buses (change)

18 (−3)

10 (−16)

22 (13)

11 (7)

Pick-up points

228

179

267

153

Gap

71.5%

60.20%

70.85%

59.45%

30

L. H. Mancera et al.

Table 2 Reassignment of pick-up points School A

School B

School C

School D

Total

School A

166

0

0

104

270

School B

0

139

229

0

368

School C

0

40

38

0

78

School D

62

0

0

49

111

Total

228

179

267

153

827

Fig. 2 Non-collaborative bus routes for School A

respect to individual routing shows that collaborative routing decreases the total distance traveled by 4.37% for a total of 3393 m. However, this strategy uses 61 buses, one more than individual routing. It is important to note that the improvement in traveled distance will have a strong impact on the children travel time from home to the school.

5 Conclusions and Future Research This paper studied the school routing problem in a particular setting of the city of Bogotá, Colombia, in which each school has its own fleet of buses to pick-up students in the mornings and drop them off in the afternoons. This paper proposed the implementation of a collaborative transportation strategy and shows benefits in

Collaborative Versus Non-collaborative Bus School Routing

31

Fig. 3 Collaborative bus routing for School A

Fig. 4 Non-collaborative bus routes for School B

terms of total distance traveled, due to the prior assignment of students to buses based on their location and not on their belonging to a particular school. This allows finding better routes for students and schools located within the same area. The above implies a change in the way school routes operate in the city, since traditionally each school manages or outsources its own bus fleet. This may require

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Fig. 5 Collaborative bus routing for School B

Fig. 6 Non-collaborative bus routes for School C

the signing of agreements between schools that clearly establish aspects such as maximum waiting times, distribution of operating costs and fleet maintenance, among others. Related to the performance of the models, it should be noted that the models implemented showed a significant gap, in some cases, against the lower bound computed

Collaborative Versus Non-collaborative Bus School Routing

33

Fig. 7 Collaborative bus routing for School C

Fig. 8 Non-collaborative bus routes for School D

by a commercial solver. So, it is important to address solution methods that can improve the performance of the models, even more so if other operating conditions are considered, for example students with collection needs, maximum number of buses leaving from a particular school, among other conditions.

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Fig. 9 Collaborative bus routing for School D

Acknowledgements This work was carried out under grant INGPHD-10-2019 from Universidad de La Sabana, Colombia.

References 1. Parvasi, S.P., Mahmoodjanloo, M., Setak, M.: A bi-level school bus routing problem with bus stops selection and possibility of demand outsourcing. Appl. Soft Comput. 61, 222–238 (2017) 2. Li, L., Fu, Z.: The school bus routing problem: a case study. J. Oper. Res. Soc. 53(5), 552–558 (2002) 3. Chalkia, E., Salanova Grau, J.M., Bekiaris, E., Ayfandopoulou, G., Feranini, C., Mitsakis, E.: Safety bus routing for the transportation of pupils to school. In: Traffic Safety, vol. 4, pp. 283–299. Wiley, Hoboken, NJ, USA (2016) 4. Toth, P., Vigo, D.: The Vehicle Routing Problem. SIAM, Philadelphia, USA (2002) 5. Newton, R.M., Thomas, W.H.: Design of school bus routes by computer. Socioecon. Plann. Sci. 3(1), 75–85 (1969) 6. Ellegood, W.A., Solomon, S., North, J., Campbell, J.F.: School bus routing problem: contemporary trends and research directions. Omega 95(C), 102056 (2020) 7. Souza Lima, F., Pereira, D.S., Vieira Conceição, S., Ramos Nunes, N.T.: A mixed load capacitated rural school bus routing problem with heterogeneous fleet: algorithms for the Brazilian context. Expert Syst. Appl. 56, 320–334 (2016) 8. Caceres, H., Batta, R., He, Q.: Special need students school bus routing: consideration for mixed load and heterogeneous fleet. Socio-Econ. Plan. Sci. 65(C), 10–19 (2019) 9. Shafahi, A., Wang, Z., Haghani, A.: SpeedRoute: fast, efficient solutions for school bus routing problems. Transp. Res. Part B 117(A), 473–493 (2018) 10. Arias-Rojas, J.S., Jiménez, J.F., Montoya-Torres, J.R.: Solving of school bus routing problem by ant colony optimization. Rev. EIA 17, 193–208 (2012)

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11. Schittekat, P., Kinable, J., Sörensen, K., Sevaux, M., Spieksma, F., Springael, J.: A metaheuristic for the school bus routing problem with bus stop selection. Eur. J. Oper. Res. 229(2), 518–528 (2013) 12. DANE Colombian Census Homepage. https://www.dane.gov.co/index.php/estadisticas-portema/demografia-y-poblacion/censonacional-de-poblacion-y-vivenda-2018/cuantos-somos. Accessed 1 April 2018

Method for Assigning Break Times in Predefined Shifts for Call Center Teleoperators Kevin Felipe Jaimes Vanegas, Sergio Andres Villamizar Lozano, and Raúl Fabián Roldán Nariño

Abstract This document studies one of the many applications and challenges that call centers face for staff scheduling. The objective of this document is to design and implement a solution technique that seeks to minimize costs due to missing teleoperators during lunch and breaks time for different operations of teleoperators with pre-defined shifts, reducing execution times and fulfilling the restrictions that each operation has. As part of the limitations identified for the development of this simulation, it was established that teleoperators have a defined shift with start and end time, according to the labor contract of each teleoperator, and the scenarios were simulated in 24-h operation as maximum, to guarantee one tool which responds to possible daily variations that may arise in different scenarios. In this context, genetic algorithm was proposed to provide a solution regarding to all requirements, achieving results near to the optimum. Besides, we defined the execution of four scenarios composed of operations with 200, 500, 2000 and 5000 teleoperators, each with different constraints and variables, to evaluate how the proposed algorithm responds. As result, solutions were generated with better performance in comparison with company’s actual scheduling model for lunch and break times, achieving on average a 42% decrease in total cost and 69% reduction in tool execution time. Also, we got better results for computational time in scenarios with 200 and 500 teleoperators, showing 76% less compared to current company’s tool, and for instances with more teleoperators (2000 and 5000), better results are presented with 60% reduction of costs delivered by the company’s tool. Keywords Call center · Genetic algorithm · Case study

K. F. Jaimes Vanegas · S. A. Villamizar Lozano · R. F. Roldán Nariño (B) Department Industrial Engineering, Pontificia Universidad Javeriana, Bogotá, Colombia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. R. Montoya-Torres et al. (eds.), Operations Research and Analytics in Latin America, Lecture Notes in Operations Research, https://doi.org/10.1007/978-3-031-28870-8_3

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K. F. Jaimes Vanegas et al.

1 Introduction The call center has positioned itself as a method used by companies to maintain direct contact with their consumers. These services are the customer’s initial bond with a company, especially in the processes related to sales. In Latin America, Colombia is one of the countries with the highest participation in this type of service with more than 130,000 teleoperators throughout the country, and they constitute around 13.1% of the sales generated in the region [1]. Consequently, Colombia has several companies responsible for providing the service nationally and internationally. Given the competitive environment in which these services are immersed, it is necessary to seek greater efficiency in service levels and cost reduction. It is important to keep in mind that in Call Centers, human resources represent the workforce and constitute the cost of the operation. For management cost is necessary to plan the assignment and staff shifts. However, the administration of human resources in a Call Center depends on several factors that are established by the requirements of each client, such as the volume of calls and the expected level of service among other indicators. In the planning, mathematical models are used to determine the number of call center teleoperators necessary to meet the established requirements of each operation. Currently, most call centers plan their workforce based on historical forecasts of the expected volume of requirements for operations. There are several external factors that can affect the planning, either due to the variation in demand or due to the variation in the available workforce. In addition, one of the problems that Call Centers face is the high turnover of employees that is generated by salary expectations, achievement of goals, demotivation, low possibility of professional development, among others [2]. Rotation significantly affects the execution and expected levels, so it is necessary for coordinators to be able to plan in a reactivated way, responding to external changes that were not evaluated in an initial planning in a very short time. Therefore, it is necessary to have rapid response technological tools that allow meeting demand, obtaining good solutions to different factors involved. Within the planning and programming of the workforce there are several factors that can be performed to meet the expected service levels. Some of them to be carried out are: (i) Programming of breaks: by legal dispositions it is mandatory to have a break time (lunches and breaks), so it seeks to optimize the times of each teleoperator in order to align the available teleoperators according to the periods of high or low expected demand evidenced with the service levels indicators, (ii) Reorganization of teleoperator: reassignment of teleoperator from areas with low demand to other operations that require additional labor and (iii) Shift Scheduling: adjust labor scheduling by validating if it is necessary to have additional shifts at times of high demand. The company under study has a tool for shift scheduling. This tool is used to perform break scheduling where the objective is to calculate the least expensive assignments within as possible. The problem it presents is that it sacrifices computation times, reaching executions of more than 20 min for operations with only 30 teleoperators. In normal operation, the company may require more than 1000 teleoperators, so the time and cost of computation, although it ends up being feasible, is

Method for Assigning Break Times in Predefined Shifts for Call Center … Table 1 Input data

Table 2 Demand required

39

ID

Entry entrada

Exit

Break duration

10,201,111

6:00

14:30

30

10,201,112

9:00

19:30

30

10,201,113

13:30

22:00

30

10,201,114

21:30

6:00

30

Hour

Demand

6:00 AM

50

6:15 AM

45

6:30 AM

45

6:45 AM

40

not very flexible in the face of external factors. The purpose is to design a solution method to the problem of assignments of breaks with a scenario predefined shifts in order to minimize the total cost due to lack of teleoperators and reduce the computational cost involved in the execution of the current tool. It is important to highlight that there is already a definition of shifts and the number of teleoperators required for each period. As an example, in Table 1, for 4 teleoperators, the start and end times of the shift are indicated, likewise, a minimum duration of the break is defined. For each operation there may be teleoperators who work different shifts and hours that must be respected by company policies. In addition, an example of teleoperator demand required for Table 2 presents each 15-min. Constraints associated with breaks include lunch and the predefined number of breaks. It is important to note that breaks cannot be set at the first or last hour of each attendee’s shift. The initial planning procedure consists of creating a matrix with all possible schedules based on the shifts of the scheduled attendants and from it finding the break times that minimize the costs of having absent attendants in each period analyzed. Due to staff turnover, attendants may be absent daily for one or more periods of time, so the weekly scheduling must receive daily updates to establish the available resources and reallocate them in a way that minimizes the costs of having absent attendants at each time. It should be noted that as the number of attendants required per time increases, there is a greater chance of reducing the breaks for each attendant, which increases the computational cost required to generate a viable solution.

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2 Literature Review For shift scheduling in a Call Center, several solution models are possible because as many constraints as necessary can be generated [3]. These constraints affect punctually each operation to be evaluated. These allocation models can be classified into shift scheduling, skill scheduling and rest day scheduling. Solutions for shift scheduling can be found in the literature such as the one proposed by [4] where a model that schedules shifts and generates rest schedules is proposed. The study requires initial information about the number of operators needed for each period and the corresponding shift information. In addition, in [5], linear programming is used to generate optimal solutions for problems with different scenarios and in [6] a column generation algorithm is proposed to assign breaks quickly for a group of nurses. An extension with respect to the previous solution approach includes flexible scheduling, which is proposed by [7] with a multi-scenario model to determine the breaks corresponding to each shift, and then through two phases search for a solution close to the optimal one, considering adjustments (flexibility) in the course of the day for each user’s shifts. Breaks scheduling is used to calculate the most convenient breaks of days to make the operation much more productive. Alfares [8] proposes an algorithm using linear programming to generate a solution that allows having two consecutive breaks days per week. Shift scheduling is used in different areas to be able to schedule teleoperators efficiently to meet the requirements of each client. Hojati [9] makes use of the Greedy algorithm to solve three different break scheduling scenarios that contemplate assignments for operations with a considerable number of teleoperators. The most commonly used methods to solve are linear regression models [10], Queueing Theory [11], simulation-based algorithms [12], stochastic models [13], Bayes’ Theorem [14], neural networks [15], graphs [16], among others. From the review it is concluded that the assignment of personnel in a Call Center is a problem that has been addressed and developed by several authors, but at the same time the number of constraints that can be derived from each operation increases its complexity and justifies the use of metaheuristics for its solution. For this reason, the purpose is to find the output schedules to minimize wastage costs without sacrificing computation times, a constraint that is constant and strongly contemplated in the reviewed literature. This study will focus on the use of a genetic algorithm to provide an efficient solution to the breakout allocation problem. In recent years, operations optimization has been used to solve the problem of worker allocation. The sectors where these techniques are most applied are airlines, hospitals, security centers and contact centers. These studies contain solutions with reactive functions or applications that use metaheuristic models in search of finding assignments near-optimal solution. In addition, the use of metaheuristics for the worker assignment problem has deepened in the literature due to the complexity of the problems. In [17], the authors employ a genetic algorithm by prioritizing better than average solutions and interrupting solutions that are below. Also Liu et al. [18] proposed the use of a genetic algorithm combining machine techniques. Finally,

Method for Assigning Break Times in Predefined Shifts for Call Center …

41

Abadi et al. [19] designed a hybrid between the Salp Swarm Algorithm and a genetic algorithm to provide a solution to the shift scheduling of nurses caring for patients with Covid-19, where despite the complexity of the problem, solutions close to the optimum are obtained. Other research such as Xue et al. [20], different constraints are applied including that teleoperators can have mixed skills, that shifts are flexible or that there are assignment criteria according to each operation. On the other hand, Krishnamoorthy et al. [21] solve task scheduling to minimize shifts in which they evaluate the skills of each teleoperator. The solution methods require algorithms that generate one or several solutions to subsequently seek specific improvements in each of them. For their part Nechita and Diosan [22] proved the assignment of tasks for staff as an NP-Hard problem for which they required introducing a metaheuristic divided into phases, thus ensuring that a good solution is found to assign teleoperators with multiple skills with a minimum number of teleoperators and no missing requirements. Generally, there are multi-channel operations, i.e. they may receive requests through different channels (chat, voice, mail), where workloads are unbalanced, so what is known in the literature as cross-training constantly arises, as it allows workers to attend more than one channel and improve productivity. Contact center crosstraining studies can be divided into single-period training and multi-period training. In single-period training, a constant arrival rate of the teleoperators to whom they are assigned is usually assumed, whereas in multiperiod training, a variable arrival rate is assumed, and the main objective is to conduct different training over time. Under this approach, Wright and Mahar [23] propose the use of a centralized model to reduce costs and improve the satisfaction of a group of nurses in a hospital. In addition, Pandey et al. [24] and Zimmerman et al. [25] propose using a mixed integer linear programming model to determine the optimal size of a work team along with its respective scheduling considering the costs of having surplus and missing personnel.

3 Method The Genetic Algorithm allows relating several parameters and constraints while maintaining a result close to the optimum and without necessarily affecting the computational costs and times of the same. For its implementation, a binary matrix is used that shows for each of the periods of the operation. In Tables 3 and 4, it is shown by teleoperators which schedules are feasible according to their hours of operation, i.e., ensuring that they comply with their start and end times and their break hours. For the development of algorithm, chromosomes are defined according with the amount of teleoperators in the operation, and the possible schedule that each teleoperator; in this way, an initial population is built with the number defined by the user and with a random selection of the possible schedules for each teleoperator, as shown in Table 5.

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K. F. Jaimes Vanegas et al.

Table 3 Timetables 6:00 am to 6:15 am

6:15 am to 6:30 am

6:30 am to 6:45 am

6:45 am to 7:00 am

7:00 am to 7:15 am

Timetable

Period 1

Period 2

Period 3

Period 4

Period 5

Period 6

Timetable 1

1

1

0

1

1

1

Timetable 2

1

0

1

1

1

1

Timetable 3

1

1

1

0

1

1

Timetable 4

0

1

1

1

0

1

Timetable n

1

1

1

1

1

0

Table 4 Timetables per teleoperator Timetable ID

Teleoperator Teleoperator 1

Timetable 1

Teleoperator 1

Timetable 2

Teleoperator 2

Timetable 2

Teleoperator 2

Timetable 3

Teleoperator n

Timetable n

Table 5 Genetic algorithm chromosome Teleoperator 1 Teleoperator 2 Teleoperator 3 Teleoperator 4 Teleoperator 5 Chromosome Timetable 1 1

Timetable 5

Timetable 3

Timetable 1

Timetable 2

Chromosome Timetable 2 2

Timetable 2

Timetable 5

Timetable 5

Timetable 3

Chromosome Timetable 3 3

Timetable 2

Timetable 7

Timetable 1

Timetable 1

Chromosome Timetable 1 4

Timetable 2

Timetable 3

Timetable 5

Timetable 5

Chromosome Timetable n n

Timetable n

Timetable n

Timetable n

Timetable 1

After knowing what schedule each teleoperator has, the objective function (fitness) is calculated, knowing what period each schedule covers and what the required demand per period is. Once all the objective functions are known, the best solutions are calculated and the 10% of the population that will automatically pass to the next generation is saved. The selection of progenitors is performed by the binary tournament method in which two chromosomes are selected completely randomly and the one with the best objective function is evaluated and that one remains as progenitor 1, the same operation is performed to select progenitor 2 guaranteeing that the same chromosome of progenitor 1 will not remain. In this way the crossover

Method for Assigning Break Times in Predefined Shifts for Call Center …

43

Table 6 Parents and their crossover Teleoperator Teleoperator Teleoperator Teleoperator Teleoperator 1 2 3 4 5 Timetable 1

Timetable 5

Timetable 3

Timetable 1

Timetable 2

Timetable 1

Timetable 2

Timetable 3

Timetable 5

Timetable 5

Timetable 1

Timetable 5

Timetable 3

Timetable 5

Timetable 5

Generation Offspring Timetable 1 i+1 1

Timetable 2

Timetable 3

Timetable 1

Timetable 2

Generation Parent 1 i Parent 2

Offspring Teleoperator Teleoperator Teleoperator Teleoperator Teleoperator 2 1 2 3 4 5

function is performed, which has a probability of 80% of being generated. In case the crossover is not generated, the two parents will pass the same to the next generation, and if the crossover function is performed, a random cut-off point is performed and two new chromosomes are generated as children, as shown in Table 6, with a cut-off point at teleoperator 3. In this way, the selection of the parents continues until the generation of a new population is completed. After the mutation function can be performed, which according to the literature reviewed was established at 5% to maintain a viable population without losing the possibility of leaving the local optima through these mutations, where upon meeting the mutation probability a random teleoperator of the evaluated chromosome changes the defined program for another feasible completely random one. In this way all the necessary instances are performed, which have a stopping criterion, which is defined in 150 generations, in which if a better solution is not found, the algorithm must stop and print the final solution, otherwise it will continue performing generations until the stopping criterion is met.

4 Results The test scenarios were established for 120, 500, 2000 and 5000 assessors. For each of the scenarios, 30 executions of the genetic algorithm were carried out in order to evaluate the variations and different solutions provided by the tool, and these were compared with the executions provided by the company, corresponding to one week’s operations. In the case of the execution of 120 consultants, the company provided the information of an operation of 200 consultants, so in order to make a comparable execution; the consultants were adjusted in the tool in order to obtain the cost under the same parameters provided by the company’s current tool. In Table 7, the comparison of the results obtained in the proposed metaheuristic and the current model of the company for the scenario of 200 consultants is made. It is evident that the proposed metaheuristic decreases in a but the current model of the company increases in 178% the costs; and as for the computational cost it can be evidenced

44

K. F. Jaimes Vanegas et al.

an improvement of 72% in the execution of the proposed metaheuristic on the linear programming time and the current model of the company. The genetic algorithm depends on mutations, crossovers and survival of chromosomes that represent better solutions, which as more iterations (generations) are performed have a probability of leaving local optima, but at the same time with each iteration a computational cost is sacrificed, which is why the stopping criterion seeks to obtain feasible solutions while maintaining a reduced execution time. Table 8 shows the average number of iterations and execution times for each of the operations. Each scenario it is presented with its results and execution time. Table 7 Comparison of models Proposed metaheuristic Scenario Variable 200

Company tool

Metaheuristic Comparison with LP Procedure Comparison with LP

FO (Costs) 691

72%

1116

178%

Time (m)

−72%

6,8

1%

1,9

Table 8 Replications summary Scenario

Replicates

Results

Genertions

Fitness

Time (min)

200

30

Average

699

691

1,9

500

2000

5000

30

30

30

Better fitness

908

612

2,7

Worse fitness

514

741

1,3

Better time

333

720

1,0

Worse time

908

612

2,7

Average

995

3261

4,8

Better fitness

1526

3175

7,3

Worse fitness

554

3413

2,7

Better time

549

3355

2,6

Worse time

1526

3175

7,3

Average

694

458

23,4

Better fitness

800

382

27,4

Worse fitness

302

605

9,8

Better time

302

605

9,8

Worse time

1079

425

37,3

Average

521

2061

36

Better fitness

1408

1865

31,3

Worse fitness

817

2276

123,4

Better time

1408

1865

31,3

Worse time

817

2276

123,4

Method for Assigning Break Times in Predefined Shifts for Call Center …

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The minimum, maximum and average results between the genetic algorithm and the company’s current tool are also compared. In Table 9, it can be seen how in each of the proposed scenarios both the cost and computation time decreases. In the case of 5000 scenario, a higher value was obtained in the time for the maximum record of the proposed algorithm, achieving on average a decrease of 42% in total cost and 69% in the execution time of the tool. However, it shows a better behavior in the decrease of costs for the cases with large operations in this example 2000 and 5000 teleoperators, and for the case of operations with fewer teleoperators 200 and 500, it presents a better behavior in the decrease of computation costs. It can be observed that there is a decrease in the costs of having missing teleoperators in the operations from 14 to 74% in comparison with the current model foreseen by the company, which represents a positive financial impact since by maintaining the same resources the total cost can be reduced and the efficiency of the operation can be increased. Likewise, when reviewing the computation times of each of the scenarios, it is observed that in the average results of the executions it was possible to reduce the time required by at least 50%, reducing in small operations between 5 and 10 min and in large operations reductions of up to 40 and 60 min per execution. This time reduction makes it possible to influence operations by guaranteeing that the equipment used for the corresponding calculations will not be occupied for the same time required for the execution of the tool and the daily planning by the coordinators can be streamlined and thus avoid not having a defined schedule at the beginning of the day’s operation. Table 9 Results by means average, minimum and maximum Scenario

200

500

2000

5000

Results

Current result of company

Current time of company

Fitness GA

Execution time GA

% Reduction fitness (%)

% Reduction time (%)

Average

1116

6,8

691

1,9

38

72

Minimum

1073

6,0

612

1,0

43

83

Maximum

1138

7,0

741

2,7

35

61

Average

3796

22,8

3261

4,8

14

79

Minimum

3737

22,0

3175

2,6

15

88

Maximum

3823

24,0

3413

7,3

11

70

Average

1754

52,6

458

23,4

74

56

Minimum

1084

51,0

382

9,8

65

81

Maximum

2240

54,0

605

37,3

73

31

Average

7106

118

2061

62,9

71

47

Minimum

5292

110

1865

31,3

65

72

Maximum

14,364

122

2276

123,4

84

−1

46

K. F. Jaimes Vanegas et al.

5 Conclusions The company studied has different contact centers with different numbers of teleoperators, so the proposed model was tested using real data from different scenarios provided by the company for 200, 500, 2000 and 5000 teleoperators. The proposed genetic algorithm obtains results under all constraints improving the solutions of the model used by the company by up to 74%. Better results are obtained in each of the 200, 500, 2000 and 5000 scenarios both in computational costs and in costs in USD for having teleoperators absent in each time. It is recommended that the company make use of the proposed algorithm in order to reduce the costs in USD for having missing teleoperators, not only in the proposed scenarios, but also in the different instances that each operation may have. Additionally, it would be interesting to explore different programming languages such as Python or Java, since the processing times can be lower for the execution of the algorithm. This would not only allow to reduce times, but would also allow to generate more solutions through parallelism, making it much easier for the contact center controllers to make decisions based on the different solutions generated.

References 1. Colombia: líder en BPO en la región en el 2021, Leggal Cent. BPO, https://leggalcenters.com/ colombia-lider-en-bpo-en-la-region-en-el-2021/. Accessed 27 April 2022 2. Mateus Mateus, J.A.: Análisis de las causas que generan rotación en el call center de Telebucaramanga. Trabajo de grado Universidad de Santander, Bucaramanga, Colombia (2017) 3. Brigandi, A.J., Dargon, D.R., Sheehan, M.J., Spencer, T.: AT&T’s call processing simulator (CAPS) operational design for inbound call centers. Informs J. Appl. Anal. 24, 6–28 (1994) 4. Türker, T., Demiriz, A.: An integrated approach for shift scheduling and rostering problems with break times for inbound call centers. Math. Probl. Eng. 2018, 1–19 (2018) 5. Bechtold, S.E., Jacobs, L.W.: implicit modeling of flexible break assignments in optimal shift scheduling. Manage. Sci. 36, 1339–1351 (1990) 6. Lim, G.J., Mobasher, A., Bard, J.F., Najjarbashi, A.: Nurse scheduling with lunch break assignments in operating suites. Oper. Res. Health Care 10, 35–48 (2016) 7. Hur, Y., Bard, J.F., Frey, M., Kiermaier, F.: A stochastic optimization approach to shift scheduling with breaks adjustments. Comput. Oper. Res. 107, 127–139 (2019) 8. Alfares, H.K.: An efficient two-phase algorithm for cyclic days-off scheduling. Comput. Oper. Res. 25, 913–923 (1998) 9. Hojati, M.: A greedy heuristic for shift minimization personnel task scheduling problem. Comput. Oper. Res. 100, 66–76 (2018) 10. Ibrahim, R., L’Ecuyer, P.: Forecasting call center arrivals: fixed-effects, mixed-effects, and bivariate models. Manuf. Serv. Oper. Manag. 15, 72–85 (2013) 11. Koole, G.M.: Call Center Optimization. MG Books, Amsterdam (2013) 12. Avramidis, A., Chan, W., Gendreau, M., L’Ecuyer, P., Pisacane, O.: Optimizing daily teleoperator scheduling in a multiskill call center. Eur. J. Oper. Res. 200, 822–832 (2010) 13. Bhulai, S.: Dynamic routing policies for multi-skill call centers. Probab. Eng. Inf. Sci. 23, 101–119 (2009) 14. Weinberg, J., Brown, L., Stroud, J.: Bayesian forecasting of an inhomogeneous poisson process with applications to call center data. J. Am. Stat. Assoc. 102, 1185–1198 (2007)

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15. Millán-Ruiz, D., Hidalgo, I.: Forecasting call centre arrivals. J. Forecast 32(7), 628–638 (2013) 16. Lai, D.S.W., Leung, J.M.Y., Dullaert, W., Marques, I.: A graph-based formulation for the shift rostering problem. Eur. J. Oper. Res. 284, 285–300 (2020) 17. Srinivas, M., Patnaik, L.M.: Adaptive probabilities of crossover and mutation in genetic algorithms. IEEE Trans. Syst. Man Cybern. 24, 656–667 (1994) 18. Liu, J., Min, F., Liao, S., Zhu, W.: A genetic algorithm to attribute reduction with test cost constraint, In: Proceedings of the 2011 6th International Conference on Computer Sciences and Convergence Information Technology (ICCIT), pp. 751–754. IEEE, Piscataway, USA (2011) 19. Abadi, M.Q.H., Rahmati, S., Sharifi, A., Ahmadi, M.: HSSAGA: designation and scheduling of nurses for taking care of COVID-19 patients using novel method of hybrid salp swarm algorithm and genetic algorithm. Appl. Soft Comput. 108, 107449 (2021) 20. Xue, N., Landa-Silva, D., Triguero, I., Figueredo, G.P.: A genetic algorithm with composite chromosome for shift assignment of part-time employees. In: Proceedings of the 2018 IEEE Congress on Evolutionary Computation (CEC, pp. 1–8. IEEE, Piscataway, USA (2018) 21. Krishnamoorthy, M., Ernst, A., Baatar, D.: Algorithms for large scale shift minimisation personnel task scheduling problems. Eur. J. Oper. Res. 219, 34–48 (2012) 22. Nechita, S., Diosan, L.: A four-phase meta-heuristic algorithm for solving large scale instances of the shift minimization personnel task scheduling problem. In: Proceedings of the 2018 20th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), pp. 394–400. IEEE, Piscataway, USA (2018) 23. Wright, P.D., Mahar, S.: Centralized nurse scheduling to simultaneously improve schedule cost and nurse satisfaction. Omega 41, 1042–1052 (2013) 24. Pandey, P., Gajjar, H., Shah, B.J.: Determining optimal workforce size and schedule at the retail store considering overstaffing and understaffing costs. Comput. Ind. Eng. 161, 107656 (2021) 25. Zimmerman, S.L., Bi, A., Dallow, T., Rutherford, A.R., Stephen, T., Bye, C., Hall, D., Day, A., Latham, N., Vasarhelyi, K.: Optimising nurse schedules at a community health centre. Oper. Res. Health Care 30, 100308 (2021)

Financial Risk Analysis for a Specialized Dairy Farm Project and Impacts of Government Interest Rate Subsidies Juan Antonio Martinez Becerra and Kathleen Salazar-Serna

Abstract The increased popularity of specialized dairy farms, mainly in the Colombian Andean region, represents an investment opportunity and a contribution to national agricultural growth. In this way, the effort to strengthen the livestock legacy, especially by young entrepreneurs, focuses on technified facilities that bet on improving production conditions for farmers, but at the same time, that contribute to the development of the local dairy industry. On the other hand, the dealers of dairy products, together with government entities, have been improving conditions for their producers through financial facilities and incentives for good livestock practices. It seeks to encourage interest in investment in Colombian agriculture, especially in dairy farms. This work aimed to evaluate the financial feasibility of the installation and operation of a specialized dairy farm in Colombia. Based on projected cash flows, financial evaluation criteria were calculated for two credit line scenarios. Additionally, through the use of the RiskSimulator simulation software, risk analysis, and a sensitivity analysis were carried out to evaluate the cash flows from the investor’s perspective, as well as to identify the critical variables for the success of the project. The results indicated the feasibility of implementing the dairy unit from the investor’s perspective, using the government financing option (Finagro). It was also identified that the costs related to cattle feeding, the sale price of milk, and the amount of milk produced are the variables to which the project indicators are most sensitive. Therefore, they are generating the greatest source of volatility in the project. Keywords Financial feasibility · Dairy farming · Simulation · Risk analysis · Sensivity analysis

J. A. M. Becerra (B) · K. Salazar-Serna Department of Civil and Industrial Engineering, Pontificia Universidad Javeriana, Cl. 18 #118-250, Cali, Colombia e-mail: [email protected] K. Salazar-Serna e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. R. Montoya-Torres et al. (eds.), Operations Research and Analytics in Latin America, Lecture Notes in Operations Research, https://doi.org/10.1007/978-3-031-28870-8_4

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J. A. M. Becerra and K. Salazar-Serna

1 Introduction Colombia is characterized by being an agricultural country, dedicated mainly to the primary sector. The variety of thermal floors and ecosystems facilitate biodiversity and the exploitation of a large number of products. However, the fact of being mainly recognized for this aspect does not mean that it has the necessary conditions for its development and growth. This is evidenced by the productivity levels of the agricultural sector in the country. Bearing in mind that the farms are mostly smallscale and that the survival of more than 30% of the country’s families depends on them, the competitive disadvantage in which agriculture is compared to the large volumes of imported products arriving in Colombia [1]. Although the Colombian dairy sector is one of the most recognized and popular, during 2020, the largest imports of milk and dairy products in recent decades were recorded, exceeding 73,000 tons. This represents a resounding blow to livestock farms that must produce under uncompetitive conditions. However, according to Asoleche, milk processors continue to make efforts not to neglect buying from local producers, even if this represents a sacrifice of potential profits due to higher prices. In addition, the short-term scenario is postulated to be less favorable, considering the near total opening of free trade agreements with the United States, the largest importer of dairy products in Colombia [2, 3]. Therefore, government entities, in collaboration with dairy associations, have established various support measures for the dairy sector, since they recognize the economic relevance that this sector represents. Similarly, the government stipulates the need to strengthen its support to the agricultural sector in order to improve the competitive position of small and medium-sized farmers in Colombia. As an example of the above, the emergence of new projects generated by new generations of farmers, more specialized and more technical, have been present in the high Colombian tropics. With them, the appropriation of the livestock culture and its specialization and productivity is sought with the help of agricultural growth policies [2, 4]. According to the current context, it is not only a question of generating new dairy farms indiscriminately as is usually done in remote areas of rural areas, but of turning them into long-lasting, self-sustaining and financially attractive projects for investors. Therefore, it is relevant to evaluate the financial viability of implementing agricultural projects, especially those focused on specialized dairy farming. Likewise, it is relevant to evaluate the impact of the financing alternatives promoted by the government for the development of the agricultural sector in the country, through the lines of credit offered by the Finagro financing fund [5]. For this purpose, in this work a comparison was made between taking credit with a traditional bank and with a special credit line Finagro which is a public fund addressed to agricultural producers, for a case study in the municipality of Restrepo, Valle del Cauca. Subsequently, a risk analysis was carried out using a simulation model through which the volatility of the cash flows of the two financing scenarios was quantified and an analysis of critical variables was made. As a result of these

Financial Risk Analysis for a Specialized Dairy Farm Project …

51

comparisons, we seek to analyze the effect of the credit rate on the viability of this type of project, as well as on its level of financial risk so that potential investors have tools for informed decision making. Likewise, this type of analysis can be an input for policy makers to evaluate the effectiveness of incentives and mechanisms aimed at the development of the sector in the country. In the following sections, the methodology applied for the financial evaluation, the parameterization of the simulation model and the risk analysis are described. Subsequently, the discussion of results is presented and in the final section, the conclusions and recommendations.

2 Methods For financial viability of this project, it was necessary to identify the requirements for the installation and operation of the dairy farm for the selected case study. After the costing was carried out, subsequently, the financial statements were projected for five years. Based on these, the cash flows were projected to evaluate them from the investor’s perspective, assuming an equity rate of 14% E.A. This rate was established with respect to the reference rate of the DTF market, which was at a value of 7% E.A. for the time of the analysis, an additional 7% was assumed as a rate of return for investors. For the first scenario the financing rate of 8.2% E.A. offered by the Finagro credit line was taken as a reference, according to the characteristics of the agricultural project to be analyzed. On the other hand, an average of 22.13% E.A. for financing rates of different banks in June-2022 was used for the base financing scenario [6–8]. Then, the Net Present Value (NPV) and the Internal Rate of Return (IRR) were calculated as evaluation criteria [9]. With the financial viability indicators established, the risk analysis associated with the project was carried out through simulation. For this, the RiskSimulator was used [10]. The following aspects were considered in the simulation model and the risk analysis process.

2.1 Simulation Parameterization In this case, three random variables were determined that represent the source of uncertainty in the project: Average milk production per cow in one day (l), sale price per liter of milk (COP) and Consumer Price Index (CPI). For each of the variables identified, a probability distribution associated with its own behavior was established, according to the literature consulted and the trends evidenced, in order to have more realistic scenarios in the simulation. shows the probability distribution that best fits each of the variables and their reference values (Table 1).

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J. A. M. Becerra and K. Salazar-Serna

2.2 Number of Simulations For this financial viability analysis, it was considered pertinent to carry out a sufficient number of iterations that would allow having a fairly broad horizon regarding the behavior of the variables. Therefore, it was determined that 5,000 iterations were sufficient to acquire the relevant information to analyze and, in this way, issue coherent conclusions about the viability of the project.

2.3 Output Variables Considering that it is a financial viability analysis; the Net Present Value and the Internal Rate of Return were established as output variables. These, according to the values obtained through the simulation, were in charge of determining if the project is attractive and if its values represent a viable scenario for its implementation and development in the analyzed period.

2.4 Sensitivity Analysis Finally, once the simulation was carried out with the determined values, the sensitivity analysis of the project was carried out. This process includes the identification of those factors that have the greatest influence on the output variables and most importantly affect their result. In this case, it translates into those factors that had a greater impact on the project’s viability indicators and can increase or decrease its implementation possibilities.

3 Case Study Results The following subsections describe characteristics of our case study project, the financial and risk analysis.

3.1 Project Description The project to be analyzed includes the installation of a dairy farm located in the rural area of Restrepo, Valle del Cauca, Colombia. This city has an altitude of 1,400 m above sea level and an average temperature of 18 °C. Therefore, it offers the appropriate environmental and meteorological conditions for a dairy farm. Also, the costs

Financial Risk Analysis for a Specialized Dairy Farm Project …

53

Fig. 1 Jerhol-type cows [11]

of renting land are considered favorable with respect to the hydric qualities and the minerals present in the soil, which favors the recovery of grazing meadows. Given that the purchase of the land could mean a considerable increase in the initial investment, the partners agreed to rent 20 blocks planted with star grass. A fixed monthly rental payment was negotiated for the next 6 years, and the acceptance to carry out the adaptation works necessary for the operation of the dairy without incurring additional costs. In addition, it should be noted that the land obtained has a cistern that allows the constant supply of water for all tasks without representing utilities expenses. The extension of rented land corresponds to the needs of sustaining 80 mediumsized Jerhol-type cows. This type of animal generates high production volumes with an excellent presence of solids in milk, as well as better tolerance to diseases and better adaptation to tropical climates. Jerhol cows can reach production peaks close to 30 L of milk under optimal feeding conditions. However, due to natural behavior, production averages are close to 18 L per day. In Fig. 1. the type of cows required on the farm is presented. Building of stables and warehouses totaling 275 m2 is required. In addition, the purchase of irrigation equipment, external pipes for handling manure, milking equipment, milk storage tanks and the motors required to run all the equipment must be incurred. Figure 2 shows the manure pump required for the fertilization of the paddocks and the type of irrigation cannon that is required to make the proper spread of manure. Likewise, a milking equipment is necessary for the 80 cows in the herd [12] and the storage tank to house the production (See Fig. 2). Finally, Table 2. shows the consolidation of the necessary equipment corresponding to the investment in fixed assets that is required for the installation of the project. It is necessary to recognize that the partners require the financing of 200 million COP for the purchase of said assets, the surplus is assumed with their own resources. It must be established that the operating costs of this exploitation correspond to the feeding of the cattle, payroll, payment of public services, purchase of medicines and fertilizers, and other expenses. The feed consists of grazing and supplementation

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J. A. M. Becerra and K. Salazar-Serna

Fig. 2 Manuer pump, Bauer Manuer spreader and Milk tank [13–15]

Fig. 3 Probability of failure of the project financed by Finagro according to NPV and IRR

Table 1 Probability distributions and reference values of input variables Input variable Average milk production per cow in one day

Probability distribution Triangular

Reference values Min

Average

Max

14

18

25

Sale price per liter of milk

Triangular

$1 300

$1 400

$1 600

Consumer Price Index (CPI)

Triangular

2,20%

3%

4,70%

in the milking parlor with concentrates with a high source of protein in relation to 1 kg for each liter of milk produced per day. In addition, the payroll, assumed by the hiring of three field workers, a Zootechnician, and a Veterinarian. Additionally, the cost of medicines corresponds to 2% of food costs. The cost for fertilizers results from the respective payment to the paddocks made eight times a year according to the 45-day rotation. The other costs correspond to 1% of the food costs. Table 3. summarizes the annual operating costs.

Financial Risk Analysis for a Specialized Dairy Farm Project …

55

Table 2 Fixed assets Fixed assets Cattle Purchased cattle Price per cow

$

4.800.000

Cattle

$

384.000.000

Milking machine Three-phase electric motor 5 hp

$

1.200.000

6 milk cans

$

1.300.000

6 units milking parlour

$

11.800.000

Total cost milking equipment

$

14.300.000

Milk tank (3000 L)

$

25.000.000

$

6.953.000

Irrigation equipment Manure pump Bauer FIIIM coupled to a three-phase motor 15 hp Manure spreader BG-180

$

1.152.000

Irrigation pipe pvc 3” X 60 m

$

74.248 60

Total pipes (360 m) Total cost irrigation equipment

$

12.559.880

$

500.000

Civil construction Cost per m2 Barn 350 m2

$

175.000.000

Warehouse 25 m2

$

12.500.000

Total building cost

$

187.500.000 $ 623.359.880

Total assest purchases Table 3 Operating cost (figures in thousands) Operative Costs

1

2

3

4

5

Annual cost concentrate feed

219.219

250.884

287.011

307.559

344.332 30.535

Annual cost fertilizer

27.000

27.810

28.922

29.645

Annual cost utilities

6.865

7.071

7.354

7.537

7.764

Annual cost medicine

2.192

2.509

2.870

3.076

3.443

4.384

5.018

5.740

6.151

6.887

Annual cost labor

95.173

97.884

101.607

104.028

107.004

Annual cost land lease

36.000

36.000

36.000

36.000

36.000

Other costs

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J. A. M. Becerra and K. Salazar-Serna

3.2 Financial, Risk and Sensitivity Analysis The projected cash flow for five years, taking advantage of the financial facilities offered by Finagro, is evidenced in Table 4. Similarly, the projected cash flow based on traditional financing methods can be seen in Table 5. Based on these flows and considering the random variables stipulated above, it was possible to carry out the financial analysis of both projects. It is important to mention that the figures present only reference values, they do not correspond to final results obtained by simulation. Starting with the financing scenario supported by the government, it is obtained that the project, from the perspective of the investor, presents a considerably high percentage of viability. According to the values obtained by simulation an average NPV equal to 24 766 415 COP and an IRR of 16.6% are obtained, both exceeding their reference values for viability. Similarly, as shown in Fig. 4, probability of failure Table 4 cash flow for investor with Finagro loan (figures in thousands) Cash flow—Finagro loan

0

1

2

3

4

5

Net income

0

89.450

126.685

163.349

190.849

233.560

Depreciation

0

52.961

52.961

52.961

52.961

52.961

Gross cash flow

0

142.411

179.646

216.310

243.810

286.521

−Assets purchase

623.360

0

0

0

0

0

−OWC investment

9.904

0

0

0

0

0

−OWC variation

0

3.703

3.458

2.800

4.253

0

+Disposals of fixed assets

0

0

0

0

0

0

+New loans

200.000

0

0

0

0

0

-Loan payments (principal)

0

20.000

20.000

20.000

20.000

20.000

Cash flow

−433.264

118.708

156.188

193.510

219.557

266.521

4

5

Table 5 Cash flow-investor traditional loan (figures in thousands) Cash flow—Trad loan

0

1

2

3

Net income

0

71.380

110.422

148.893

178.200

222.718

Depreciation

0

52.961

52.961

52.961

52.961

52.961

Gross cash flow

0

124.341

163.383

201.854

231.161

275.679

−Assets purchase

623.360

0

0

0

0

0

−OWC investment

9.904

0

0

0

0

0

−OWC variation

0

3.703

3.458

2.800

4.253

0

+Disposals of fixed assets

0

0

0

0

0

0

+New loans

200.000

0

0

0

0

0

-Loan payments (principal)

0

20.000

20.000

20.000

20.000

20.000

Cash flow

−433.264

100.638

139.925

179.054

206.908

255.679

Financial Risk Analysis for a Specialized Dairy Farm Project …

57

Fig. 4 Tornado diagram

for this case is set at 31.1%, representing almost 70% financial viability for this case. This success rate turns out to be attractive under most investment profiles. It is necessary to recognize that the risk associated with this project may generate a certain reserve, since the values of the indicators may be highly volatile. For the NPV, values as favorable as 209 million COP can be reached, but at the same time it could generate significant losses of -103 million COP, which represents a probability of risk to be considered. However, the average of the simulation shows a considerably attractive value to invest. In addition, the internal rate of return could reach values close to 37% or even as low as 3%, so its range of behavior is considered quite wide, but the chances of financial success favor the viability of the project. Comparatively, as a result of the feasibility analysis carried out for the traditionally financed scenario, values as attractive as in the past scenario were not obtained. The probabilities of failure associated with the output variables analyzed are higher than 70% indicating infeasibility for this project. In this case, the NPV yields negative values, so the financial infeasibility of this project is evident. As in the past scenario, the ranges of the indicators are quite wide, since the NPV can reach values close to 153 million COP, but also significant losses of -141 million COP, resulting in a much more discouraging scenario than the previous. The IRR could reach values of 31%, but negative rates are also recorded. According to the above, a clear difference can be seen between the indicators of each of the scenarios, while with the financing of Finagro the exploitation could have a NPV of over 205 million COP and return rates of over 37%, through Traditional financing could reach NPV values close to 150 million COP and IRR close to 31%. However, under the second scenario, the probabilities of incurring losses are considerably high, reaching up to more than 140 million COP and yielding rates below 0%, which is not attractive for any investor. Turning to the sensitivity analysis, it was evidenced by means of the tornado diagram generated by RiskSimulator that the factors that have the greatest incidence in the behavior of the viability indicators are: The price of the concentrates, the price paid for each liter of milk and the liters of milk produced daily. Figure 4, shows the tornado diagram. It can be seen in the figure how the increase in concentrate prices has a strong and negative effect on the performance indicators. Therefore, the reduction of these costs could increase the chances of success of the project.

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J. A. M. Becerra and K. Salazar-Serna

Similarly, the increase in both daily production and the price paid per liter, which is determined by the quality of the product, would make it possible to obtain better performance indicators.

4 Conclusions It is necessary to establish that the financing scenario through Finagro presents a considerable superiority compared to traditional financing in terms of indicators. Although it is necessary to recognize the high variability that the project may have, the probability of success greater than 69% supports it, being able to generate profits of more than 205 million COP. Once the comparison between the two financing scenarios is made, a high influence of the interest rates imposed by the financial entities on the viability of the projects is evident. Thus, those projects that are favored with lower interest rates or even subsidized, as is the case with this project, have a significantly higher financial viability than those financed by traditional entities. It is evident that the aid offered by government entities plays a strong role in the implementation of agricultural projects, even more so in a scenario of high volatility, economic uncertainty such as the one currently going through the world economy. Therefore, state incentives can become promoters of productive and technological growth in national agriculture. Now, emphasizing the variable that reflected the greatest influence in the sensitivity analysis, the price per kg of concentrate, it is necessary to issue certain considerations in this regard. In the first place, considering that the increase in feed consumption in order to potentiate milk production represents a high increase in production costs, a nutritional balance of the concentrate rations must be found. Additionally, another branch of analysis represents food self-sufficiency. In this option, the possibility would have to be contemplated, in conjunction with specialist agronomists and zootechnicians, of implementing crops and manufacturing their own food. However, this represents further analysis. This consideration arises as a response to the scenario of scarcity of foreign raw materials at convenient prices for the domestic market. In addition, the dependence on external sources creates a limitation in national agricultural growth. On the other hand, considering that the price paid per liter and the amount of milk produced occupy important places of incidence in the project, special care must be paid to the quality standards managed in livestock farms. According to the payment methods stipulated by the producing plants, the increase in the price of milk is directly influenced by the quantity and quality of solids in milk, somatic cells, cleanliness and whey.

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59

5 Recommendations As a main recommendation, help is sought with respect to obtaining agricultural inputs that allow a competitive margin of costs without sacrificing the quality of the final product. As evidenced in the financial analysis, government intervention in agricultural projects represents a substantial increase in their chances of success. In addition, considering the influence of the quality and quantity of the product on the success of the project, it is pertinent to recognize the importance of having excellent livestock practices that enhance animal welfare and that represent an increase in these standards. Since it is a project in which living beings and environmental factors that directly affect them are involved, the conditions provided for their correct management must be analyzed with special care. Additionally, it should be noted that economic aid from the government, rather than lighten the economic burden of ranchers, could be considered as opportunities for improvement and national agricultural development.

References 1. DANE: Encuesta Nacional de Calidad de Vida ECV 2019 Resultados-identificación subjetiva de la población campesina. Departamento Nacional de Estadística, Colombia (2020) 2. Manrique Horta, F.M.: Se firmó pacto por el crecimiento del sector lechero. Contexto Ganadero (2019). https://www.contextoganadero.com/economia/se-firmo-pacto-por-el-crecimiento-delsector-lechero. Accessed 26 Nov 2022 3. González, X.: Durante 2020, se recibieron más de 73.600 toneladas de productos lácteos importados, Agronegocios (2021). https://www.agronegocios.co/ganaderia/durante-el-ano-pasadoel-pais-importo-mas-de-73-600-toneladas-de-productos-lacteos-3132053. Accessed 26 Nov 2022 4. Páez Muzzulini, R.: El resurgimiento de nuestras raíces «Volver al Campo». AsoJersey Colombia (2021). https://www.asojersey.com/el-resurgimiento-de-nuestras-raicesvolver-alcampo/. Accessed 26 Nov 2022 5. Fondo para el financiamiento del sector agropecuario | Finagro, https://www.finagro.com.co/. Accessed 17 June 2022 6. Simulador de Crédito | Finagro. https://www.finagro.com.co/operaciones-en-linea/simuladorcredito. Accessed 17 June 2022 7. Tasas de Crédito Banca Personal Aplica para Clientes Bancoomeva. https://www.bancoomeva. com.co/publicaciones/163812/tasas-y-tarifas/. Accessed 17 June 2022 8. Tasas-Credito-Microempresarios. https://www.bancocajasocial.com/portalserver/bcs-public/ inicio/pequenas-empresas/creditos/cupos-de-credito. Accessed 17 June 2022 9. Ross, S., Westerfield, R., Jordan, B.: Fundamentals of Corporate Finance. McGraw Hill, New York, USA (2010) 10. Software Shop - Risk Simulator (2022). https://www.software-shop.com/producto/risk-sim ulator. Accessed 17 June 2022 11. USJersey: American Jersey Cattle Association & National All-Jersey Inc. https://www.usjersey. com/. Accessed 17 June 2022 12. Equipo de Ordeño Fijo 5 y 6 puestos para vacas. https://suplagro.company.site/Equipo-deOrde%C3%B1o-Fijo-5-y-6-puestos-para-vacas-p192047678. Accessed 17 June 2022 13. Bomba Estercolera | Acoplada FIIIM | Comercial de Riegos (2022). https://comercialderiegos. com/product/bomba-estercolera-acoplada-fiiim/. Accessed 17 June 2022

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14. Cañon Estercolero BG-180 | Aspersor | Comercial de Riegos. https://comercialderiegos.com/ product/canon-estercolero-bg-180-aspersor/. Accessed 17 June 2022 15. Tanques horizontales media cana—Maxitanques. https://maxitanques.com/producto/tanqueshorizontales-media-cana/. Accessed 17 June 2022

Brand Positioning Analysis for the Automotive Lubricants Industry Using Perceptual Maps Juan Sebastián Gil Castro , Juan Diego González , Julián David González , Andrés Felipe Martínez , Nicolás Rodríguez , Edward Steven Rojas , Juan Diego Román , and Karen Dayane Santana

Abstract A positioning analysis was performed to 8 different brands of automotive lubricants in Colombia. For the analysis, information was collected on the perception that the interviewees (managers of automotive lubricant sales points) had about 13 characteristics of the brands along with their perception about what they considered to be an ideal brand. From the information, graphic tools known as perceptual maps were produced, allowing us to identify the best perceived attributes of the brands, their similarities and differences with the ideal brand and the brands that compete with each other. Features such as warranty, product availability, discounts, and a focus on heavy-duty products are associated with an ideal brand, while attributes related to product quality and performance are associated with traditional brands in the market. J. S. G. Castro (B) · J. D. González · J. D. González · A. F. Martínez · N. Rodríguez · E. S. Rojas · J. D. Román · K. D. Santana Universidad Sergio Arboleda, Bogotá, D.C, Colombia e-mail: [email protected] J. D. González e-mail: [email protected] J. D. González e-mail: [email protected] A. F. Martínez e-mail: [email protected] N. Rodríguez e-mail: [email protected] E. S. Rojas e-mail: [email protected] J. D. Román e-mail: [email protected] K. D. Santana e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. R. Montoya-Torres et al. (eds.), Operations Research and Analytics in Latin America, Lecture Notes in Operations Research, https://doi.org/10.1007/978-3-031-28870-8_5

61

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Keywords Positioning · Perceptual maps · Principal component analysis · Ideal brand

1 Introduction At the end of 2021, 17,020,461 vehicles were registered with the Registro Único Nacional de Tránsito (RUNT), Colombian Single National Transit Registry, of which 10,136,593 were motorcycles (59.5%), 6,701,970 cars, SUVs, trucks, buses and dump trucks (39.4%) and the rest, heavy machinery vehicles (1.1%). According to official records, that same year is the year with the highest number of new registers (new vehicle sales) since the system was implemented, with a total of 993,787, distributed among 106,556 car units, 114,631 SUVS and pick-up trucks, 725,963 motorcycles. and 46,637 units of other types of vehicles. The previous statistics show the magnitude of the automotive market, not only in the purchase of new vehicles, but also in its influence on transversal markets: auto parts, accessories, spare parts, luxuries, repair shops, additives, etc. For the same year mentioned, the lubricants market reported a production and marketing value of approximately 56 million gallons, shared between large national and international producing companies such as Shell, Mobil, Texaco, Castrol, Gulf, Terpel, etc., and other brands with local and regional coverage. Although they do not have a large market share, they do have a strong presence in small towns in the Colombian territory. For brands, positioning represents the possibility of being in the minds of consumers and encompassing a significant amount of market share because the customer recognizes, compares and values various attributes of the brand over those of its competitors [14]. For consumers, the permanent search for the best possible quality at a low cost, guided by the brand image, the suggestion of their supplier and even the publicity to which they are subjected, benefits those products with a strong recognition in the market and a wide distribution in the territories where it is marketed. In summary, the magnitude of the market, the arduous competition and the increasingly large and challenging demand reveal the need for organizations to highlight their products, identifying the best perceived attributes of their brands, the differential aspects of the competition and, In general, the most valued characteristics by consumers so that this allows them to focus their economic, logistical and operational efforts on designing more efficiently the appropriate promotion and communication strategies for their products. The objective of this study is to evaluate how the various attributes of lubricant brands influence consumer perception by showing the analysis of brand positioning and evaluating similarities and differences between the brands selected for field research performed in the cities of Bogotá, Medellin, and Barranquilla. Initially, a bibliographic review of positioning concepts, perceptual maps and principal component analysis are presented, as well as a review of the state of the art of similar studies performed in other countries. The methodology describes how the data collection and

Brand Positioning Analysis for the Automotive Lubricants Industry …

63

processing were executed to generate the principal components of analysis. Subsequently, the results of the perceptual maps developed for each city and their general comparison are presented, followed by the conclusions and recommendations for future studies.

2 Literature Review This section deals with the literature review of three important concepts that support the study: (1) positioning (seen from the field of marketing through the perspective of different authors); (2) perceptual maps and their contribution from graphic analysis to the comparison of characteristics between brands; and (3) principal component analysis as a mathematical tool whose usefulness lies in dimensional reduction.

2.1 Positioning Positioning is the process of designing the image of the company’s products and services based on consumer perceptions in relation to the ones of their competitors [13]. There are 6 constructs that describe the concept of positioning: brand identity, brand personality, brand communication, brand awareness and brand image [15]. Other perspectives evoke positioning as a strategic concept that helps a brand to achieve a better position in the market against the competition [18] and as a concept of marketing and advertising to ensure that a product has an important and unique solid position in the market [16].

2.2 Perceptual Maps Perceptual maps are tools that contribute to the knowledge of the characteristics of any product. They are very important for any company due to their ability to relate all the best features and obtain insights, paths in a marketing project or simply knowing the market for a new product. When used correctly, it can identify opportunities, enhance creativity, and direct marketing strategy to research areas that are likely to attract consumers [8]. In the perceptual map, the position of the product is represented by a point in a subspace that can be a three-dimensional or two-dimensional grid, where the dimensions or axes represent key attributes of the product [19].

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J. S. G. Castro et al.

2.3 Principal Component Analysis (PCA) Principal component analysis is a mathematical procedure that converts a set of correlated variables into a compressed data set without correlated variables, called Principal Component, which contains most of the information of the original data set [1]. The PCA fulfills two main objectives: the reduction of the dimensionality of the data set and the identification of new underlying variables. In order to select the number of main components that will explain the position of each variable, the accumulated variance ratio is considered, which is calculated by the ratio between the eigenvalue and the rate of the covariance matrix. Other authors propose including only those components whose eigenvalues are higher than the mean [11]. The downside of this selection criterion is that it tends to select very few components when the number of original variables is greater than twenty, considering that the number of components must reach the required cumulative variance frontier. For this, there are other measurements where it is established that the number of components specified by the maximum p-value (accumulated variance) is close to the percentage specified by the researcher [4]. In many cases, the expertise of the researcher could determine the number that explains the behavior of the data [17].

3 State of the Art Brand positioning is the process of creating the brand’s image, distinctive attributes, positive associations and values in the mind of consumers for the purpose of crafting a sustainable brand image and also to ensure consumer loyalty [5]. This concept should be based on the reasons why customers prefer to deal with the company and not with its competitors, conveying these motives to the target audience [6]. A study held in Indonesia in 2016 aimed to analyze the positioning strategies for different brands of motor lubricants for passenger cars, using perceptual maps and multiple discriminant analysis and evaluating the perception of six attributes: performance, durability, ease of purchase, price, packaging and popularity of the brand. It was found that the attributes of the lubricants can influence consumer evaluations of the brand, positioning and differences between each brand [22]. Another study conducted in India documented the importance of brand positioning for the automotive lubricants market in that country. Multiple regression analysis was used to determine the relationship between brand positioning and its most important attributes. The results presented four relevant characteristics: reliability, quality, marketing strategy and accessibility. As a recommendation, it is mentioned that if the lubricant-producing companies focus on the aforementioned factors, they will definitely obtain the benefit in the future and their market share will increase [20].

Brand Positioning Analysis for the Automotive Lubricants Industry …

65

4 Methodology 4.1 Study Design and Data Collection For the development of the study, a matrix was designed in which the perceptions of the respondents were evaluated regarding 13 attributes (power, performance, price, discounts, brand perception, quality, technology, international origin, availability, guarantee, line for motorcycles, line for automobiles and line for heavy vehicles) in which 8 different brands of lubricants present in the Colombian market were rating their perception from 1 to 10, where 10 represents the best perception of the attribute. Each brand was listed with a number from 1 to 8 to avoid bias in the analysis: Castrol (number 1), Terpel (number 2), Mobil (number 3), Total (number 4), Gulf (number 5), Valvoline (number 6), Shell (number 7), Petrobras (number 8). Similarly, respondents were asked to rate the attributes upon which they considered an “ideal brand”, this being brand number [9] in the report. In total, data was collected from 33 commercial establishments of sales and distribution of lubricants randomly selected from three cities in the country: Bogotá D.C. (12), Medellín (11) and Barranquilla (10), between March and May, 2022. The surveys were performed directly at each point of sale, asking the person in charge of the place to fill out the matrix described above according to their perception.

4.2 Data Preparation and Preprocessing Once the matrices were filled by the sellers of each automotive lubricant point in the principal cities mentioned above. It was grouped by location and averaged in order to get a summary of the perception by city. Those averaged matrices (Bogota D.C., Medellin, Barranquilla) were centered and scaled in such a way that the data had mean equal to 0 and standard deviation equal to 1 avoiding misbalanced data: Z=

x−X σ

(1)

In order to find the principal components, it needs to calculate the covariance matrix of the scaled values that were found above, that shows the joint variation of each variable x j . the covariance matrix must be quadratic due that the columns and rows are the same. For this study, there are 13 different variables hence, the dimensionality of the covariance matrix will be (13 × 13) where:

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⎛

⎞ var (x1) cov(x1, x2) cov(x1, x13) ··· ⎜ cov(x2, x1) var (x2) cov(x2, x13) ⎟ ⎜ ⎟ S=⎜ ⎟ .. .. . . ⎝ ⎠ . . . cov(x13, x1) cov(x13, x2) · · · var (x13)

(2)

4.3 Principal Components Generation The construction of the principal components is given from the concept of linear combinations, where each component is: yj =

p 

ajxj

(3)

j=1

where a j are the loading values that maximize the variance for the first components [10]. The processes of maximization generally are made through Lagrange multipliers that according to [16] when the function to optimize the Eq. (4) will have a restriction (5) and it will generate (6). In order to find those vectors a j that maximize the variance is necessary to obtain the (7) partial derivate of (6). In this case. f (x)= a tj Sa j

(4)

g(x) = a tj a j = 1

(5)



L = a tj Sa j − λ a tj a j − 1 = 0

(6)

∂L = 2a j S − 2λa j = 0 ∂a j

(7)

The partial derivate is equal to 0 due that is necessary to find critical points. Into the equality it can be observable that the partial derivate generates the formula to calculate the eigenvectors. Sa j = λa j

(8)

That is a system of linear equations that find the a j vectors composed by the loads used in the linear combination. The principal eigenvalues of the covariance matrices of each city will be presented below (Table 1). Each of those Eigenvalues will generate a respective eigenvector which contain the a j values of the linear combination in order to create the first principal component.

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Table 1 Eigenvalues calculated for each city Bogotá eigenvalues 1

9.247480

Medellín eigenvalues

Barranquilla eigenvalues

8.735243

9.982097

2

1.656853

2.268690

1.633502

3

9.395965 × 10−1

8.310006 × 10−1

4.821019 × 10−1

4

5.790054 × 10−1

5.062432 × 10−1

3.781436 × 10−1

5

2.869410 × 10−1

3.345820 × 10−1

2.272995 × 10 −1

6

2.238232 ×

10−1

10−1

1.486830 × 10−1

7

5.021814 ×

10−2

8

1.608266 × 10−2

2.369366 ×

10−2

1.152130 × 10−1

1.24568 × 10−2

3.296046 × 10−2

7.48481 ×

9.681768 ×

10−16

10

−9.534525 ×

10−17

11

−1.112614 × 10−16

−6.252515 × 10−17

−4.800665 × 10−17

12

−1.471348 ×

10−16

10−16

−7.225183 × 10−17

13

−1.714552 × 10−16

−7.007714 × 10−16

−1.680442 × 10−16

9

2.655277 ×

10−16

3.940556 × 10−16

−5.893143 ×

10−17

7.549960 × 10−17

−1.192158 ×

In this case, the linear combination of the first principal components presented in Bogota, for instance. y Bog 1 = −0.317 × 1 − 0.311 × 2 + 0.073 × 3 − 0.238 × 4 − 0.291 × 5 − 0.319 × 6 − 0.310 × 7 − 0.301 × 8 − 0.205 × 9 − 0.297 × 10 − 0.233 × 11 − 0.318 × 12 − 0.279 × 13

(9)

y Bog 2 = 0.102 × 1 + 0.154 × 2 − 0.699 × 3 − 0.494 × 4 + 0.116 × 5 − 0.007 × 6 + 0.070 × 7 + 0.208 × 8 − 0.279 × 9 − 0.216 × 10 + 0.138 × 11 + 0.009 × 12 − 0.155 × 13

(10)

4.4 Attributes a Brands Plotting In order to generate the coordinates in the new sub-space created by the principal components, it is necessary to use the linear combinations explained bellow, putting the scaled values in x j and operating to find the PC1 and PC2 positions in the plane of the brands and attributes. In this case, it will present the rotated coordinates of the study for only two principal components mentioned above. Here it is shown the first five rotated coordinates of the brands of the study only for the Bogota case (Table 2). Secondly, the generation of the coordinates for the attributes in the first two principal components needs to plot the attributes for a correct and complete analysis.

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Table 2 Principal components and brands relationship Marca

PC1

1

−1.10704246

PC2 0.5805408

2

2.58963166

2.2693613

3

−1.19013935

−1.1080088

4

−0.07396641

0.7210609

5

2.80541065

−0.9998367

6

0.45110009

−1.3193501

7

−3.53241828

−1.2107250

8

4.72300410

−0.2554354

9

−4.66558001

1.3223929

Table 3 Principal components and attributes relationship Attribute Power Performance Price Discounts

PC1

PC2

0.9623381

−0.19404458

1.0113623

−0.2516156

−0.2623505

0.88115580

1.0091846

0.82251440

Brand perception

1.4809961

−0.17333674

Quality

1.0747555

−0.06396744

Technology

0.9376642

−0.18919198 −0.36599615

International origin

0.9476799

Availability

1.0274463

0.71282013

Guarantee

0.5340407

0.09892702

Line for motorcycles

0.9632177

−0.33792934

Line for automobiles

1.0127949

−0.09484446

Line for heavy vehicles

1.1858345

0.27690395

Those rotated coordinates attributes are generated with the same product of the linear combination. The first five coordinates of the attributes evaluated by the seller’s perception in Bogota are shown as follow (Table 3).

4.5 Number of Components In order to determine the number of components to use, it requires to consider that the principal objective of this statistical tool is to reduce the dimensionality, having a maximum variance explanation in few components. For this purpose, the selection of number of components was based in the proportion of cumulative explained variance,

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just like [4] specified. In this case, Bogotá obtain the 83.8% between the linear combination of the two first principal components previously shown. It is considered relevant to say that the path to generate Bogotá’s principal components is the same of those principal components of Barranquilla, Medellin and the general map that will be shown in the next part of the article.

5 Results and Discussion Through the observation of the perceptual maps generated with the analysis of principal components, the essential characteristics of the brands in each of the cities that were visited in the field work will be discussed. The aim is to determine the behavior of the variables that represent the best perceived attributes in these areas.

5.1 Bogotá The perceptual map for the capital city (Fig. 1) collects 83.8% of the explained variance in its first two main components (71.1% in the first and 12.7% in the second). This represents a good amount of information collected by these new variables. That is to say, the behavior of the data can be well explained by these two dimensions. It is evident that the main component 1 is correlated with the variables: quality, focus online for automobiles, technology and power, while the main component 2 is characterized by the variable price. In Bogotá, it is essential that a brand be

Fig. 1 Perceptual map for the data collected in Bogotá D.C. Source own elaboration

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recognized for its focus on the line of heavy vehicles, the high level of guarantee and the availability of the product to be considered close to the ideal brand in the perception of customers. According to the treatment of the data, none of the 8 brands studied is close to the ideal brand (9). Brand 1 only has traits of high Availability, whereas brands 8 and 5 are completely opposite to the ideal brand.

5.2 Medellín The first two dimensions of the principal component analysis for this city collect 67.2% and 17.5% of the information, respectively, for a total accumulated variance of 84.7%. That is to say that the first component collects the two thirds of the original information, while the second component collects a value of less than 20%. The characteristics that best describe this first component are power, guarantee, brand, and product availability, while the second component is strongly correlated with the original variable price (Fig. 2). For Medellin, the ideal brand is described based on variables such as good perception of the brand, focus on automobiles and heavy vehicles. For this area, the brand most like the concept of an ideal brand is number 3, which is well perceived in characteristics such as focus on products for heavy vehicles, issuing discounts and product availability. On the contrary, the brands that are the furthest from being considered like an ideal brand are numbers 4 and 5, which are perceived by customers as weak in the brand concept and with low evidence of products in the lines of automobiles and heavy vehicles.

Fig. 2 Perceptual map for the data collected in Medellín. Source own elaboration

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Fig. 3 Perceptual map for the data collected in Barranquilla. Source own elaboration

5.3 Barranquilla The cumulative variance ratio of just two components equals 89.4% (PC1: 76.8%, PC2: 12.6%). In this case, the first principal component has the ability to explain more than three quarters of the information and can be described from the variable’s technology, quality and power, while PC2 explains a value greater than 10% and it can be characterized from the perception of products for the line of automobiles and heavy vehicles (Fig. 3). In this city, the variables that best describe the concept of an ideal brand are associated with the focus on the line for heavy vehicles and automobiles and with the perception of the brand as an international one. In this case, no brand was perceived as like the ideal. In fact, the ones that are the furthest from this label are numbers 4 and 5. Additionally, brands 3 and 7 are considered very similar in terms of brand quality, availability, performance, and discounts.

5.4 General The general analysis compiled the information of the three cities and built the perceptual map without discriminating the geographical origin of the information (Fig. 4). In this case, the two-dimensional diagram (Principal Components 1 and 2) manages to explain 90.4% of the original information, distributed between 80.1% for PC1 and 10.3% for PC2. PC1 is related to the variables guarantee, heavy vehicles, technology, quality and brand, while PC2 is related to the price of the products.

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Fig. 4 Perceptual map for the data collected in Barranquilla. Source own elaboration

Similar brands can be associated more easily compared to the study made by cities. It is observed that, in general terms, brands 4, 5, 6 and 8 can be considered similar in having a low perception of characteristics such as price, discount offer and product availability. In addition, brands 1, 3 and 7 are similar in variables associated with power, international origin, performance and products for the automobile line. The ideal brand can be characterized based on the variables of guarantee, availability and discounts, but none is perceived as similar or close to it.

6 Conclusions and Recommendations The common attribute that controls the characterization of an ideal brand in the different cities focus on products from the line of heavy vehicles, the fact that the brand offers products for that line of vehicles is perceived as valuable also that it can be attributed some sort of relationship between the brand and that type of car. furthermore, according to the characteristics based on the perception of the ideal brand, such as guarantee, product availability and communication of discounts, companies in the process of growth should focus their strategies on better ways to communicate such attributes, creating a differentiating factor. Compared to the rest of the other brands. For our study, brands such as Total, Gulf and Petrobras should focus their strategies on strengthening such characteristics of their product as they are the furthest from the ideal brand. Well-established brands in the market, such as

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Mobil and Shell, are perceived as similar in terms of brand recognition, quality, and product performance. A more detailed study by region showed that in Bogotá the perception of aftersales service and product warranty are perceived as differentiating factors. In this way, brands should focus their promotion strategies on such attributes. For Medellin, that companies offer coverage in the line of vehicles (not heavy) also highlight brand attributes that allow their wide recognition, will be the recommended strategy. Finally, in Barranquilla, seeking to position the brand through strategies that communicate its international origin should be the way forward. For future studies, it is advisable to collect larger data to reduce the error in the statistical procedure and establish a stronger foundation for dimensional reduction. In the same way, it is recommended to perform the study in other cities of the country where the dynamics of marketing and positioning of the brands are different from those that occur in the large cities of the country.

References 1. Araneo, D.C.: Introducción al Análisis de Componentes Principales, Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales (IANIGLA) (2008) 2. Asociación Colombiana del Petróleo y Gas (ACP): Informe Económico Evolución 2021 y perspectivas 2022–2030 del mercado de combustibles líquidos en Colombia. Bogotá D.C., Colombia (2021) 3. Chiang, I.P., Lin, C.Y., Wang, K.M.: Building online brand perceptual map. Cyberpsychol. Behav. 11(5), 607–610 (2008) 4. Cuadras, C.M.: Nuevos Métodos de Análisis Multivariante. CMC Editions. Barcelona, España (2010) 5. Fayvichenko, D.: The concept of brand positioning. Mignarodnii naukovo-praktuchniy gurnal «Tovaru i runki» 1(21), 25–32 (2016) 6. Fayvichenko, D.: Formation of brand positioning strategy. Balt. J. Econ. Stud. 4(2), 245–248 (2018) 7. Grupo Empresarial Terpel. Informe de Gestión y Sostenibilidad Terpel 2021, Colombia (2021) 8. Hauser, J.R., Koppelman, F.S.: Alternative perceptual mapping techniques: relative accuracy and usefulness. J. Mark. Res. 16(4), 495–506 (1979) 9. Hoyos, R.: Branding El Arte de Marcar Corazones. 1ra ed. Ecoe Ediciones. Bogotá D.C., Colombia (2016) 10. Jolliffe, I.T., Cadima, J.: Principal component analysis: a review and recent developments. Philos. Trans. R. Soc. A 374, 20150202 (2016) 11. Kaiser, H.F.: The application of electronic computers to factor analysis. Educ. Psychol. Measur. 20, 141–151 (1960) 12. Kolman, B., Hill, D.: Álgebra Lineal. 8a Ed. Pearson Educación. México (2006) 13. Kotler, P.: Marketing Management Analysis, Planning, Implementation, and Control, 9th edn. Prentice-Hall, Englewood Cliffs, NJ (1997) 14. Kotler, P., Keller, K.L.: Marketing Management, 14th edn. Pearson Prentice Hall, New Jersey (2012) 15. Malik, A., Sudhakar, B.D.: Brand positioning through celebrity Endorsement—A review contribution to brand literature. Int. Rev. Manag. Mark. 4(4), 259–275 (2014) 16. Peña, D.: Análisis de Datos Multivariantes, 1a edn. McGraw Hill, Madrid (2003) 17. Restrepo, L.F., Posada, S., Noguera, R.: Application of the principal—component análisis in the evaluation of three grass varieties. Rev. Colomb. Cienc. Pecuarias 25(2), 258–266 (2012)

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18. Ries, A., Trout, J.: Positioning: The Battle for Your Mind. New York, NY (1981) 19. Sinclair, S.A., Stalling, E.C.: Perceptual mapping: a tool for industrial marketing: a case study. J. Bus. Ind. Mark. 5(1), 55–66 (1990) 20. Srivastava, G.: Importance of brand positioning for Indian automotive lubricants market. Sch. J. Econ. Bus. Manag. 5(12), 1165–1171 (2019) 21. Sánchez, C.: Tema 5. Análisis de Componentes Principales. Análisis Multivariante. Máster en Técnicas Estadísticas (2009) 22. Wibawa, B.M., Vanany, I., Kunaifi, A., Anggara, F.: Brand positioning strategies based on consumer preferences and perceptions of passenger car motor oils. In: 2nd International Conference on Future Business Environment and Innovation (2016)

Applications in Production, Logistics, and Supply Chain Management

Comparison of Nawaz-Enscore-Ham Algorithm and Local Search Operator in Flowshop Scheduling with Learning Effects Yenny Alexandra Paredes-Astudillo , Jairo R. Montoya-Torres , and Valérie Botta-Genoulaz

Abstract Attention to scheduling problems with learning effect has increased, since the factors that influence productivity of manual tasks are being considered recently. The flowshop system is one of the most frequent configurations of hand-intensive production systems; it belongs to the class of NP-hard combinatorial optimization problems. Thus, this article develops an algorithm to resolve the flowshop scheduling problem with learning effect with makespan minimization. Four models for calculating the learning effect referred to in the literature are considered (according to the position and the sum of the processing times). This paper proposes the NawazEnscore-Ham Algorithm (NEH) with two local search operators. This algorithm is tested through computer experiments. Keywords Scheduling · Flowshop · Learning effect · NEH · Local search · Makespan

1 Introduction In recent years, scheduling problems with learning effect have received increased attention. Given this variation of the classic problem, the single machine scheduling problem had had the largest number of contributions, however, there is a growing Y. A. Paredes-Astudillo (B) · J. R. Montoya-Torres School of Engineering, Universidad de La Sabana, Km 7 Autopista Norte de Bogotá D.C., Chía, Colombia e-mail: [email protected]; [email protected] J. R. Montoya-Torres e-mail: [email protected] Y. A. Paredes-Astudillo · V. Botta-Genoulaz Univ Lyon, INSA Lyon, Université Claude Bernard Lyon 1, Univ Lyon 2, DISP-UR4570, 69621 Villeurbanne, France e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. R. Montoya-Torres et al. (eds.), Operations Research and Analytics in Latin America, Lecture Notes in Operations Research, https://doi.org/10.1007/978-3-031-28870-8_6

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interest in the flowshop scheduling problem (FSSP), because it is a common configuration in real manufacturing systems (e.g., textile, footwear, automotive, etc.) [1, 2]. Hand-intensive industries involve workers in their operations, reason why the job processing time may be subject to change because of the learning effect of monotonous tasks [3]. This phenomenon has started to be considered in the literature where several approximations have been suggested for modeling the learning effect. It is known that the flowshop scheduling problem minimizing the makespan (Cmax ) with three or more resources becomes NP-hard. The case with two resources can be optimally solved using the Johnson’s rule. However, when including the learning effect (independent on the modeling approaches), the problem is NP-hard even for the case of two resources, which means that some algorithms such as the Johnson rule does not obtain an optimal solution [4]. Therefore, to solve such a problem, it is necessary to use innovative methods such as heuristics and metaheuristics. The learning effect was introduced by Wright (1936), which occurs mainly in monotonous tasks [5] and as result of experience. Since 1999, the first studies have appeared where the learning effect is introduced into the scheduling problem, which has become the basis in this area [6, 7]. In general terms, learning effect models are based on the principle of position in the schedule or the sum-of-processingtimes. Despite the advances that have been done in this topic, especially in the single machine scheduling problem, the flowshop has gained in importance. Recently, some authors have addressed this problem through heuristics. On one hand, for example, the dispatching rules have been proposed such as, the shortest processing time (SPT) [4, 8–12], the weighted shortest processing time (WSPT) [8, 10, 13, 14], or the earliest due date (EDD) [8, 15]. On another hand, some heuristics began to gain strength given the positive results they demonstrated. Among those, we have the Framinan and Leisten heuristic (FL) [16, 17] and the Nawaz-Enscore-Ham algorithm (NEH) [18–22]. Since greedy algorithms represent a promising method to approach the problem, the solutions obtained could be improved through local search operators. The objective of this paper is to identify and select different approaches to model the learning effect in flowshop scheduling problem and propose an extension of NEH approach with two local search operators. It is expected to compare the models and determine the impact on the objective function and computational processing time. This paper addresses the problem with benchmark data sets; in the future, these models could be also applied to real-life contexts. The paper is organized as follows. Section 2 describes the problem under study. The solution approach is presented in Sect. 3, while the experimental setting and analyses of results are presented in Sect. 4. Finally, conclusions and future research opportunities for are mentioned in Sect. 5.

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2 Problem Description Formally speaking, this paper considers the flowshop scheduling problem (FSSP) with a set of n independent jobs, j = 1, . . . , n, to be processed by a set of m workers, i = 1, . . . , m, in order to minimize the makespan. Each worker can process one job at a given time, all the resources process the jobs in the same sequence and preemption of a job is not allowed. Thus, P i j is the baseline job processing time of the job j in the i-th resource and Pi jr is the actual processing time of the job j in the i-th resource once it is executed in the r-th position of the schedule. The Nawaz-Enscore-Ham (NEH) algorithm has shown outstanding performance solving this type of problems. To compare the performance of NEH with local search (LS) operators, four cases to compute Pi jr are studied. They are adapted from the position and sum-of-processingtime-based learning effect approaches (with and without truncation) referred to by [23, 24]. The proposed cases are described as below: • Case 1: with position-based learning Pi jr = P i j r α • Case 2: with truncated position-based learning Pi jr = P i j max{r α , β} • Case 3: with sum-of-processing-time based learning Pi jr α   −1 1 + θ rk=1 Pi jk P i j • Case 4: with truncated sum-of-processing-time based learning Pi jr α    −1 max 1 + θ rk=1 Pi jk , β P i j

= =

Where α is a parameter of learning effect (α < 0), and β is a control parameter with 0 < β < 1 which indicates the learning limitation.

3 Solution Approach In this section we present the heuristic proposed to solve this problem. This algorithm is composed by the NEH plus a local search operator performed under the precept of the first improvement. These components are presented below (Fig. 1). The details are explained in the next subsections.

3.1 NEH Algorithm The NEH algorithm is a greedy heuristic adapted as follows: 1. Calculate the total processing time (TPT) on all machines for each job j. 2. Sort all jobs in a list by decreasing order of TPT. 3. Select the two jobs with the highest TPT and remove them from the list. Two possible sequences are obtained with these jobs.

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Fig. 1 Flowchart of the algorithm

4. Calculate the actual processing time of each job j according to the corresponding case (1, 2, 3, or 4) as outlined above. 5. Compute the Cmax for each sequence and select the sequence with the minimum Cmax . 6. Select the next job from the list, calculate all possible inserts within the sequence. Return to steps 4 and 5. Keep the sequence with the lowest values of the makespan. This sequence will be the initial solution (S) for the improvement phase.

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3.2 API-LS Operator This operator swaps jobs in adjacent positions as follows: 1. In this case K 1 = 1 and K 2 = K 1 + 1, subsequently the jobs between position K 1 and K 2 are swapped respectively. 2. The new solution is noted S0 . 3. If Cmax (S0 ) < Cmax (S), then S is replaced by S0 and the local search algorithm finishes; otherwise, let K 1 = K 1 +1 and K 2 = K 2 +1 and the process is repeated until the Cmax (S) can be improved or up to K 1 = n − 1.

3.3 NAPI-LS Operator This operator swaps jobs from non-adjacent positions as follows: 1. Let K 1 = 1 and K 2 = K 1 + 2, subsequently the jobs between position K 1 and K 2 are swapped respectively. 2. The new solution is noted S0 . 3. If Cmax (S0 ) < Cmax (S), then S is replaced by S0 and the local search algorithm finishes. Otherwise, K 1 = K 1 + 1 and K 2 = K 2 + 2 and the process is repeated until the Cmax (S) can be improved or up to K 1 = n − 2.

4 Computational Experiments and Analysis of Results Computational experiments were carried out to compare the performance of both heuristics. The heuristics were coded in Python and run on a PC with processor AMD Ryzen 7 4700U 2.0 GHz and RAM 8 Gb. Job processing times were generated from a uniform distribution with parameters 1 and 100. The α values were fixed to be −0.152, −0.322, and −0.515, while the values of β were fixed to be 0.25, 0.50, and 0.75. These are the most common values referred to in the dataset benchmark [25]. A full factorial experimental design was carried out evaluating the four cases of learning effect. The number of workers was set to be m = 5 and 10, and the number of jobs n = 20 and 50. Each combination was encoded such as Case_m_n_α_β (for example, C1_5_100_-0.515_0.25, corresponds to Case 1 with 5 workers, 100 jobs, α = -0.515 and β = 0.25). A total of 10 instances for each combination of factors was considered, as well as three repetitions per instance. A summary of the experimental design is provided in Table 1. To compare the quality of the solution obtained of NEH algorithm with the local search operators API and NAPI, experiments have been carried out. Once the results were obtained, the variable answer was transformed, giving the relative deviation percentage (R D P) as the response variable of the experiments, computed as follows:

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Table 1 Experimental design summary Combinations or blocks (144)

Factor

Parameter

Levels

Values

m

2

5,10

n

2

20,50

Cases of learning effects

4

Case 1, 2 3 and 4

α

3

−0.152, −0.322, −0.515

β (for Case 2 and 4)

3

0.25, 0.5,0.75

LS operators

2

API, NAPI

Total instances per Block

(10 * 144) = 1440

Total instances per Block x Treatments

21 * 1440) = 2880

RDP =

Si − S ∗ S∗

(1)

where Si is the solution obtained with the NEH+LS operator for each combination, S ∗ is the lowest makespan value for each combination in any experiment. The experiments were analyzed by an Analysis of Variance (ANOVA). Table 2. ANOVA results presents the results. The effect of local search operator appears to be significant (p-value < 0.05). As well as it was possible to argue that there is a significant difference (p-value < 0.05) between the CPU time obtained with the NEH with API and NAPI local search operators. Table 3 shows the performance of results of the NEH with API and NAPI operator. Since the stop criterion is the max number of iterations set to 50. Figure 2 shows that the NEH algorithm performs better with API than with NAPI local search operator. Thus, the percentage of deviation from the best solution found (RDP) on average is better by combining the NEH with API local search operator. Table 3 shows the average results, combining NEH with API and NAPI local search operator. In addition to Fig. 2, the CPU time is significantly higher when using the local NAPI search operator. For example, considering the combination C3_10_20_-0.152_0.75, Fig. 3 shows the performance of NEH using the API and NAPI local search operators, taking three instances per combinations respectively (I2, I2 and I3). As shown, the makespan value is the smallest for algorithms that use the API operator. It was also noted that the improvement over the solution is achieved in the first iterations; so larger number of iterations could be unnecessary. This can be the result of the fact that the proposed algorithm has only intensification operators, but it does not include diversification operators, which allow to leave local optimal solutions. The lowest performance of Table 2 ANOVA results

F value Block Local_search

P-value

101.6

1, l ∈ L

i−1

) ( D ji ≥ Dki + U jil − M 3 − X jki − Y jil − Ykil ∀ j, k ∈ A |k /= j, i ∈ I, l ∈ L

( D ji ≥ Dk i+1 − M 3 − X j

k i+1

− Yj

i+1 l

− Yk i+1 l

(16)

(18) (19)

) (20)

.

∀ j, k ∈ A |k /= j, i ∈ I |i < 4, l ∈ L ) ( Dki ≥ D ji+1 − M X j k i+1 − M 2 − Y j i+1 l − Yk i+1 l . ∀ j, k ∈ A |k /= j, i ∈ I |i < 4, l ∈ L

(21)

Cmax ≥ Di4 ∀ j ∈ A

(22)

Cmax , D ji ≥ 0 ∀i ∈ I, j ∈ A

(23)

X jki , Y jil ∈ {0, 1} ∀ j, k ∈ A, i ∈ I, l ∈ L

(24)

.

.

.

Constraint set (13) ensures that each aircraft uses a suitable vertiport infrastructure component per stage. Constraint set (14) observes the earliest landing time for each aircraft, while Constraints (15) observe the latest landing time. Constraint set (16) observes the minimum separation time between consecutive landing aircraft. Constraint set (17) computes the aircraft departure time from the TLOF pad. Constraint (18) computes the aircraft departure time from the remaining stages (taxiing to gate, unloading, and taxiing to staging stand). Constraint sets (19), (20), and (21) are the blocking constraints. Constraint set (22) calculates the makespan of the landing operations which is minimized in the objective function. Lastly, constraint sets (23) and (24) define the nature of decisions variables.

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Table 1 Aircraft utilization time in each stage in seconds, adapted from [11] Vertiport operation Aircraft type Small Medium Large Staging stand to gate taxi-time (s) Loading/unloading time (s) Gate to TLOF pad taxi-time (s) Preparation time at TLOF pad (s)

5–30

30–60

60–90

30–90

90–150

150–210

5–30

30–60

60–90

30–90

90–150

150–210

4 Computational Experiments and Results We consider a heterogeneous fleet with three types of aircraft as follows. First, the Hyundai’s S-A1 model, a large sized air taxi with a capacity of four passengers [14]. Second, the Volocopoter, a medium sized air taxi for two passengers [15]. Last, the Airbus Vahana, a small sized, self-piloted aircraft [17]. To ensure an adequate minimum lateral separation distance and avoid two or more aircraft simultaneously in the vertical flight phase at the same TLOF pad, we set a separation time of 90 s, as stated by the work of [17]. The utilization time for each type of aircraft in each stage is obtained using a discrete uniform distribution based of the values estimated by [11] and shown in Table 1. Last, we tested two vertiport size configurations as follows. The first comprises one taxiway 1 (from the stating stand area to the gates) and one taxiway 2 (from gates to TLOF pads). Besides, it has three gates: one small gate, one medium, and one large. Last, we considered three TLOF pads, one small, one medium, and a large. The second configuration maintains the number of taxiways of configuration one but increases the number of gates and TLOF pad as follows. A total of six gates: two small, two medium and two large. Six TLOF pads: two small, two medium, and two large. We performed ten replications for each instance, totaling 110 runs, varying the number of vehicles and vertiport configurations. As Gantt diagrams, Fig. 2 presents the solution of one take-off and one landing instance of nine vehicles (three small-sized, three medium-sized, and three large-sized). Different models’ features are illustrated in the Gantt diagrams. First, the blocking constraints guarantee that the aircraft remains in its current infrastructure component until the assigned component of the next stage is available. It generates waiting times denoted in gray in the Gantt diagrams. Another model’s feature is the separation rules at the TLOF pads. Aircraft take-off or land with at least 90 s of difference from the previous aircraft of the same TLOF pad. Tables 2 and 3 present the minimum, average, and maximum results of the objective function and computational time for each vertiport configuration considering all instances for the problems at hand. Different conclusions can be drawn from the information contained in these tables. First, the computational time increases when solving large-sized problems.

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Fig. 2 Example solution of nine vehicles for the take-off (above) and landing (below) Table 2 Descriptive statistics of experimental results for the take-off problem Config. .n Makespan (s) Computational time (s) Min. Average Max. Min. Average Max. 1

2

6 9 12 15 6 9 12

595 742 914 1063 561 681 811

623.8 784.2 950.8 1103.9 596.6 720.4 845.3

694 831 991 1138 652 753 890

0.314 1.783 11.126 269.144 1.196 6.487 602.337

0.6243 2.717 31.1239 1227.4 1.7611 16.9 2124.1

0.776 3.697 61.645 2455.9 2.067 29.982 6858.5

Table 3 Descriptive statistics of experimental results for the landing problem Config. .n Makespan (s) Computational time (s) Min. Average Max. Min. Average Max. 1

2

6 9 12 15 6 9 12

563 731 902 1061 517 649 797

610.3 780.4 936.1 1101.3 570.9 699 828

644 793 948 1123 601 739 840

0.432 1.233 14.985 565.4 0.453 3.077 31.791

0.6007 2.2527 33.4 3897.7 0.68 3.94 152.1

1.003 3.418 75.259 12839.8 1.03 6.101 312.107

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Moreover, the computational time increases when solving instances of vertiports with more infrastructure components, even if the number of vehicles and their processing times remain the same remain the same. Furthermore, the objective function decreases with a vertiport with more infrastructure components.

5 Conclusions and future work With the latest technological advances in electric vertical take-off and landing vehicles and the private and public interest in expanding UAM services, the urban skies will be crowded with AAM aircraft transporting people and cargo. A crucial aspect of this expansion is the management of eVTOL take-off and landing zones known as vertiports. In this context, we have addressed the problem of aircraft sequencing and scheduling in vertiports. We presented an integer linear programming model to plan such operations considering minimum separation rules, landing time windows, and avoiding aircraft simultaneously using the same vertiport infrastructure. One limitation when conducting the experiments is computational execution time. Larger instances with more aircraft and infrastructure components would require approximate solution methodologies. After this study, multiple opportunities for future research arise. For example, address other objective functions, such as minimizing the maximum delay. In addition, future researchers can consider other decisions such as the vertiport location and fleet assignment.

References 1. Research and Markets, Urban Air Mobility Market By Component (Infrastructure, Platform), By Operations (Piloted, Autonomous, Hybrid), By Range (Intercity, Intracity), and By Region, Forecasts to 2030, https://www.marketsandmarkets.com/Market-Reports/urban-air-mobilitymarket-251142860.html. Last accessed 16 June 2022 2. Thipphavong, D.P. et al.: Urban air mobility airspace integration concepts and considerations. In: 2018 Aviation Technology, Integration, and Operations Conference. American Institute of Aeronautics and Astronautics (2018). https://doi.org/10.2514/6.2018-3676 3. Holden, J., Goel, N.: Fast-Forwarding to a Future of On-Demand Urban Air Transportation. UBER 1–98 (2016) 4. Kleinbekman, I.C., Mitici, M.A., Wei, P.: eVTOL arrival sequencing and scheduling for ondemand urban air mobility. In: 2018 IEEE/AIAA 37th Digital Avionics Systems Conference (DASC), pp. 1–7. IEEE (2018). https://doi.org/10.1109/DASC.2018.8569645 5. Kleinbekman, I.C., Mitici, M., Wei, P.: Rolling-horizon electric vertical takeoff and landing arrival scheduling for on-demand urban air mobility. J. Aerosp. Inf. Syst. 17, 150–159 (2020). https://doi.org/10.2514/1.I010776 6. Kim, S.H.: Receding Horizon scheduling of on-demand urban air mobility with heterogeneous fleet. IEEE Trans. Aerosp. Electron. Syst. 56, 2751–2761 (2020). https://doi.org/10. 1109/TAES.2019.2953417 7. Shao, Q., Shao, M., Lu, Y.: Terminal area control rules and eVTOL adaptive scheduling model for multi-vertiport system in urban air mobility. Transp. Res. Part C Emerg. Technol. 132, 103385 (2021). https://doi.org/10.1016/j.trc.2021.103385

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8. NUAIR, Crown Consulting, Mosaic ATM & NASA. High-Density Automated Vertiport Concept of Operations. https://ntrs.nasa.gov/citations/20210016168. Last accessed 16 June 2022 9. Justin, C.Y., Payan, A.P., Briceno, S.I., German, B.J., Mavris, D.N.: Power optimized battery swap and recharge strategies for electric aircraft operations. Transp. Res. Part C Emerg. Technol. 115, 102605 (2020). https://doi.org/10.1016/j.trc.2020.02.027 10. Garrow, L.A., German, B.J., Leonard, C.E.: Urban air mobility: a comprehensive review and comparative analysis with autonomous and electric ground transportation for informing future research. Transp. Res. Part C Emerg. Technol. 132, 103377 (2021). https://doi.org/10.1016/j. trc.2021.103377 11. Vascik, P.D., Hansman, R.J.: Development of vertiport capacity envelopes and analysis of their sensitivity to topological and operational factors. In: AIAA Scitech 2019 Forum. American Institute of Aeronautics and Astronautics (2019). https://doi.org/10.2514/6.2019-0526 12. Ruiz, R., Vázquez-Rodríguez, J.A.: The hybrid flow shop scheduling problem. Eur. J. Oper. Res. 205 (2010). https://doi.org/10.1016/j.ejor.2009.09.024 13. Mollaei, A., Mohammadi, M., Naderi, B.: A bi-objective MILP model for blocking hybrid flexible flow shop scheduling problem: robust possibilistic programming approach. Int. J. Manag. Sci. Eng. Manag. 14, 137–146 (2019). https://doi.org/10.1080/17509653.2018.1505565 14. Hyundai.: Hyundai and Uber Announce Aerial Ridesharing Partnership, Release New FullScale Air Taxi Model at CES. https://www.hyundai.com/worldwide/en/company/newsroom/0000016369. Last accessed 16 June 2022 15. Volocopter.: VOLOCITY The air taxi that’s a cut above. https://www.volocopter.com/en/ product/. Last accessed 16 June 2022 16. Airbus.: AIRBUS Vahana. https://www.airbus.com/innovation/zero-emission/urban-airmobility/vahana.html. Last accessed 16 June 2022 17. Goodrich, K.H., Barmore, B.: Exploratory analysis of the airspace throughput and sensitivities of an urban air mobility system. In: 2018 Aviation Technology, Integration, and Operations Conference. American Institute of Aeronautics and Astronautics (2018). https://doi.org/10. 2514/6.2018-3364

Inter-cities Model Proposal for Potato’s Last Mile Logistics: Case Study in Bogotá, Colombia and Cochabamba, Bolivia Camilo Ernesto Bejarano Cubillos, Juan David Chavarrio Rojas, Valentina Gama Gutiérrez, Loredana Angélica Orellana Delgadillo, Paola Andrea Ospina Baracaldo, María Alejandra Rojas Trigo, Agatha Clarice da Silva-Ovando, and Gonzalo Mejía

Abstract This paper presents a mathematical model of a potato supply and distribution chain in Latin America. We formulate a model for the distribution process from a set of potato producers to a set of nanostores (small retailers, common in Latin American countries) in both Bogotá, Colombia, and Cochabamba, Bolivia. In this model, we located a set of warehouses to consolidate and facilitate the distribution. The objective function was to minimize the sum of all costs subject to capacity, demand satisfaction, and coverage constraints. This model was implemented on the GAMS software; the results were translated into valuable information used to give shape to the distribution chain and to perform an analysis to further understand how the change in some of the input data could affect the optimal solution. The results show that even though the model implemented in both countries is the same, the results obtained are widely different because of each country’s characteristics. This research opens the doors for future research that might consider traffic in the cities, criteria for the availability of producers, and even a vehicle routing solution for the delivery trucks. This model was developed jointly by students of Universidad de La Sabana and of Universidad Privada Boliviana as a part of a COIL (Collaborative Online International Learning) project. Keywords Collaborative online learning · Fresh food supply chain · Potato supply chain C. E. Bejarano Cubillos · J. D. Chavarrio Rojas · V. Gama Gutiérrez · P. A. Ospina Baracaldo · A. C. da Silva-Ovando (B) · G. Mejía Universidad de La Sabana, Campus Universitario Puente del Común. Autopista Norte de Bogotá Km 7, Chía, Colombia e-mail: [email protected] G. Mejía e-mail: [email protected] L. A. Orellana Delgadillo · M. A. Rojas Trigo · A. C. da Silva-Ovando Centro de Operaciones Logísticas, Universidad Privada Boliviana, Campus Julio León Prado, Av. Capitán Víctor Ustariz, Km. 6.5, Cochabamba, Bolivia © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. R. Montoya-Torres et al. (eds.), Operations Research and Analytics in Latin America, Lecture Notes in Operations Research, https://doi.org/10.1007/978-3-031-28870-8_9

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1 Introduction Many countries all over the world, especially in Latin America, suffer from the consequences of having a large chain of intermediaries between farmers in the countryside and the consumers. This inefficient supply chain causes spoilage and loss of food [1]; at the same time, it also increases the prices for the clients, create problems of handling and transportation and generates low profits for the producers; while the intermediaries are the ones who perceive higher profits in the whole chain [2]. The project’s objective is to find a way to reduce the number of links in a food supply chain and optimize the distribution processes; therefore, we propose the opening of distribution centers to build a direct bridge between farmers and their consumers, most specifically between farmers and nanostores. This paper focuses on potato distribution which is one of the most important tubers both in Colombia and in Bolivia. This product is not only part of their basic basket; but it also represents culture and tradition in the region. Many studies show that in the coming years, the demand for this tuber will increase [3, 4]; that is why we need to optimize the supply chain in both countries. Generally speaking, the potato chain has between 6 and 8 intermediaries from farm to end consumer. A possible alternative to reduce intermediation is the use of food distribution centers or logistics hubs located in peri-urban areas. This alternative has been suggested and partially implemented in Bogotá. The questions that arise are (i) how many DCs are needed and (ii) where they should be located. The purpose of this paper is to answer to these questions.

2 Literature Review 2.1 Distribution Methods for Fragmented Markets In Latin America, nanostores dominate the retail landscape [5]. However, the distribution to these businesses is very expensive and inefficient. This does not only limit the inefficient operation of small points of sales but also pinpoints their infrastructural and financial limitations to purchase and store larger amounts of products [5, 6]. For that reason, innovative logistics models must be used to generate a tailored alternative to these channels. In this direction, many new alternatives proposed are focused on the implementation of technologies and online solutions to improve service quality [5, 7, 8]. Even though the use of technology will be determinant to design more efficient and responsive supply chains, the design of a multi-tier network design for channels spread along a region is important to generate solutions in the last mile [6, 9]. Multi-tier systems are highly beneficial for emerging economies where the population density

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is high. These structures allow the combination of different sizes and types of vehicles, helping to reduce the distribution costs, improving operational efficiency, and overcoming restrictions of access [6]. The Urban logistics spaces (ULS) are spaces that play a key role in the distribution of various types of products to fragmented and densely populated regions [6]. Depending on their design, they may be platforms near the city centers as Urban consolidation centers (UCCs), or as nearby delivery areas (NDAs) in the outskirts of main towns [9]. UCCs are operatively costly and require a higher interaction among actors to work together. NDAs, on the other hand, present coverage limitations, but their operation is cheaper than the previous [9].

2.2 Fresh Food Distribution Models Fresh products by themselves have a higher level of complexity in their supply chains. In these supply chains, producers and consumers generally are not directly connected, and coordination depends mostly on intermediaries. This fact leads to low levels of coordination among different echelons in the supply chain, and most intermediaries obtain large margins due to such lack of coordination [10, 11]. Many authors approached the concept of sustainable supply chains for fresh food. However, the development of models for emerging countries is still limited, compared to developed regions. Primarily, models consider distance among authors as the main factor. However, in this supply chain, other variables may play a relevant role. For example, freshness is one of the factors considered by authors to model this type of supply chains [12]. Another recent trend regards the environment. Chen et al. [13] expands the models considering the CO2 emissions as a relevant factor as well. The complexity and difficulties of the supply chain can be modeled as well, looking to reduce its inefficiency and variability regarding the food loss during distribution processes [10, 14]. In latest models, e-commerce and the use of artificial intelligence can be found, as presented by Wu and Lamiae et al. [15, 16].

3 Methodology 3.1 Data Collection Nano Stores The observation was used as a method to determine which stores were a fit for what we define as a nano store, which is a small retailer of a varied assortment of household products. All the stores in Bolivia were pinned through Google Maps, where we could find their respective coordinates. On the other hand, in Colombia,

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we used the app “Tienda Cerca” to pin all the stores in a determined area, where we could find their coordinates too.

3.2 Data Recollection for Farmers and the Distribution Centers The farmers were located with the help of the QGIS software, where we determined their locations by approximating to producing regions. Therefore, in both countries, we chose a determined zone known to produce potatoes, obtaining the coordinates of each farmer respectively. We used the same method to determine all the possible distribution centers. Having all the coordinates to the three types of points we establish and the respective distance between them.

3.3 Mathematical Model We used linear programming coded in the GAMS software. We considered productivity, capacity, distance, and availability constraints. The problem is a variant of the well-known facility location problem in which the objective function was the cost minimization subject to the above constraints.

4 Numerical Setting In both Bogotá (Colombia) and Cochabamba (Bolivia), we located 100 nanostores in the city area. We sought both transited and commercial areas respectively. Based on the division of retailers made by the Logistics Capacity Assessment LCA [17], we assigned one of the five categories to each nano store. For each category, we determined the approximated demand for the store. Using this, we calculated the total demand of each city. For each country, we pinned a total of 100 possible farmers and assigned each one a different capacity of production based on a self-made simulation of probabilities, all according to different historical data found in both countries [18–20]. For the distribution centers, we used the same methodology, having 50 possible centers in each country, from which we would choose as many as necessary. Finally, to define the capacity we based the results on the following formula [21]. Required space (ft2/month) = Monthly demand Lb. × 0.029762

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Fig. 1 Nanostores, centers of distribution and farmers at Cochabamba, Bolivia

The prices we used were according to each country’s real estate rate, in Bolivia 10 $/m2 and in Colombia 25.000 pesos/m2 . Figure 1 (Cochabamba) and Fig. 2 (Bogotá) show the location of the farmers, distribution centers, and nanostores.

5 Mathematical Model This section describes the mathematical model which we formulated as a mixedinteger linear program. Sets: I Set of farmers indexed in i. J Possible location’s group for distribution centers. K Retailers group. Data: fj Demk qpi qj aij

Operation cost for distribution center. Potatoes’ demand of customers of the retailer k. Storage capacity of farmer i. Storage capacity of possible distribution center j. 1 if farmer i is inside the coverage radio of the possible distribution center (CD) j; 0 otherwise. CapTruck Truck capacity.

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Fig. 2 Nanostores, centers of distribution and farmers at Bogotá, Colombia

Covert Factor

M

CD’s minimum coverage level***. Proportionality factor that establishes the assumption that the operation cost of a distribution center is approximately 50% of the renting cost of the distribution center. Big number.

Variables: yi xj Eij Sjk NoTruckjk tottransp

1 if farmer i is covered by at least one of the open DC’s. 1if CD open; 0 otherwise. Quantity of potatoes sent from the farmer i to the DC j. Quantity of potatoes sent from the CD j to the retailer k. Number of trucks sent from the CD j to retailer k. Total cost in transportation between CD’s and retailers.

Obj =



f j × f actor × x j + tottransp j

j∈J



S jk = Dem k ∀k

(1)

j∈J

 i∈I

Ei j =

 k∈K

S jk ∀ j

(2)

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E i j ≤ qpi ∀i

(3)

S jk ≤ q j x j ∀ j

(4)

j∈J

 k∈K

N oT r uck jk ≥ Cap × S jk ∀ j, k  i

yi ≥ Cover t × 100% 

(5) (6)

ai j x j ≥ yi ∀i

(7)

ai j x j ≤ M y i ∀i

(8)

j

 j



Ei j ≤ M x j ∀ j

i

100yi ≤



E i j ∀i

(9) (10)

j

  j

S jk ≤ M j ∀ j

(11)

k

2 × Ctr × D jk × N oT r uck jk = tottransp

(12)

k

E i j ≤ Ma i j x j ∀i, j

(13)

Total cost is the result of adding the renting cost of the open distribution center(s) and the total transporting cost between the farmers and the possible distribution centers and between the possible distribution centers and the retailers. Constraint set (1) is related to the satisfaction of the demand of each covered retailer, where the sum of all the shipments from all the open distribution centers to a retailer must be equal to the demand of the retailer. Constraint set (2) defines the balanced relationship of arrives and shipments of all the open distribution centers, where the sum of all the arrives from all the farmers covered, must be equal to all the shipments to all the retailers. Constraint set (3) establishes that all the shipments from a farmer must be less or equal to the maximum production capacity of this farmer. Constraint set (4) establishes that the capacity of each distribution center must be greater or equal to the sum of the shipments from each distribution center to the covered retailers. Constraint set (5) determines the number of trucks sent from each covered farmer to each open distribution center, where the number of trucks must be greater or equal to the ratio between the shipment size from the farmer to the

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distribution center and the truck’s capacity. Constraint (6) is related to the minimum proportion of covered farmers, where the number of covered farmers must be greater or equal to the desired minimum proportion of farmers covered by multiplying the size of the set of farmers. Constraint set (7) defines that a farmer is covered only if there is at least one open distribution center that covers this farmer. Constraints set (8) establishes that is enough to have an open distribution center to cover a farmer. Constraint set (9) determines that there cannot be arrivals to a distribution center that is not open. Constraint set (10) establishes that if a farmer is covered, he must send at least 100 kg of potatoes to the retailers. Constraint set (11) determines that there cannot be shipments from a distribution center that is not open. Constraints (12) define the transport costs, which are counted as the number of trucks that are going from one point to another, the distance that they are driven, the cost per kilometer, and the round-trip. Constraint set (13) establishes that there cannot be shipments from a farmer to a distribution center if the farmer is not covered by the distribution center in question or if the distribution center is not open. Further considerations of the model. Constraint set (5) assumes that identical trucks with the same capacity are used to simplify the model. Constraint 6 guarantees that the minimum percentage of farmers covered is met, if the minimum desired percentage of farmers covered is 90%. Constraint set 10 guarantees that if a farmer is sending potatoes to one or more distribution centers, each shipment size must be greater or equal to 100 kg to ensure that the shipment travel is not being sub used. The binary table aij models the coverage of a farmer in terms of the distance between the farmer i and the distribution center j, assuming that no farmer will be willing to travel more than 30 km to any DC.

6 Results The results of the mathematical model show that only one distribution center will be opened in each country. In Colombia’s case, the chosen distribution center has a capacity of 18 tons, 602 square meters, and rent of USD 4112, for this country the model gives a 99% farmer coverage rate. The chosen DC is located in an area that’s in between the retail stores and the farmers as we see in Fig. 3. In Bolivia’s case, the chosen distribution center has a 3.8-ton capacity, a rent of USD 5070, and 507 square meters. In this case, the DC is closer to the stores than to the farmers and the coverage rate is 100% as we see in Fig. 4. In both cases the results seem to be similar, however, they differ in how the total costs are composed, as shown in Table 1. The cost of opening the distribution center for Colombia is of $6285, cheaper than the $7605 that it costs to open the one in Bolivia, a predictable result because of the difference in real states’ costs in each country, being Colombia’s 6 $/m2 less expensive than Bolivia’s 10 $/m2 . The cost of transportation in Colombia is $28,758 due to the distance from the distribution center to the stores. On the other hand, Bolivia has a very low cost since

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Fig. 3 Nanostores, chosen center of distribution and farmers at Bogotá, Colombia

the distance from the distribution center to the stores is much shorter. This is why in Bolivia the total cost is $9036 against the $35,043 of Colombia. Table 2 shows how costs are divided in each country and shows the difference in the model results. It is evident that there is a big difference in the cost composition between the two countries. The main reason is the big distances from the DC to the stores in Colombia, these are larger than the ones in Cochabamba and make the transportation cost very high which then translates into a higher operation cost for the Colombian network. Also, the optimal result shows only one distribution center should be opened in each network, this is because the selected DCs have the capacity to supply all of the network’s demand, eliminating the need and the additional cost of opening and operating another DC. This is also influenced because the cost of operating another DC is higher than the savings it could cause on the transportation costs. The size of these distribution centers is small given that only one product and only a portion of the potential farmers were considered. A realistic case would include more products and a larger number of farmers.

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Fig. 4 Nanostores, chosen center of distribution and farmers at Cochabamba, Bolivia

Table 1 Costs comparison between countries

Table 2 Cost percentage between countries

Cost (USD/week)

Colombia

Bolivia

Distribution center

$6285

$7605

Transportation

$28,758

$1431

Total

$35,043

$9036

Cost (USD/week)

Colombia (%)

Bolivia (%)

Distribution center

18

84

Transportation

82

16

100

100

Total

7 Future Research The results obtained from the research open the doors to future research and improvement of the current work. Vehicle routing could be used to decrease transportation costs since the current model is using one truck from the distribution center to each of the nano stores, with vehicle routing a single truck could be used to provide various demand points; besides it would also be useful for cities like Bogotá which have very

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heavy traffic. On the other hand, criteria of minimum potato order quantity could be established for each farmer, this to take into account that according to the distance between the farmer and the distribution center for some farmers it won’t be viable to cross the distance for little order quantities. Finally, in future research traffic conditions (time in traffic and infrastructure of roads) could also be considered as a factor to determine the distribution center that will be opened.

8 Conclusions Throughout the analysis carried out it is possible to conclude that the proposed model is feasible to be applied and that despite being the same model, applied in two different countries the results differ significantly due to the conditions of each territory. This means that with a better data gathering the proposed model can be applied to any country or city and that the results may change depending on the specific geographic and economic conditions of the selected location. This is very relevant since the model directly connects nano-stores to farmers in an efficient way that could be further refined by considering time in traffic and other specific conditions that could be relevant in the context. This means further studies should include traffic conditions and even vehicle routing to further increase the model´s efficiency and reach. However, the proposed solution will always optimize the network´s costs through the selection of the optimal distribution centers to be opened and used to distribute potato or any other perishable product. Acknowledgements The authors of this paper would like to thank Universidad de La Sabana and Universidad Privada Boliviana for their technical and methodological support for carrying out this project. This project was part of the COIL (Collaborative Online International Learning) initiative that brings out together students of different countries working on real life problems.

References 1. Raúl, B.: Pérdidas y desperdicios de alimentos en América Latina y el Caribe. Oficina Regional de la FAO para América Latina y el Caribe, [En línea]. https://www.fao.org/americas/noticias/ ver/es/c/239393/. Accessed 5 Aug 2022 2. Gaudin, Y., Padilla, R.: Los intermediarios en cadenas de valor agropecuarias. Comisión Económica para América Latina y el Caribe (CEPAL), no. 186 (2020) 3. Colombia: El consumo per cápita de papa durante el 2020 se incrementó un 31% respecto a 2019. Argenpapa, 3 junio 2021. [En línea]. https://www.argenpapa.com.ar/noticia/10758colombia-el-consumo-per-capita-de-papa-durante-el-2020-se-incremento-un-31-respecto-a2019. Accessed 6 Aug 2022

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4. Entre el arroz y la papa, los alimentos que más consumen los colombianos. San Martín Fundación Universitaria, 10 diciembre 2020. [En línea]. https://www.sanmartin.edu.co/1/ noticias/entre-arroz-y-papa-alimentos-que-mas-consumen-colombianos/#:~:text=As%C3% AD%20mismo%2C%20se%C3%B1alan%20que%20el,kilogramos%20en%20el%20medi ano%20plazo. Accessed 6 Aug 2022 5. Escamilla: Improving Agility, Adaptability, Alignment, Accessibility, and Affordability in Nano Store Suplly Chains (2020) 6. Fransoo: Reaching 50 Million Nano Stores (2017) 7. Seitz: Online Grocery Retailing in Germany: an Explorative Analysis (2017) 8. Droogenbroeck, Hove, V.: Adaptation and Usage of E-Grocery Shipping: A Context-Specific UTAUT2 Model (2021) 9. Merchan: Transshipment networks for last-mile delivery in congested urban areas. In: 6th International Conference on Information Systems, Logistics and Supply Chain (2016) 10. Rakesh, P., Sunil, A.: A mathematical model formulation to design a traditional Indian agri-fresh food supply chain: a case study problem. Benchmark Int J 27(8), 2341–2363 (2020) 11. Bruzzone, M.M., Bocca, E.: Fresh-food supply chain. In: Merkuryev, Y., Merkuryeva, G., Piera, M., Guasch, A. (Eds.) de Simulation-Based Case Studies in Logistics. Springer, London (2009) 12. Zhang, J., Fu, S.: Study on location of fresh food distribution center with demand influenced by the. In: de The 4th International Conference on Operations and Supply Chain Management, Hongkong & Guangzhou (2010) 13. Chen, J., Gui, P., Ding, T., Na, S., Zhou, Y.: Optimization of transportation routing problem for fresh food by improved ant colony algorithm based on Tabu search. Environ. Sustain. Appl. 11(23), 6584 (2019) 14. Zhao, Z., Li, X.: Optimization of transportation routing problem for fresh food in time-varying road network: considering both food safety reliability and temperature control. PLoS ONE (2020) 15. Wu, X.: Optimization of distribution mode of the fresh food logistics front warehouse from the perspective of intelligent logistics. In: 2021 IEEE Conference on Telecommunications, Optics and Computer Science (TOCS), pp. 307–311 (2021) 16. Lamiae, D., Jabri, A., El Barkany, A., Darcherif, A.: Optimization of fresh food distribution route using genetic algorithm with the best selection technique. In: de Constraint Handling in Metaheuristics and Applications, Springer, Singapore (2021) 17. L. C. A. LCA: Logistics Capacity Assessment. Atlassian Confluence, [En línea]. https://dlca. logcluster.org/display/public/DLCA/3.5.1+Bolivia+Proveedores+de+Alimentos 18. E. L. República: La Replública. [En línea]. https://www.larepublica.co/empresas/tiendas-debarrio-equivalen-al-21-de-los-comercios-en-colombia-segun-informe-2539861 19. López, R.: Captura Consulting. [En línea]. https://www.capturaconsulting.com/estructura-delretail-tradicional-en-bolivia/ 20. Guarín: Análisis Socioeconómico de Tiendas de Alimentos en Áreas Urbanas de Bajos Recursos. Organización de la Naciones Unidas para la Alimentación FAO (2009) 21. López, S.: Ingeniería Industrial Online (2019). [En línea]. https://www.ingenieriaindustrialo nline.com/gestion-de-almacenes/dimensionamiento-de-almacenes/

Applications in Humanitarian and Health Logistics

Road Prioritization for the Reconstruction of an Area Affected by a Disaster Lorena S. Reyes-Rubiano

and Elyn Solano-Charris

Abstract In this paper, we consider the problem of prioritization of road reconstruction in a disaster-affected rural network. We propose a solution based on a labeled network that aims to maximize the accessibility to victim locations. The proposed solution approach uses a labeled network in which the edges have an assigned priority. The labeled network refers to the road network, where each road edge has a value representing the road prioritization for recovery. We propose two criteria, road travel time and connectivity, to determine which roads should first be recovered to improve road access to victim locations. We present numerical studies using artificial instances with different disruption levels. The results indicate that the best prioritization criteria depend on the location of the disaster management center and disruption level. In addition, this paper provides insights on using flow network properties to design criteria for considering the structure of the damaged road network. Keywords Labeled network · Road recovery · Road accessibility · Connectivity · Node degree

1 Introduction Disasters are unexpected events characterized by a negative impact on lives lost and high logistical costs during and after the disaster. The impact of a disaster can be estimated by analyzing the affected population and the magnitude of the disaster. We are interested in determining strategies to deal with the impact of a disaster on L. S. Reyes-Rubiano (B) · E. Solano-Charris International School of Economics and Administrative Sciences, Universidad de La Sabana, Chía, Colombia e-mail: [email protected]; [email protected] E. Solano-Charris e-mail: [email protected] L. S. Reyes-Rubiano Chair of Data & Business Analytics, RWTH Aachen University, Aachen, Germany © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. R. Montoya-Torres et al. (eds.), Operations Research and Analytics in Latin America, Lecture Notes in Operations Research, https://doi.org/10.1007/978-3-031-28870-8_10

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accessibility to victim locations, such as villages. Disasters generate disrupted roads such as collapsed bridges or blocked roads which hinder the relief of victims. The number of studies concentrating on the recovery operation is scarce. Çoban et al. [8] provide an overview of post-earthquake recovery operations for a road network affected by a disaster. The authors state that there is a research GAP in mapping operations in a post-disaster situation. The authors recognize that there is a lack of methodologies able to process information in real-time to make mapping decisions. Briskorn et al. [3] give insights into the recovery operations for a road network. The authors state the decision to recover a road depends on the expected recovery time. Maya and Sörensen [5] consider the road travel time as a criterion to determine which roads need to recover to maximize the road accessibility to victim locations. The authors define accessibility as the number of inhabitants that can be reached using the road network. Bešinovi´c et al. [1] are studying the recovery of the public transport network. The solution approach focuses on determining where to include extra resources to recover passenger flow. Bešinovi´c et al. [1] define the reconstruction criteria by a scenario-based method. The authors evaluate different reconstruction scenarios. The solution is determined by the scenario that minimizes the negative impact of disruptions on the public transport network. Akvari et al. [2] study how to recover a disrupted road network. The authors propose a time-weighted graph and aim to reconnect all nodes in the road network within a minimum time. In summary, the road network recovery decisions are tackled by (1) adding new resources to recover passenger flow through the road network; (2) recovering the roads first with a short travel time; or (3) recovering the roads first that requires a short recovering time. The problem addressed in this paper is to determine a criterion for determining which roads should be recovered within 72 h after the disaster [7]. The objective is to improve accessibility for victims, given a maximum budget to recover roads. Road recovery involves operations from debris removal to road reconstruction. We assume that all recovery and rescue operations are deployed from a disaster management center (DMC). We assume that the DMC functions as an administrative center where recovery operations are coordinated. It is assumed that the set of disrupted roads in the road network is known with certainty. Thus, we define accessibility as the number of victims that can be reached from the DMC using the road network. The road network contains the DMC, victim locations, and road crossings locations. Recovery decisions depend on the number of disrupted roads in the network and the resources available to conduct road recovery. We pose the following research question: How to determine which routes should be recovered first given a limited amount of resources and the objective to maximize accessibility to victim locations?

To answer this research question, we propose a labeled network to determine the relevance of each road edge in terms of accessibility to victim locations. We consider two criteria, i.e., road connectivity and road travel time. The road connectivity criterion aims to catch the relevance of each road. The road travel time criterion indicates how long it takes to visit the road. Thus, each road edge has a label representing its importance regarding accessibility to the victim locations in terms of connectivity

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Fig. 1 Disrupted road network

and travel time. We contribute to the literature by proposing the connectivity criterion to prioritize the recovery of roads leading to reaching victim locations. Additionally, this paper compares the connectivity criterion against the traditional criterion, the road travel time. The rest of this paper is structured as follows. In Sect. 3 presents our solution approach. Section 4 provides a description of the artificial instances and experiments addressed. The solution approach is presented in Sect. 3. The computational results are provided in Sect. 4.2. Finally, Sect. 5 presents the main conclusions and proposes future work.

2 Problem Description The problem addressed is determining which streets should be repaired first to improve accessibility to the victim locations. In the disaster response phase, not all the necessary resources are available to recover the roads affected by the disaster. In the first instance of a disaster, it is crucial to be selective about which roads need to be repaired first to improve response operations. Figure 1 exemplifies a disrupted road network with multiple paths from the DMC to each victim location. Not all paths benefit accessibility to all victims. The objective of this paper is to determine a strategy for deciding which roads to repair first to improve accessibility to victims and contribute to the efficient deployment of humanitarian aid.

3 Labeled Network The labeled network refers to the road network in the pre-disaster phase, the edges represent roads, and the nodes represent facilities in the road network. Thus, we can evaluate the relevance of the missing roads to reach the victim locations from DMC. Based on the road network, we define the structure of the labeled network. Each edge in the labeled network has a label that indicates the priority of a road edge to

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Fig. 2 Roads recovered following the connectivity criterion.

be recovered to enhance the road accessibility from DMC to victim locations. We consider the road travel time or connectivity edge to compute the recovery priority. For computing, the labeled network, one of the two mentioned criteria is used. Following, we describe the criteria: . Edge travel time: We compute the shortest path from the DMC to each victim location. Thus, the priority value refers to the road travel time leading to the location of the victims from the DMC. Then, road edges are sorted in ascending order according to the travel time. The first road edges in the list are the first road edges to be recovered. Figure 2 shows the recovered road network based on the travel time criterion. The edge travel time criterion aims at computing a spanning tree with the minimum travel time rooted in the DMC. . Edge connectivity: Based on the ideas presented in [6], this criterion represents the relevance of an edge to reach a victim node from the DMC. This criterion intends to consider the characteristics of the road network, such as node degree, network connectivity, and location of the victim locations. Based on the connectivity criterion, road edges are sorted in descending order. Thus, the edge with the highest value has the highest priority to be recovered. Figure 3 presents the recovered road network following the network connectivity criterion. The connectivity criterion is oriented to repair first the roads connecting nodes that allow reaching the victim locations from the DMC. We compute the travel time and the connectivity criterion as independent criteria. Following the road travel time criterion, we labeled each edge in the road network with its travel time. The road edge with a short travel time has a higher priority to be recovered than road edges with a long travel time. This decision is based on the fact that time-shortest roads may require fewer resources to be recovered. Therefore, recovery decisions aim at recovering a large number of time-shortest roads. The travel time criterion could recover road edges belonging to the time-shortest paths from DMC to all victim locations.

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Fig. 3 Roads recovered following the travel time criterion

Following, we provide more detail about the labeled network based on the connectivity criterion 1. Select all nodes in the road network. 2. Mark the road crossing with a static score .b and victim nodes and DMC with a static score .a. 3. Compute dynamic score for each node. 4. Compute a score for each edge. The edge score is defined by the sum of dynamic scores of origin and end node. 5. Determine the maximum dynamic score over all edges. 6. Compute the connectivity value for each edge. The connectivity is defined by the proportion of the dynamic score of the edge and the maximum dynamic score. The dynamic score is intended to measure the node degree and to indicate the type of nodes adjacent to each node. The dynamic score for each node .n is computed as follows: 1. Select adjacent edges to node .n. 2. Considering the list of adjacent edges as a reference, select the nodes connected to node .n by the adjacent edges. 3. Sum up the static score of node .n and the nodes selected in point 2.

4 Computational Experiments We test our solution approach on a set of 7 artificial instances based on [4]. The number of nodes varies between 20 and 101 nodes. We adjust the instances by randomizing the location of the victims. We assume that 25% of the nodes in the network are victim locations. Table 1 presents the characteristics of the instances. The algorithm is implemented in JAVA and the experiments were run on a personal computer with core i5 and 8 GB RAM.

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Table 1 Characteristics of the tested instances Instance Total nodes Total of victim nodes p1.2.b p5.2.a p7.2.a p3.2.a p4.2.a p2.2.a p6.2.a

32 65 101 32 99 20 63

8 5 8 24 16 15 25

Node degree

DMC location

2.65 3.47 2.45 2.5 2.48 2.5 2.63

Center Center Center Center side Center side Corner Corner

4.1 Experiment Settings In this section, we evaluate the impact of the accessibility percentage for a given budget, a given level of disruption, and a given road prioritization criterion. The algorithm takes almost 30 s to resolve the instance with 101 nodes. The experiments aim to determine the suitable criterion to prioritize the roads that need to be recovered first to enhance accessibility to victim locations. For the experiments, we consider: – Three levels of disruption: We randomly set the disrupted roads. Thus, the level of disruption indicates the share of disputed roads in the road network. – The priority of recovering roads is defined according to the travel time criterion or the connectivity criterion, as described in Sect. 3. – The number of roads to be recovered depends on the availability of the Budget. The budget is measured by the number of roads able to recover. We assume that a Budget is available to recover 25% or 50% of the disrupted roads.

4.2 Experiment Results We want to evaluate the impact of budget and prioritization criteria on the accessibility to victim locations. We compute the average accessibility for each budged, network connectivity, and disruption level over all instances. Figure 4 presents our result. First, we study the scenario in which the decision-maker can only recover the 30% of the disrupted network. The results indicate that the travel time and connectivity criteria reach the same accessibility percentage for network low disrupted. For road networks with a medium disruption level, the connectivity criterion provides an accessibility percentage of almost 68%, and the travel time criterion provides an accessibility percentage of about 72%. However, for the highly disrupted road network, the connectivity criterion provides a better accessibility percentage of 52% than the accessibility percentage of about 42% provided by the travel time criterion. Now, we study the scenario where decision-makers can recover at most 50%

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Fig. 4 Comparison of road prioritization criteria and budget for road recovery

Fig. 5 Comparison of prioritization criteria given a budget to recover 30% of the disrupted roads and DMC located at the center of the road network

of the disrupted road network. The results demonstrate that in scenarios where the decision-maker has enough resources to recover the 50% of the disrupted network, the accessibility is equal to 1 for both criteria. Regarding the impact of the connectivity and travel time criterion on the accessibility percentage, given the specific structure of the road network and a maximum budget enough to recover the 30% of disrupted roads. Considering the location of the DMC specified in Table 1, we present the best criterion to recover roads, given that the DMC is located at the center of the road network. Figures 5, 6 and 7 report the numerical results. Figure 5 presents the results of accessibility percentage for each disruption level over all instances with the DMC located at the center of the road network. The results demonstrate that connectivity is the winner criterion to determine which road should be first recovered to enhance road accessibility to victim locations. Similarly, we study instances where the DMC is located at the center side of the road network. Figure 6 presents the average accessibility percentage obtained with each budget, each network connectivity, and each disruption level over instances where the DMC is located at the center side of the road network. For road networks

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Fig. 6 Comparison of road prioritization criteria given a budget to recover 30% of the disrupted roads and DMC located at the center side of the road network

Fig. 7 Comparison of prioritization criteria given a budget to recover 30% of the disrupted roads and DMC located at the corner of the road network

with a disruption level higher than 50%, the travel time criterion is the best prioritization criterion to recover roads and improve accessibility to victims locations. However, results demonstrate that connectivity is the winner criterion when the road network has a disruption level of up to 30%. Considering instances where the DMC is located at the corner of the road network. Figure 7 shows that the connectivity criterion provides a higher accessibility percentage, in road networks with a disruption level of 0.75. Travel time criterion is the winner criterion for recovering roads in road networks with disruption levels of 0.5 and 0.75. However, when the road is highly disrupted the best criterion for recovering roads is the connectivity criterion with road accessibility of about 42% (Table 2).

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Table 2 Best criterion to determine the road recovery criterion given the location of the DMC and disrupted level Disruption level Best criterion DMC location Center

Center side

Corner

0.25 0.5 0.75 0.25 0.5 0.75 0.25 0.5 0.75

Connectivity Connectivity Connectivity Connectivity Travel time Travel time Travel time Travel time Connectivity

5 Conclusions This paper addresses the problem of determining which road should first be recovered in the post-disaster phase. We consider two criteria to determine the priority for recovering the road network and improving the accessibility to victim locations. We compute the travel time and connectivity for each edge to determine its priority. Priorities for all edges are computed based on travel time or connectivity. We perform a comparison of both criteria. The results demonstrate that after recovering the 50% of the disrupted edges, all victim locations are reached, i.e., both criteria get an accessibility percentage of 1. However, if the budget is enough to recover at most 30% of the total disrupted roads, then the best criterion for determining the priorities depends on the location of the DMC and the disruption level of the road network. Other lines of research in this work can focus on planning to recover the road network after a disaster. The solution approach can be extended by considering a multi-period recovering operation to catch the dynamism of the availability of resources in disaster management. Furthermore, the synchronization of material, machinery to remove debris, and machinery to recover damage to infrastructure.

References 1. Abazari, S.R., Aghsami, A., Rabbani, M.: Prepositioning and distributing relief items in humanitarian logistics with uncertain parameters. Socio-Econ. Plan. Sci. 74, 100933 (2021). https://doi.org/10.1016/j.seps.2020.100933, www.sciencedirect.com/science/article/ pii/S0038012119303489 2. Akbari, V., Shiri, D., Salman, F.S.: An online optimization approach to post-disaster road restoration. Transp. Res. Part B 150, 1–25 (2021). https://doi.org/10.1016/j.trb.2021.05.017 3. Briskorn, D., Kimms, A., Olschok, D.: Simultaneous planning for disaster road clearance and distribution of relief goods: a basic model and an exact solution method. OR Spectr. 42(3), 591–619 (2020). https://doi.org/10.1007/s00291-020-00589-7

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4. Chao, I.M., Golden, B.L., Wasil, E.A.: The team orienteering problem. Eur. J. Oper. Res. 88(3), 464–474 (1996). https://doi.org/10.1016/0377-2217(94)00289-4 5. Duque, P.M., Sörensen, K.: A GRASP metaheuristic to improve accessibility after a disaster. OR Spectr. 33(3), 525–542 (2011). https://doi.org/10.1007/s00291-011-0247-2 6. Reyes-Rubiano, L., Voegl, J., Rest, K.D., Faulin, J., Hirsch, P.: Exploration of a disrupted road network after a disaster with an online routing algorithm. OR Spectr. 43(1), 289–326 (2021) 7. Van Wassenhove, L.N.: Humanitarian aid logistics: supply chain management in high gear. J. Oper. Res. Soc. 57(5), 475–489 (2006) 8. Çoban, B., Scaparra, M.P., O’Hanley, J.R.: Use of or in earthquake operations management: a review of the literature and roadmap for future research. Int. J. Disaster Risk Reduct. 65, 102539 (2021). https://doi.org/10.1016/j.ijdrr.2021.102539, www.sciencedirect.com/science/ article/pii/S2212420921005008

Heuristic Method for the Emergency Water Delivery Problem with Deprivation Costs Nicolás Giedelmann-L, William J. Guerrero, and Elyn L. Solano Charris

Abstract Humanitarian operations are characterized by the need to provide aid to affected populations in an efficient manner for minimizing the effects caused by humanitarian crises. Humanitarian operations include the distribution of aid and scarce resources such as water, medicine, and food, with the total cost of operation being one of the criteria most used by decision-makers and researchers. However, in the last two decades, the inclusion of social costs such as the deprivation cost and equity as part of the decision criteria in these problems has become a trend of great relevance. This research presents a heuristic method to establish a drinking water distribution plan in post-disaster scenarios including the estimation of the deprivation cost experienced by the people affected by humanitarian disasters. Twenty instances are solved based on available information from the department of Cundinamarca, Colombia. Results show superior performance on the drinking water distribution cost by the proposed method versus a commercial optimizer. Keywords Humanitarian logistics · Disaster relief · Vehicle routing · Metaheuristics · Deprivation costs · MINLP · Colombia

N. Giedelmann-L · E. L. Solano Charris Operations and Supply Chain Management Research Group, International School of Economic and Administrative Sciences, Universidad de La Sabana, 250001 Cundinamarca, Colombia W. J. Guerrero (B) Faculty of Engineering, Research Group in Logistic Systems, Universidad de La Sabana, 250001 Cundinamarca, Colombia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. R. Montoya-Torres et al. (eds.), Operations Research and Analytics in Latin America, Lecture Notes in Operations Research, https://doi.org/10.1007/978-3-031-28870-8_11

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1 Introduction 1.1 A Subsection Sample Humanitarian disasters are characterized by their unpredictability and the magnitude of the effects caused to the populations affected by them. Regardless of their origin, each disaster must be dealt with in the shortest possible time and all humanitarian activities must be focused on minimizing the short-, medium- and long-term impacts that affected people may experience. Among the approaches most used by researchers and decision-makers, the monetary cost has positioned itself as a robust metric that allows to direct and align humanitarian operations in a post-disaster scenario [19]. Among the operations conducted to minimize the impact of humanitarian disasters, there are four main groups into which it is possible to group various activities carried out by one or several actors within the humanitarian logistics chain [2]. The most important of these are the approaches to assigning shifts for personnel and machinery in care and rescue work [14], which are conducted during the immediate response phase of the disaster. The location and relocation of shelters and facilities are concentrated in the planning and response stages [21], seeking to establish optimal geographical locations to reduce the damage caused by humanitarian disasters and to allow rapid attention by humanitarian bodies. Distribution, debris, and rubble collection, as well as transportation of the wounded, are classified as routing problems in humanitarian operations [12], seeking to reduce periods of scarcity among populations or planning activities necessary to clear access routes or remove debris. Finally, efforts aimed at the proper management of inventories of medicines, supplies, and food are characterized by seeking an appropriate distribution of resources in different geographical areas, as well as the application of mathematical methods for estimating the demand for each good and the design of inventory management policies that seek to minimize the waiting time for affected populations to receive humanitarian supplies [7]. However, the economic approach to cost minimization in humanitarian operations has been gradually combined with other decision criteria [4]. In recent years, new trends have emerged regarding the various objectives that can guide humanitarian efforts, including maximizing coverage [1], minimizing response time [18], minimizing the risk of transporting resources or waste to and from areas affected by a humanitarian catastrophe, and pre-positioning resources to anticipate the occurrence of a disaster and minimize potential damage [17]. Among the approaches mostly developed in the last decade, the inclusion of noneconomic costs and social criteria in humanitarian work, the concepts of equity, urgency, and deprivation stand out, which are related as measures of population affectation that, even though they are not economic indicators, allow the inclusion of human suffering as decision criteria [8]. Equity in humanitarian logistics is achieved when relief goods are distributed as equally as possible among the affected population aiming to fulfilling each one of

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their needs [4]. Karsu and Morton [6], Marsh and Schilling [8] are often referred as the principal literature reviews of equity measures. In particular, the deprivation cost is formally defined as the quantitative valuation of human suffering by lack of access to a good or service [5, 15, 4] and it allows to calculate the expected impact of late delivery times during humanitarian operations. Furthermore, the deprivation cost includes different externalities to the decisionmaking process such as the individual income or the local economy behavior to include a differential behavior among the affected populations during a disaster’s aftermath [15]. Concerning previous contributions dealing with deprivation cost as a decision criterion in humanitarian logistic problems, Holguín-Veras et al. [5] proposed a mathematical procedure based on econometric approaches to calculate the deprivation cost which is defined as the price inhabitants are willing to pay to access scarce resources, like water, as a function of the elapsed time from the last time they could access it, and specific constant values that vary depending on the life cost and other econometric characteristics, providing insights about the impact that water scarcity has among populations. Thus, deprivation cost is considered in different contexts, e.g., optimizing location, transportation, and fleet sizing in post-disaster relief operations [10]. The distribution operations integrated with facility location decisions during a disaster with fairness contemplations are also a relevant matter in humanitarian logistics [9]. Given the volatile and uncertain context, they use fuzzy logic and mathematical programming-based heuristics to optimize decisions. The contribution of this research is twofold. First, a variant of the vehicle routing problem is formulated to include both, transportation, and deprivation cost during humanitarian aid operations regarding water distribution operations. Second, a heuristic method is developed to compute near-optimal solutions. A real-life case is presented, and real instances are solved to evaluate the overall operative cost and the capability of the algorithm. Given the importance of the deprivation cost in humanitarian decision-making, we consider this criterion for the emergency drinking water distribution problem. Previously, Smadi et al. [16] studied the problem of designing the drinking water supply chain in post-disaster humanitarian relief in Jordan, but they do not consider routing decisions. However, to our knowledge, the problem of resource distribution in humanitarian settings has not been studied by incorporating the cost of deprivation as a decision and analysis criterion for the planning of humanitarian care and relief efforts. This research aims to incorporate this criterion as a practical approach that allows decisionmakers to plan their operations based on the non-economic costs of humanitarian work. This paper seeks to include the deprivation cost criterion applied to drinking water distribution tasks, a case study is made based on data collected from the department of Cundinamarca, Colombia, and a heuristic method is proposed to provide a solution to the instances of this problem. Section 2 presents a description of the problem to be studied. Sections 3 and 4 present the proposed heuristic method and the

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results obtained in the first phase of experimentation on multiple randomly generated instances. Section 5 shows the conclusions obtained and presents the guidelines for future research paths.

2 Problem Description Water delivery operations are commonly executed after any disaster, whether manmade or natural originated. Clean water delivery constitutes one of the most important operations that need to be carried out to minimize the expected impact of said disasters. This is explained by two main reasons, the first one been the need to mitigate the impact of tainted water and water scarcity during the immediate moments after a disaster occurrence. Hence, increasing the recovery speed that can be achieved by any population after a disaster. Secondly, clean water prevents viral and disease outbreaks that can pose a risk to human life. The studied problem aims to determine not only the fastest or cheapest routes to provide water to a set of n affected populations but to consider the deprivation cost as part of the objective function of providing equity-driven criteria for the decisionmaking process. In this problem, it is assumed that the total amount of inhabitants demands clean water for consumption and that there is only one deposit from which said resource is transported. Each one of the affected populations has associated with two deprivation factors which are based on the published work of Holguín-Veras et al. [5] which classifies the affected population into one of three groups according to the life-cost and the expected increase in clean bottled water cost. Said coefficients introduce an additional cost in the overall operational cost, and allow the decision makers to quantify the expected suffering experienced by the affected populations, an example can be seen in Fig. 1 where the affected populations that need aid have an associated deprivation as a function of the elapsed time between the disaster occurrence and the clean water delivery cost where green indicates a low-cost growth and orange indicates a quick growth in deprivation costs. The Cundinamarca state is in the central region of Colombia and is formed by the main city, Bogotá, and 116 municipalities that are scattered throughout diverse zones that are often considered high-risk areas due to the ground conditions which favor landslides occurrences. Additionally, most of the municipalities share a common economic behavior in which some of the locally produced goods are consumed, nonetheless, most populations in this region depend on external trade to fulfill their primary need. Additionally, some of the municipalities located in the Cundinamarca region are also subjected to draught seasons, caused by multiple climatological phenomena that affect the natural water reservoirs generating drinking water shortages [20], increasing the risk of populations wellbeing being diminished.

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Fig. 1 Problem example

Even though some municipalities that can sustain a self-sufficient behavior, need to consider bigger cities as the principal supplier of goods such as food, medicine, and clean water [11]. Also, due to its location, Bogotá city plays a key role in the distribution operations that are bound to take place while addressing any sudden humanitarian crisis. Additionally, it is known that most of the municipalities in the studied region are interconnected by a third-tier road network, composed of only a handful of wide pavemented roads and multiple smaller roads that dramatically reduce the traveling speed and increases the complexity of delivery operations. It is estimated that over 3 million people live in geographically scattered communities throughout Cundinamarca, and most of the inhabitants have fragile drinking water supply systems. Thus, in case of a disaster, these communities will depend on water supply by trucks. In this scenario, it is required to prepare a plan for distribution operations to provide a quick response in disaster scenarios to avert any major harm to the population’s autonomy and expected recovery time. The main questions addressed in this study are formulated to determine what is the sequence (route) that each of the available vehicles needs to follow to distribute the drinking water while minimizing the total operative cost which considers the transportation and deprivation cost. This problem is different from a classical vehicle routing problem since deprivation costs must be considered when planning the operations. To model the water delivery problem, a nonlinear programming model adapted from a classical CVRP that includes deprivation cost as a decision criterion is considered. This model is presented in Giedelmann Lasprilla et al. [3]. Furthermore, due to the NP-hard nature of routing problems we present and explain a heuristic method designed to solve instances of such a problem. The main objective of the proposed

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Cost ($)

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1.4 1.2 1 0.8 0.6 0.4 0.2 0 0

5

10

15

20

25

30

Arrival Time (hours) Theta= 0.0025 Alpha=0.15

Theta=0.15 Alpha=0.06

Theta= 0.15 Alpha=0.03

Fig. 2 Water deprivation cost example

method is to provide decision-makers with a competitive tool in terms of speed and solution quality for planning water delivery operations during the aftermath of a disaster. The model of water distribution in humanitarian emergency scenarios contemplates an objective function that is divided into two sections, the first one seeks to minimize the total cost of transporting this resource before being delivered to the affected populations and a second part that includes an estimate of the total cost of deprivation experienced by the people waiting for this resource, this estimate is formulated as a non-linear function of the time elapsed between the time of the disaster and the arrival of the water at the place of consumption [15] and depends on two pre- established coefficients that start from the cost of living of the populations. The estimated deprivation cost is shown in Eq. (1) and the behavior of the deprivation cost (β) is exemplified in the following figure for different values of the coefficients: β = θ ∗ e(α∗T )

(1)

where θ[$] and α[1/T] are coefficients calculated based on the life cost of each population, and T represents the arrival time (Fig. 2).

3 Proposed Heuristic Method To solve the problem and given the inherent complexity of resource distribution problems such as the one in this study, a heuristic method was formulated. This approach was selected due to the good results that heuristic methods have achieved in similar problems [13]. The proposed method consists of two sub-procedures that are consecutively executed to obtain a solution for the studied problem, however,

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this process is repeated a finite number of times to provide different initial solutions that are separately improved and store the value of the best solution obtained for each of the solved problem instances. Both procedures are described as follows: The first procedure (1) consists of the creation of an initial solution to the problem generated by including random criteria on the allowed cost that this solution may have. subsequently, in the procedure (2) an improvement method is applied to the solutions found in which the consecutive exchange of the nodes that have been assigned to each of the routes is allowed to find improvements in the final cost of the solution. The proposed method assumptions and the description of each procedure are explained below. Proposed method assumptions: • • • •

All affected populations must be visited once. The deprivation coefficients are based on each population’s life cost. All the vehicles have the same transport capacity. Both calculated costs have the same relative importance in the studied problem, hence there is no normalization procedure to be carried out in the objective function.

Initial solution procedure: the first procedure aims to create feasible solutions for the initial routing by generating different routes and calculating the associated cost based on the arrival time of each node visited, and the deprivation cost constant associated with the water requirements. The procedure is described below.

4 Initial Solution Generation 1. If there are unvisited nodes: 2. for each vehicle 3. for each unvisited node a. Define a random slack value. b. calculate the total cost and add the slack value. c. Select the node with the lowest cost. i. If the node can be visited with the selected vehicle, then 1. Update the route for that vehicle. 2. Update the vehicle capacity. 3. Mark the node as visited. 4. Repeat from step 2. 5. Calculate the total cost of the solution S To generate an initial feasible solution, the proposed method is carried out until all nodes are visited once. For each vehicle, the unvisited nodes are ordered using the minimum distance criterion, then a random slack cost is added to the total cost calculated for each node. The node with the highest calculated total cost is selected

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from the list of candidates if the demand can be loaded on the vehicle. The node is then assigned, otherwise, the process is repeated for the next vehicle until all nodes are visited. After the initial solution generation, the second procedure is carried out, whose objective is to evaluate different neighborhoods to improve the total cost of the solution as follows. Definition of the Improvement Procedure 1. INSERT: Firstly, the relocation of nodes in different paths is evaluated by removing them from one path and inserting them in a position of another path. Secondly, a local relocation of the inserted node within the target path is evaluated. The upgrade procedure is composed of two consecutive tasks that are executed a finite number of times until the stop condition is satisfied. The following diagram illustrates the proposed heuristic method (Fig. 3).

Fig. 3 Proposed heuristic method

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5 Preliminary Results During the calibration phase of the proposed method, three experimental factors were defined: the number of maximum iterations before the end of the algorithm (I), the seed for the generation of random numbers (II), and the allowed variation in the incremental cost associated with the generation of initial solutions (III). The levels used for each factor are summarized Table 1. The experimental results obtained by solving three randomly generated instances suggest that the random seeds used do not have a significant impact on the quality of the best solution obtained, however, the remaining two factors suggest an impact on the quality of the solution. After conducting statistical tests to prove the existence of a statistically significant difference in the results obtained by the proposed heuristic method, 20 randomly generated instances were solved using a commercial optimizer (GAMS version 29.3) with a non-linear SOLVER (COIN-OR) and the heuristic method developed in Python language using Spyder Ver 5.2 as compiler. The results obtained during the experimentation phase are shown in Table 1 where the first column shows the number of the solved instance, the second and third columns show the best solution obtained by the heuristic method, and the solution provided by GAMS when solving the instances, finally, the fourth column shows the relative GAP between the results obtained where a negative GAP indicates an improvement obtained by the proposed method compared to the best solution found by the commercial optimizer. The obtained results show a better performance of the proposed heuristic method in all the solved instances, nonetheless, instance 18 wasn’t solved by gams after 3600 s of processing, implying that in some cases, the inclusion of the non-linear objective function, the problem’s complexity may increase. Figure 4 shows the relation between the total deprivation cost and the transportation cost suggesting that the consideration of deprivation cost measurement has a great impact on the overall operation cost.

6 Conclusions The proposed method allows finding solutions to the drinking water distribution problem in humanitarian aid scenarios. Based on the results obtained during the experimental phase, it is concluded that the proposed heuristic method outperforms a commercial optimizer in terms of solution quality. Nevertheless, the results of the mathematical model suggest that the emergency drinking water distribution problem has a high complexity possibly attributed to the consideration of the deprivation cost. Future work is suggested to investigate various instances to consider the socioeconomical characteristics of other regions of Colombia to develop a framework for decision-making in the routing of vehicles and delivery of humanitarian aid where deprivation cost is included as an important criterion for minimizing the total cost of

14,537.1047

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91,713.9

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Instance 4

3

2

4

Instance 1

Instance 2

1

Instance

Table 1 Solutions

16 17 18 19 20

−1.87 −54.09 −82.75 −40.04

15

−49.40 −22.06

13 14

−66.16 −54.27

Instance 20

Instance 19

Instance 18

Instance 17

Instance 16

Instance 15

Instance 14

Instance 13

Instance 12

Instance 11

11 12

−69.55 −35.11

Instance

GAP (%)

23,353.35

28,544.3

7997.42

18,263.85

6596.405

23,804.05

27,689.9

6857.755

14,278.35

15,007.75

BKS

52,034.53

21,769.48

–

74,211.1889

47,179.652

37,326.2975

48,222.1732

15,308.2129

16,028.8617

33,081.1747

GAMS solution

−55.12

31.12

–

−75.39

−86.02

−36.23

−42.58

−55.20

−10.92

−54.63

GAP (%)

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Cost ($)

Deprivation cost- Transport cost $ 100,000.00 $ 90,000.00 $ 80,000.00 $ 70,000.00 $ 60,000.00 $ 50,000.00 $ 40,000.00 $ 30,000.00 $ 20,000.00 $ 10,000.00 $ 0.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Instance Deprivation cost

Transport cost

Fig. 4 Deprivation cost-transport cost relation

operation. Finally, the proposed method could be subjected to multiple diversification methods to further improve the obtained solutions.

References 1. Cordeau, J.F., Furini, F., Ljubi´c, I.: Benders decomposition for very large scale partial set covering and maximal covering location problems. Eur. J. Oper. Res. 275(3), 882–896 (2019) 2. da Costa, S.R.A., Bandeira, R.A.M., Campos, V.B.G., Mello, L.C.B.B.: Humanitarian supply chain: an analysis of operations in natural disasters | Cadeia de suprimentos humanitária: uma análise dos processos de atuação em desastres naturais. Producao 25(4), 876–893 (2015) 3. Giedelmann Lasprilla, N., Guerrero, W.J., Solano-Charris, E.L.: On the emergency water distribution problem: optimizing vehicle routing with deprivation costs considerations. IFAC-PapersOnLine 55(10), 3166–3171 (2022) 4. Gutjahr, W.J., Fischer, S.: Equity and deprivation costs in humanitarian logistics. Eur. J. Oper. Res. 270(1), 185–197 (2018) 5. Holguín-Veras, J., Amaya-Leal, J., Cantillo, V., van Wassenhove, L.N., Aros-Vera, F., Jaller, M.: Econometric estimation of deprivation cost functions: a contingent valuation experiment. J. Oper. Manag. 45, 44–56 (2016) 6. Karsu, Ö., Morton, A.: Inequity averse optimization in operational research. Eur. J. Oper. Res. 245(2), 343–359 (2015) 7. Kunz, N., Reiner, G., Gold, S.: Investing in disaster management capabilities versus pre- positioning inventory: a new approach to disaster preparedness. Int. J. Prod. Econ. 157(1), 261–272 (2014) 8. Marsh, M.T., Schilling, D.A.: Equity measurement in facility location analysis: a review and framework. Eur. J. Oper. Res. 74(1), 1–17 (1994)

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9. Mohammadi, S., Avakh Darestani, S., Vahdani, B., Alinezhad, A.: A robust neutrosophic fuzzybased approach to integrate reliable facility location and routing decisions for disaster relief under fairness and aftershocks concerns. Comput. Ind. Eng. 148, 106734 (2020) 10. Moreno, A., Alem, D., Ferreira, D., Clark, A.: An effective two-stage stochastic multi-trip location-transportation model with social concerns in relief supply chains. Eur. J. Oper. Res. 269(3), 1050–1071 (2018) 11. OCHA: Darfur Humanitarian Needs Overview (2018). https://reliefweb.int/sites/reliefweb.int/ files/resources/Darfur_Humanitarian_Overview_A3_1_Feb_2018.pdf 12. Pedraza-Martinez, A.J., van Wassenhove, L.: Transportation and vehicle fleet management in humanitarian logistics: challenges for future research. EURO J. Transp. Logist. 1(1–2), 185–196 (2012) 13. Pirabán-Ramírez, A., Guerrero-Rueda, W.J., Labadie, N.: The multi-trip vehicle routing problem with increasing profits for the blood transportation: an iterated local search metaheuristic. Comput. Ind. Eng. 170, 108294 (2022) 14. Rauchecker, G., Schryen, G.: An exact branch-and-price algorithm for scheduling rescue units during disaster response. Eur. J. Oper. Res. 272(1), 352–363 (2019) 15. Shao, J., Wang, X., Liang, C., Holguín-Veras, J.: Research progress on deprivation costs in humanitarian logistics. Int. J. Disast. Risk Reduct. 42, 101343 (2020) 16. Smadi, H., al Theeb, N., Bawa’neh, H.: Logistics system for drinking water distribution in post disaster humanitarian relief, Al-Za’atari camp. J. Human. Logist. Supply Chain Manage. 8(4), 477–496 (2018) 17. Su, L., Sun, L., Karwan, M., Kwon, C.: Spectral risk measure minimization in hazardous materials transportation. IISE Trans. 51(6), 638–652 (2019) 18. Thompson, M.P., Wei, Y., Calkin, D.E., O’Connor, C.D., Dunn, C.J., Anderson, N.M., Hogland, J.S.: Risk management and analytics in wildfire response. Curr. Forest. Rep. 5(4), 226–239 (2019) 19. Tomasini, R., van Wassenhove, L.: Logistics of humanitarian aid. Humanitarian Logistics, INSEAD Business Press Series, pp. 1–16. Palgrave Macmillan, London (2009). https://doi. org/10.1057/9780230233485_1 20. UNGRD: Fenomeno El Niño analisis comparativo 1997–1998 // 2014–2016 (2016). http:// repositorio.gestiondelriesgo.gov.co/bitstream/handle/20.500.11762/20564/Fenomeno_nino2016.pdf?sequence=3&isAllowed=y 21. Zhao, X., Chen, J., Xu, W., Lou, S., Du, P., Yuan, H., Ip, K.P.: A three-stage hierarchical model for an earthquake shelter location-allocation problem: case study of Chaoyang District, Beijing, China. Sustainability 11(17), 4561 (2019)

A Simulation Approach to Analyze the Operational Response Plans in an Emergency Department Under the COVID-19 Pandemic David Mora-Meza, Julián Alberto Espejo-Díaz, and William J. Guerrero

Abstract Emergency departments in hospitals are a crucial part of the healthcare systems around the world. They provide emergency medical services to patients who need urgent treatments. Due to the multiple sources of variability and uncertainty in their operations, they are considered complex systems. In addition, since the onset of COVID-19, hospitals have adapted their operations to decrease the contact between patients and medical staff to minimize the infection rate. In this work, we study the operations of an emergency department which made changes in its processes as a strategy to face the COVID-19 pandemic. The changes include the incorporation of a new area for respiratory patients, reallocating resources, and the modification of the patients’ journey in the emergency department. We propose a discrete event simulation approach to represent the operations before and after the changes in the emergency department services. The proposal was developed with collaboration of the emergency department managers and validated using the performance measures before the start of the COVID-19 pandemic. The main computational results show that the changes in the emergency department were effective to distribute the limited resources and limit the medical staff and non-respiratory patients’ exposure to suspected COVID-19 patients. However, in a post-COVID-19 scenario, such differentiation is no longer effective when the percentage of respiratory patients is less than 30%, since it increases the patients’ wait times, mainly for the non-urgent patients classified with less critical triage. Keywords Emergency department · Discrete event simulation · COVID-19 pandemic · Healthcare management · Healthcare systems · Operations research

D. Mora-Meza · J. A. Espejo-Díaz (B) · W. J. Guerrero School of Engineering, Research Group Logistics Systems, Universidad de La Sabana, Campus Universitario, Puente del Común Km. 7 Autopista Norte de Bogotá D.C., Chia, Colombia e-mail: [email protected] W. J. Guerrero e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 J. R. Montoya-Torres et al. (eds.), Operations Research and Analytics in Latin America, Lecture Notes in Operations Research, https://doi.org/10.1007/978-3-031-28870-8_12

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1 Introduction Emergency departments (EDs) are a crucial part of healthcare systems worldwide. They are responsible for providing healthcare services to patients who arrive at medical facilities in need of urgent medical attention. To do so, the EDs count on trained onsite personnel and adequate infrastructure to provide initial treatment to a range of injuries or illnesses. The random nature of patient arrivals, the large variety of possible symptoms to treat, the high level of human involvement, and other factors make EDs complex systems. Therefore, planning the operations of EDs is a challenging activity. It must consider multiple factors such as limited budgets, the lack of personnel, and multiple operational variables such as the number of beds [1, 2] A usual consequence of failure in planning ED service operations is overcrowding. It deteriorates patients’ health by causing long wait times and even patients leaving without being seen by a physician [3]. Richardson and Mountain [1] concluded that the leading causes of ED overcrowding are the staff and physical capacity being overwhelmed by a large volume of patients seeking medical attention. This can result from managers planning the EDs operations without the knowledge of the current state of the processes and not evaluating beforehand the impact of their decisions. Furthermore, EDs can be subject to disruptions in their operations. Such disruptions change the usual way of providing emergency medical attention. For instance, disasters can bring large amounts of patients in short periods. To face such conditions, EDs count on strategies such as setting up an alternate care facility for less critical patients [4]. Another type of possible disruption EDs can face is pandemics. Recently, the COVID-19 pandemic made hospitals reorganize their services to minimize the contact between patients and the medical staff [5]. In this work, we studied the operations of an ED in a hospital in Colombia which changed its working routine and processes due to the COVID-19 pandemic. These changes were made to manage the waves of COVID-19 patients and fulfill the regulations from the public health ministry in Colombia. Like others EDs, the main changes in its operations consisted of establishing areas and allocating resources to respiratory patients while keeping the service to non-respiratory patients in “clean” areas. To analyze the operations under these changes, we conducted a time study of the ED processes. Next, we built two discrete event simulation models to represent the system and evaluate policies for post-covid scenarios. Similar works such as [6] have studied the COVID-19 pandemic in ED using discrete-event simulation models. However, no one, to the best of our knowledge, has studied the impact of classifying respiratory patients and allocating exclusive resources to them in a case study. The main contribution of our work is to provide insights to the ED managers regarding the patients’ classification and resource allocation. This strategy may be replicated in other EDs around the world. The remainder of this paper is organized as follows. Section 2 presents the methodology framework for the techniques used in this work and reviews the related works in the field. Section 3 describes the emergency department subject of this study. Section 4 details

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the discrete event simulation models. Section 5 presents the results of the computational experiments, and Sect. 6 concludes and provides some recommendations for future research in the area.

2 Methodological Framework Discrete event simulation (DES) models have been proposed in the literature to represent complex systems in multiple knowledge fields. The main characteristic of such models is their event-driven and discrete-state properties [7]. In other words, the evolution of DES models relies on the occurrence of asynchronous discrete events. For example, in EDs, the patients’ arrival (random and asynchronous) corresponds to events that change the system’s state. DES is a technique that has been widely utilized for representing EDs [8]. It has the advantage of capturing the system complexity given by the multiple interactions between the processes (e.g., triage and medical examination) and the stochastic nature of some of their variables (e.g., medical examination time). In addition, DES models allow decision-makers to evaluate different strategies before their implementation. Research in DES for ED is abundant. For instance, Farahi and Salimifard [9] proposed a methodology to assess the ED response to a crisis, coupling a DES model with an optimization methodology. In this work, the ED system and the crisis scenarios were modeled using DES, and the optimization methodology determined the distribution of resources. Another work that uses DES to model and support the decisions of EDs is [10]. In this work, the authors proposed a decision support tool using DES that represents and compares the baseline service with different scenarios. The support tool was developed for a large medical facility in England, allowing the comparison of multiple performance metrics. Recently, in [11], the authors studied the patient flow in an ED considering the COVID-19 pandemic. The authors used an agent-based simulation model to capture the patient behavior and a DES model to represent the resources in the ED. Another work that studied the performance of ED under the COVID-19 pandemic is [6]. There, the authors evaluate the resource requirements at the peak of the pandemic in the St. Olavs Hospital in Norway. In addition, the authors determined the number of ambulances required to maintain the pre-COVID-19 response times during the pandemic’s peak. For a complete review of DES models in ED see [8]. Boyle et al. [12] classified the DES models for EDs as generic, generalizable, and specific. The generic models are abstract, theoretical, address general problems of hospitals, and can be built without data from a case study. The generalizable models balance the level of abstraction and specificity and can be used for representing a particular ED by customizing the data input. Last, the specific models comprehensively capture the functioning of a single hospital ED. In this work, we study a particular ED in the Cundinamarca department in Colombia. Thus, we develop a specific DES model that captures in detail this complex system’s processes and interactions. The model analyzes the impact of establishing exclusive zones and

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allocating resources to patients with respiratory symptoms. In addition, we evaluate multiple scenarios for validating the performance of such changes in a post-COVID19 scenario. We believe this work’s findings can be applied to similar EDs. The next section describes the case study.

3 Case Study Description This study was conducted in a private hospital in the Colombian department of Cundinamarca. For confidentiality purposes, the name of the hospital is not disclosed. The hospital is recognized for providing high-quality surgery, emergencies, hospitalization, pharmacology, diagnostic images, laboratory, rehabilitation, and outpatient clinic services. The hospital ED attended more than 84,000 patients per year before the COVID-19 pandemic. Since then, the average of attended patients has decreased to 50,000 yearly. It resulted from people preferring to stay at home rather than go to the EDs that were overcrowded with COVID-19 patients. Thus, the overall number of attended patients in the EDs during the pandemic decreased. However, the workload of healthcare professionals increased as more patients required intensive care and stayed for more extended periods as in other EDs worldwide [13]. Like in other EDs, patients are classified according to the severity of the injury or illness. This classification is known as the triage system [14]. The ED under study classifies the patients using a 5-tier triage system. Notably, this ED treats patients classified as triage 1, 2, or 3 since they are the most urgent. Level 1 patients are in the most critical condition and require urgent medical attention. However, some triage 4 or 5 patients affiliated with specific insurance companies are treated in the ED. The remaining patients are asked to leave the ED and request an appointment with their healthcare provider. Between January 2017 and June 2021, most of the patients in the case study were classified as triage 3 (62.3%) and triage 2 (22.25%). The most severe patients (triage 1) represented 0.9%. The triage 4 and 5 patients represented the remaining 14.55%. Figure 1 presents the steps in the patients’ attention in the ED (patients’ journey). However, depending on the patient’s condition, the journey can differ. For instance, the critical patients skip the triage classification and are moved straight to the procedure room to deal with life-threatening situations. To provide emergency care services, the ED has the following areas: . . . . . .

A reception area where the patients are registered in the hospital. Three triage cabins where nurses classify the patients using the triage system. Five consulting rooms where doctors evaluate patients. An examination room where a specialized ED nurse makes additional analysis. A procedure room where nurses perform minor surgical procedures. An observation unit for monitoring patients before their admission to hospitalization.

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Reception

Triage classification

Hospital admission

Medical evaluation

153 Exams, medication or procedures

Observation Reevaluation Discharging

Fig. 1 Patients’ journey in the emergency department under study

. Three separated patient waiting rooms for (i) triage classification, (ii) medical evaluation, and (iii) medical re-evaluation. As a strategy for dealing with the increasing number of COVID-19 patients in the ED, the hospital managers annexed a hospital area (the new area is referred to as the expansion zone and the original area as the main zone). This new area changed the ED distribution as follows: . A new consulting room was established in the expansion zone for serving the less critical patients (triage 3, 4, or 5). Besides, the initial consulting rooms are now for urgent patients (triage 2 or respiratory patients). . A new procedure room is established in the expansion area. . A new waiting room for respiratory patients is established in the main zone. . The observation room is now divided into respiratory and non-respiratory patients. In addition to the distribution changes, now the ED changed the patients’ journey to classify respiratory and non-respiratory patients. The classification decreases the medical staff and the non-respiratory patients’ exposure to suspected COVID-19 patients. Consequently, the new patients’ journey in the ED is the following. First, the patient registers in the reception. There, the administrative staff ask them if they have respiratory symptoms. Next, the patients wait for the triage classification as follows. The identified respiratory patients wait in the new respiratory waiting room. The non-respiratory patients wait in the normal triage waiting room. Then, the patients are asked to go to the triage cabins, where a nurse determines the patient triage classification and whether the patient is respiratory or not. If the patient is non-respiratory, they wait for the doctor’s assessment in a clean waiting room in either the expansion zone or the main zone. If the patient is respiratory, they go to the respiratory waiting room in the main zone. Then, based on the triage classification and resource availability, they are assessed by an ER doctor in a consulting room. If the doctor determines that the patient condition requires admission to the hospitalization unit, the patient goes to the observation unit (which is divided into respiratory and non-respiratory patients). If the patient does not require admission, a nurse conducts the additional exams, provides the medication, or performs minor procedures based on the doctor’s guidelines. Next, the ED doctor performs a follow-up revision to determine if the patient meets the criteria to go home, stay on the system for additional exams, or if they must be admitted. The following section presents the DES models.

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4 Proposal We developed two DES models for the ED under study. The first one was made for validation purposes and represented the system without the expansion zone nor the new resource allocation for respiratory patients. The second model, which is detailed in Fig. 2 as a flowchart, represents the current state of the ED. The DES models were implemented in Anylogic Version 8.7.12 in a computer with 32 GB of RAM, 3.70 GHz processor, and Windows 10 Pro. To validate the DES models, we first employed the “face validity” technique by asking practitioners and ED managers to review the simulation models. They concluded that the models work reasonably. Next, we compared historical data to determine whether the DES model behaves as the real-life system. As we have historical data from before the COVID-19 pandemic, we used the first DES model in the validation step. We employed the performance measure triage opportunity 3, which the ED defines as the mean time between triage 3 patients’ arrival and the finalization of the first medical assessment. We obtained a P-value of 0.1539 in Welch’s t-test, which compares the mean of two normal populations with different variances. Thus, it is impossible to reject the hypothesis that the populations’ means are the same. The following section presents the experimentation and results of multiple scenarios considering changes in the COVID-19 pandemic.

5 Experimentation and Results Since January 2022, the number of COVID-19 cases started to drop in Colombia [15]. Consequently, the Colombian government has gradually lifted restrictions and health measures in the country. However, there is a concern among healthcare authorities that it would lead to a rise in infections [16]. In this work, we analyzed the performance of the ED under study. To do so, we evaluated the current operation scheme of the ED varying the proportion of respiratory patients. We proposed four scenarios with 5, 30, 60 and 90% of the patients classified as respiratory patients. For each replication, we simulated 41 days of ED operation and we considered a warm-up period of 7 days. A total of five replications per scenario were made, which was verified with an ANOVA analysis, with an error type II of less than 2%. Next, we present and analyze the results. An initial statistical analysis of the time between the patients’ arrival and the first assessment for the respiratory, triage 2, and triage 3 patients show that these groups are statistically different (Kruskal Wallis test with p-value