Operations Research Proceedings 2004: Selected Papers of the Annual International Conference of the German Operations Research Society (GOR) - Jointly ... Research (NGB), Tilburg, September 1-3, 2004 3540242740, 9783540242741

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Operations Research Proceedings 2004 Selected Papers of the Annual International Conference of the German Operations Research Society (GOR). Jointly Organized with the Netherlands Society for Operations Research (NGB) Tilburg, September 1–3, 2004

Hein Fleuren · Dick den Hertog Peter Kort Editors

Operations Research Proceedings 2004 Selected Papers of the Annual International Conference of the German Operations Research Society (GOR). Jointly Organized with the Netherlands Society for Operations Research (NGB) Tilburg, September 1–3, 2004

With 104 Figures and 59 Tables

123

Professor Dr. Hein Fleuren Professor Dr. Dick den Hertog Professor Dr. Peter Kort Warandelaan 2 5037 AB Tilburg The Netherlands E-mail: [email protected] E-mail: [email protected] E-mail: [email protected]

Cataloging-in-Publication Data Library of Congress Control Number: 2005924438

ISBN 3-540-24274-0 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com © Springer-Verlag Berlin Heidelberg 2005 Printed in Germany The use of general descriptive names, registered names, trademarks, 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. Cover design: Erich Kirchner Production: Helmut Petri Printing: Strauss Offsetdruck SPIN 11375272

Printed on acid-free paper – 42/3153 – 5 4 3 2 1 0

Preface This volume contains a selection of papers referring to lectures presented at the symposium "Operations Research 2004" (OR 2004) held at Tilburg University, September 1-3, 2004. This international conference took place under the auspices of the German Operations Research Society (GOR) and the Dutch Operations Research Society (NGB). The symposium had about 500 participants from more than 30 countries all over the world. It attracted academicians and practitioners working in various fields of Operations Research and provided them with the most recent advances in Operations Research and related areas in Economics, Mathematics, and Computer Science. The program consisted of 4 plenary and 19 semi-plenary talks and more than 300 contributed presentations, selected by the program committee, to be presented in 20 sections. Due to a limited number of pages available for the proceedings volume, the length of each article as well as the total number of accepted contributions had to be restricted. Submitted manuscripts have therefore been reviewed and 59 of them have been selected for publication. We would like to thank the GOR-board for the abundant collaboration, which we always found to be helpful and fruitful. We are grateful to all the reviewers, which were asked to review one or more submitted papers. Finally, we would like to thank our colleague Annemiek Dankers and Barbara Fess from Springer-Verlag for their support in publishing this proceedings volume. Tilburg, March 2005 Hein Fleuren Dick den Hertog Peter Kort

Committees Organizing Committee Prof.dr. Hein Fleuren (chair), Tilburg University Dr. Willem Haemers, Tilburg University Dr. Herbert Hamers, Tilburg University Drs. Maaike van Krieken, Tilburg University Mw. Use van de Pol, Tilburg University Prof.dr. Dolf Talman, Tilburg University

Program Committee Prof.dr. Micheal Jiinger, University of Cologne Prof.dr. Thomas Spengler, Braunschweig University of Technology Prof.dr. Brigitte Werners, Ruhr-Universitat-Bochum Prof.dr. Rainer Kolisch, Technische Universitat Miinchen Prof.dr. Dick den Hertog, Tilburg University Prof.dr. Peter Kort, Tilburg University Prof.dr. Marc Salomon, Tilburg University Prof.dr. Henk Zijm, University of Twente

Reference Committee Prof.dr. Prank van der Duyn Schouten, Tilburg University Prof.dr. Lodewijk Kallenberg, Leiden University Prof.dr. Alexander Rinnooy Kan, Board ING-group Prof.dr. Jan Karel Lenstra, National Research Institute for Mathematics and Computer Science Prof.dr. Lex Schrijver, The National Research Institute for Mathematics and Computer Science in the Netherlands Prof.dr. Stef Tijs, Tilburg University

Sections and section leaders Reverse Logistics Rommert Dekker (Erasmus University Rotterdam) Karl Inderfurth (Otto-von-Guericke-Universitat Magdeburg) OR in Entertainment and Sports Gerard Sierksma (University of Groningen) Andreas Drexl (Christian-Albrechts-Universitat zu Kiel) Service Management Ger Koole (Free University of Amsterdam) Stefan Helber (Universitat Hannover) Telecommunication Stan van Hoesel (University of Maastricht ) Arie Koster (Zuse Zentrum fiir Informationstechnik Berlin) Production, Logistics and Supply Chain Management Jalal Ashayeri (Tilburg University) Hans-Otto Giinther (Technischen Universitat Berlin) Transportation and Traffic Gees Ruijgrok (Tilburg University) Dirk Mattfeld (University of Bremen) Project Management and Scheduling Han Hoogeveen (Universiteit Utrecht) Rainer Kohsch (Technische Universitat Miinchen) Marketing Tammo Bijmolt (Tilburg University) Reinhold Decker (Bielefeld University) Energy, Environment and Health Paul van Beek (Wageningen University) Peter Letmathe (Universitat Siegen) Optimization of Bio Systems Stephan Pickl (Universitat zu Koln) Finance, Banking and Insurances Antoon Kolen (University of Maastricht) Hermann Locarek-Junge (Technische Universitat Dresden)

VIII Simulation and Applied Probability Jack Kleijnen (Tilburg University) Ulrich Rieder (University of Ulm) Continuous Optimization Kees Rocs (Delft University of Technology) Florian Jarre (Heinrich-Heine-Universitat Diisseldorf) Discrete and Combinatorial Optimization Gerhard Woeginger (University of Twente) Josef Kallrath (BASF-AG, Ludwigshafen) A.I., Fuzzy Logic and Multicriteria Decision Making Heinrich Rommelfanger (Johann Wolfgang Goethe-Universitat Frankfurt am Main ) Econometrics, Game Theory and Mathematical Economics Dolf Talman (Tilburg University) Clemens Puppe (Universitat Karlsruhe ) Managerial Accounting Anja De Waegenaere (Tilburg University) Hans-Ulrich Kiipper (Ludwig-Maximilians-Universitat Miinchen) Business Informatics Hennie Daniels (Tilburg University) Leena Suhl (Universitat Paderborn) OR in Engineering Dick den Hertog (Tilburg University) Otto Rentz (Universitat Karlsruhe ) Revenue Management Gerrit Timmer (Free University of Amsterdam) Alf Kimms (Technische Universitat Bergakademie Freiberg )

Contents GOR

Awards

Koordination von Abruf- und Lieferpolitiken in Supply Chains E. Sucky

1

Ein Entscheidungsunterstiitzungssystem zur Verschnittoptimierung von Rollenstahl I. Steinzen

10

Conflict-free Real-time A G V Routing R.H. Mohring, E. Kohler, E. Gawrilow, B. Stenzel

18

Dynamical Configuration of Transparent Optical Telecommunication Networks A. Tuchscherer

25

Reverse

Logistics

The Value of Information in a Container Collection System for End-of-life Vehicles I. le Blanc, R. Schreurs, H. Fleuren, H. Krikke

33

Approximate Policies for Hybrid Production and Rework Systems with Stochastic Demand and Yield C. Gotzel, K. Inderfurth

41

Life Cycle Considerations in Remanufacturing Strategies - a Framework for Decision Support W. Stolting, T. Spengler

50

Service

Management

Stochastic Models of Customer Portfolio Management in Call Centers O. Jouini, Y. Dallery, R. Nait-Abdallah

Production^ Logistics and Supply Chain

59

Management

A n Milp Modelling Approach for Shelf Life Integrated Planning in Yoghurt Production M. Liitke Entrup, M. Grunow, H.O. Giinther, T. Seller, P. van Beek

67

X

D y n a m i c Optimization of R o u t i n g in a Semiconductor Manufacturing Plant H. Gold

76

Blood P l a t e l e t P r o d u c t i o n : a M u l t i - t y p e Perishable Inventory P r o b l e m R. Haijema, J. van der Wal, N.M. van Dijk

84

Zeitdiskrete Modellierung der Wechselwirkungen der P l a n - V o r g a b e n bei Verwendung der Liefertreue als Leistungsgrofie fur die interne Supply C h a i n in der Halbleiterindustrie K. Hilsenbeck, A. Schomig, W. Hansch

93

Sequencing a n d Lot-size Optimisation of a P r o d u c t i o n - a n d - i n v e n t o r y - s y s t e m w i t h Multiple I t e m s using Simulation a n d Parallel Genetic A l g o r i t h m M. Kampf, P. Kochel

102

Ein Dekompositionsverfahren zur B e s t i m m u n g der P r o d u k t i o n s r a t e einer Fliefiproduktionslinie mit M o n t a g e s t a t i o n e n u n d stochastischen B e a r b e i t u n g s z e i t e n M. Manitz

110

A D y n a m i c M o d e l for Strategic Supplier Selection E. Sucky

118

Functional Analysis of Process-Oriented Systems

127

P. Buchholz, C. Tepper

Transportation

and

Traffic

Finding Delay-Tolerant Train R o u t i n g s t h r o u g h Stations G. Caimi, D. Burkolter, Th. Herrmann R o u t e r : A Fast a n d Flexible Local Search A l g o r i t h m for a Class of Rich Vehicle R o u t i n g P r o b l e m s U. Derigs, Th. Dohmer

136

I n t e g r a t e d Optimization of School S t a r t i n g Times a n d P u b l i c B u s Services A. Fiigenschuh, A. Martin, P. Stoveken

150

144

XI A Decision Support Framework for the Airline Crew Schedule Disruption Management with Strategy Mapping Y. Guo

158

Tail Assignment in Practice M. Gronkvist, J. Kjerrstrom

166

Ein praxistauglicher Ansatz zur Losung eines spezifischen D-VRSP-TW-UC O. Kunze

174

Freight Flow Consolidation in Presence of Time Windows J. Schonberger, H. Kopfer

184

Minimizing Total Delay in Fixed-Time Controlled Traffic Networks E. Kohler, R.H. Mohring, G. Wiinsch

192

Project Management

and Scheduling

On Asymptotic Optimality of Permutation Schedules in Stochastic Flow Shops and Assembly Lines R. Koryakin

200

A n Exact Branch-and-Price Algorithm for Workforce Scheduling C. Stark, J. Zimmermann

207

A Single Processor Scheduling Problem with a Common Due Window Assignment A. Janiak, M. Winczaszek

213

Marketing Modeling SMEs' Choice of Foreign Market Entry: Joint Venture vs. Wholly Owned Venture X. Zhao, R. Decker

221

Pattern Detection with Growing Neural Networks — A n Application to Marketing and Library Data R. Decker, A. Hermelbracht

230

XII The Quality of Prior Information Structure in Business Planning - A n Experiment in Environmental Scanning S.W. Scholz, R. Wagner

238

Product Line Optimization as a Two Stage Problem

246

B. StauB, W. Gaul

Energyy Environment

and

Health

Optimising Energy Models for Hydrothermal Generation Systems to Derive Electricity Prices D. Most, I. Tietze-Stockinger, W. Fichtner, O. Rentz Simulation of the Epidemiology of Salmonella in the Pork Supply Chain M.A. van der Gaag, H.W. Saatkamp, F. Vos, M. van Boven, P. van Beek, R.B.M. Huirne

Optimization

of Bio

254

263

Systems

Modeling Signal Transduction of Neural System by Hybrid Petri Net Representation S.C. Peng, H.-M. Chang, D.F. Hsu, C.Y. Tang

271

Mathematical Modeling and Approximation of Gene Expression Patterns F.B. Yilmaz, H. Oktem, G.-W. Weber

280

Finance,

Banking

and

Insurances

On the Empirical Linkages between Stock Prices and Trading Activity on the German Stock Market R. Mestel, H. Gurgul, P. Majdosz

Simulation

and Applied

288

Probability

Numerical Transform Inversion for Autocorrelations of Waiting Times H. Blanc

297

A Note on the Relationship between Strongly Convex Functions and Multiobjective Stochastic Programming Problems V. Kankova

305

XIII Two-Step Drawing from Urns S. Kolassa, S. Schwarz

313

Total Reward Variance in Discrete and Continuous Time Markov Chains K. Sladky, N.M. van Dijk

319

Continuous

Optimization

A n Efficient Conjugate Directions Method Without Linear Searches E. Boudinov, A.I. Manevich

Discrete and Combinatorial

327

Optimization

The Robust Shortest Path Problem by Means of Robust Linear Optimization D. Chaerani, C. Roos, A. Aman

335

Approximation Algorithms for Finding a Maximum-Weight Spanning Connected Subgraph with given Vertex Degrees A.E. Baburin, E.Kh. Gimadi

343

Multiprocessor Scheduling Problem with Stepwise Model of Job Value Change A. Janiak, T. Krysiak

352

The Prize Collecting Connected Subgraph Problem 360 - A N e w NP-Hard Problem arising in Snow Removal Routing P.O. Lindberg, G. Razmara A Less Flexibility First Based Algorithm for the Container Loading Problem Y.-T. Wu, Y.-L. Wu

A.I.y Fuzzy Logic and Multicriteria

Decision

368

Making

ScheduHng with Fuzzy Methods W.A. Eiden

377

Generalized DEA-Range Adjusted Measurement A. Kleine, D. Sebastian

385

XIV A Fuzzy D E A Approach - Ranking Production Units in Taiwanese Semiconductor IndustryE. Reucher, W. Rodder

393

Verkniipfung von Standortdaten und Vegetationsmodellen liber die Zeigerwerte nach Ellenberg E. Rommelfanger, W. Kohler

400

Extracting Rules from Support Vector Machines K.B. Schebesch, R. Stecking

408

Econometrics^ Game Theory and Mathematical Economics A Square Law for Power of Positions in a Network

416

H. Monsuur

Business

Informatics

Automated Business Diagnosis in the OLAP Context E. Caron, H. Daniels User-Oriented Filtering of Qualitative Data C. Felden, P. Chamoni

425

Vorstellung einer erweiterbaren Selbstlernumgebung ,,Operations Research" als Beispiel fiir exploratives, Web-basiertes E-Learning im Hochschulumfeld M. Lutz, J. Kern

443

Partially Integrated Airline Crew Scheduling for Team-oriented Rostering M.P. Thiel, T. Mellouli, Y. Guo

452

OR in

Engineering

Multi Objective Pinch Analysis (MOPA) for Integrated Process Design J. Geldermann, H. Schollenberger, M. Treitz, O. Rentz

Revenue

434

461

Management

Revenue Management in a Make-to-Order Environment S. Rehkopf, Th. Spengler

470

Hierarchical Multilevel Approaches of Forecast Combination S. Riedel, B. Gabrys

479

Koordination von Abruf- und Lieferpolitiken in Supply Chains Eric Sucky Seminar fiir Logistik und Verkehr, Johann Wolfgang Goethe-Universitat, Mertonstr. 17, 60054 Frankfurt am Main, [email protected],de

1

ElnleJtung

Der Materialfluss in Supply Chains, von der Rohstoffgewinnung tiber die einzelnen Veredelungsstufen bis hin zum Endkunden, resultiert aus der Verknupfung von Beschaffungs-, Produktions- und Transportprozessen einzelner, in der Supply Chain agierender Untemehmen. Die zeitlichen und quantitativen Auspragungen dieser Wertschopfimgsprozesse werden in individuellen Abrufund Lieferpolitiken spezifiziert. Aufgrund der bestehenden zeitlichen und quantitativen Interdependenzen ist die zielgerichtete, untemehmensubergreifende Koordination von Abruf- und Lieferpolitiken eine zentrale Aufgabe des Supply Chain Management. Sowohl in der relevanten Literatur als auch in kommerziellen Softwaresystemen werden Planungsansatze des Supply Chain Management weitgehend auf der Basis zentraler Koordinationsprinzipien diskutiert. In real existierenden Supply Chains sind i.d.R. jedoch nicht die Voraussetzungen fur eine zentrale Koordination gegeben: Eine zentrale Koordination bedingt, dass die Untemehmen in der Supply Chain 1.) ihre Planungsautonomie aufgeben, 2.) alle planungsrelevanten Informationen (d.h. auch sensible Kosten- und Kapazitatsinformationen) einer zentralen Koordinationsinstanz zur Verfiigung stellen und 3,) ihre Handlungen an ubergeordneten Supply Chain-Zielen ausrichten [8]. Darin ist der Grund zu sehen, warum kommerzielle Softwaresysteme des Supply Chain Management (Advanced Planning Systems), bisher lediglich untemehmensintem eingesetzt werden, obwohl sie fur einen untemehmenstibergreifenden Einsatz entwickeh wurden [9]. Zentrale Planungsansatze bilden relevante Problemstellungen des Supply Chain Management nicht adaquat ab. Praxisrelevante Fragestellungen der Allokation von Supply Chain-Gewinnen in Win-Win-Situationen oder der Kompensation von Akteuren in Win-Lose-Situationen sowie relevante Rahmenbedingungen, insbesondere Informationsbedingungen und Machtverhaltnisse, werden nur bedingt oder gar nicht beriicksichtigt. Zur Unterstiitzung der

Koordination des zielgerichteten Zusammenwirkens der verteilten Leistungserstellung in Supply Chains liefem zentrale Planungsansatze daher nur einen geringen Beitrag. Wahrend produktionswirtschaftliche und logistische Ansatze zur Planung integrierter Materialflusse durch eine weitgehende Vemachlassigung von Wettbewerbsaspekten und der Dominanz hierarchischer Koordinationsprinzipien gekennzeichnet sind, eignen sich spieltheoretische Ansatze, die strategische Interaktion zwischen Untemehmen zu analysieren und eine dezentral abgestimmte Planung zu unterstiitzen [4].

2

Das Koordinationsproblem

Dem zu analysierenden Koordinationsproblem liegen folgende Annahmen zu Grunde: Es wird ein Abnehmer (A) und ein Lieferant (P) eines bestimmten Produkts betrachtet, fur das eine im Zeitverlauf gleichbleibende Nachfrage in konstanter Hohe besteht. Fijr die Phasen des Materialflusses werden auf Lieferantenseite Produktion und Warenausgangslager und auf Abnehmerseite Beschaffung und Wareneingangslager, wie in Abbildung 1 dargestellt, unterschieden. Supply Contract Lieferant (P)

c

tf>

(D

p 2

5 2>

Q.

>

O)

Verhandlungen

Abnehmer (A) c

Abruf

i V)

Lieferung

GQ

w - •

Materialfluss

.£ D) 0) (0

a> O)

^ s > >

(0 O)

Informationsfluss

Abb. 1. Betrachtete Lieferanten-Abnehmer-Beziehung 1st die vom Lieferanten an den Abnehmer zu liefemde Periodenquantitat gegeben, muss festgelegt werden, zu welchen Lieferzeitpunkten welche Lieferquantitaten erfolgen, d.h. es muss eine gemeinsame Abruf- und Lieferpolitik ermittelt werden. Die Abru^olitik des Abnehmers lasst sich durch die Anzahl der Abrufe je Periode, den Abrufzyklus, d.h. der Zeitspanne zwischen zwei Abrufen sowie der Quantitat je Abruf charakterisieren, Der Lieferant legt simultan die Produktions- und Lieferpolitik fest. Wahrend sich die Lieferpolitik an der Anzahl der Lieferungen je Periode, dem Lieferzyklus sowie der Quantitat je Lieferung konkretisiert, ist die Produktionspolitik durch die Anzahl der Losauflagen je Periode, dem Produktionszyklus sowie der LosgroBe je Losauflage gekennzeichnet.

2.1

Individuelle Planungsprobleme der Supply Chain-Partner

Die bekannte Periodenquantitat des vom Lieferanten an den Abnehmer zu liefemden Produkts, gemessen in Mengeneinheiten je Periode, betragt b [ME/PE]. Der Lieferant, der das vom Abnehmer nachgefragte Produkt im Rahmen einer Serien- bzw. Sortenfertigung erzeugt, plant simultan seine Liefer- und Produktionspolitik unter dem Ziel der Minimierung seiner relevanten Periodenkosten. Dabei ist zu beachten, zu welchem Zeitpunkt fertiggestellte Produkteinheiten eines Produktionsloses zur Weitergabe an den Abnehmer zur Verfugung stehen. Im Folgenden wird angenommen, dass der Lieferant seine Liefer- und Produktionspolitik auf der Basis einer Lot-for-Lot-Politik disponiert, d.h. direkt nach Abschluss der Bearbeitung eines Produktionsloses wird das gesamte Produktionslos vollstandig an den Abnehmer weitergegeben; die Lieferquantitat entspricht der ProduktionslosgroBe. Die Periodenkapazitat des Lieferanten betragt d [ME/PE]. Es gilt d > b und die Nachfrage des Abnehmers wird durch y

Lieferungen identischer Quantitat

X [ME] gedeckt. Die variablen Produktions- und Transportkosten je Mengeneinheit werden als im Planungszeitraum konstant angenommen und sind daher nicht entscheidungsrelevant. Die Summe der relevanten Riist- und Lagerkosten je Periode stellt somit die ZielgroBe dar; als Hohenpraferenzrelation gilt „Minimierung". Die Rtistkosten, die bei jeder Losauflage in gleicher Hohe anfallen, betragen R [GE]. Der Lagerhaltungskostensatz sei mit hp [ G E / M E P E ] bezeichnet. Die relevanten Periodenkosten, die individuell optimale Produktions- und Lieferpolitik sowie die resultierenden minimalen Periodenkosten des Lieferanten lauten [1]: Zp

«-MT^--=il^- 0%) is always less costly than migrating towards a Dedicated System {p = 0%). For example, consider a Portfolio Dedicated System with n == 10. If the OPTF proportion is p = 5%, we need to increase the service rate by 4.91%. However, with a proportion p = 20% we need only to increase the service rate by 1.17%. We explain this advantage by the fact that the OPTF flow is used to reduce idle periods of servers while customers are waiting in the Portfolio Dedicated System. Idle times would not exist in the case of p = 100% (Pooled System).

30% n

P e r c e n t a g e s of Service Rate Increase

25% • ^ • ^ p = 0 %

^.-""^l^!^

—•—p=5%

^^^^^t^^^^^^^^^""^

20% •

—*—p=10%

^^^^^^^^^^^^^^•^^^'"^'^^

15% • -^*—2Ci% 10% •

.^^*^^^^^^^^^^^^''''''^'^^

^.-'^.--^[l,^^

^^.-""^

^

^.^^^^^^

Wn

=0.18 min

5% y^mr^^^^f^ ---"•"''^

0

10

n

20

30

40

50

Fig. 6. Percentages of required service rate increase according to number of pools n in a Portfoho Dedicated System in order to achieve ]/^^^°^^^ =0.18 min

66

4

Conclusion

We focused on a fundamental problem in the design and management of call centers, and in general, stochastic service systems, that is, pooling effects versus team management benefits. We argued how team management benefits, that comes from the portfolio/team one to one link, may outweigh the economy of scale associated with the pooled organization. First, we study partitioning of a large call center into identical and separated call centers, where agents of a same team are dedicated to one portfolio of customers. Queueing models involved in this part of the study are simple. They give us important insights and help us to understand the behavior of more complicated systems. Then, we extend our analysis to the more general situation with an additional out-portfolio flow. We show that the costs of migrating towards the Dedicated System are not as important as it may appears. We also present further insights, as robustness of dedicated systems regarding errors in the estimation of the arrival rate. In a future study, we will extend our models by considering abandonments and limited waiting lines and more general service times distributions. We will also try to improve the approximation models discussed here to get more accurate analysis. Finally, a more ambitious extension will be to investigate the introduction of team-based organization in a call center where agents have specific skills.

References 1. Gans N., Koole G., Mandelbaum A. (2003) Telephone Call Centers: Tutorial, Review, and Research Prospects. Manufacturing Sz Service Operations Management. 5, 73-141 2. Kleinrock L. (1976) Queueing Systems, Computer Applications. A WileyInterscience Publication. Vol II 3. Smith B., Donald R., Whitt W. (1981) Resource Sharing for Efficiency in Traffic Systems. Bell System Technical Journal. 60, 39-55 4. Rothkoph M. H., Rech P. (1987) Perspectives on Queues: Combining Queues is not Always Beneficial. Operations Research. 35, 906-909 5. Whitt W. (1992) Understanding the efficiency of multi-server service systems. Management Science. 38, 708-723 6. Whitt W. (1999) Partitioning Customers into Service Groups. Management Science. 45, 1579-1592 7. Whitt, W. (2002) Stochastic models for the design and management of customer contact centers: Some research directions. Department of Industrial Engineering and Operations Research, Columbia University 8. Fischer M., Garbin D. et al. (1999) Traffic engineering of distributed call centers: Not as straight forward as it may seem. Mitretek Systems 9. Boudreau J., Hopp W. et al. (2003). On the interface between operations and human ressources management. Manufacturing Sz Service Operations Management. 5, 179-202 10. Kella O., Yechiali U. (1985) Waiting times in the non-preemptive priority M/M/C queue. Stochastic models. 1, 257-262

AN MILP MODELLING APPROACH FOR SHELF LIFE INTEGRATED PLANNING IN YOGHURT PRODUCTION M. Lutke Entrup\ M, Grunow\ H.O. Gunther^ T. Seiler^ and P. van Beek^ ^ Department of Production Management, Technical University Berlin, Wilmersdorfer Str. 148, D-10585 Berlin, e-mail: [email protected] ^ Operations Research and Logistics Group, Wageningen University, Hollandseweg 1, NL-6706 KN Wageningen, e-mail: [email protected] Abstract. In the production of perishable products such as dairy, meat, or bakery goods, the consideration of shelf life in production planning is of particular importance. Retail customers with relatively low inventory turns can benefit significantly from longer product shelf life as wastage and out-of-stock rates decrease. However, in today's production planning and control systems shelf life issues with regard to specific products or customers are seldom taken into account. Therefore the objective of this paper is to pay attention to these issues. The way to do that is by means of optimization models in which shelf life aspects are integrated into operational production planning and scheduling functions. Specifically we make use of so-called Mixed Integer Linear Programming (MILP) models. Our research is based on an industrial case study of yogurt production. Relying on the principle of block planning, an MILP model for weekly production planning is presented that is based on a combination of a discrete and a contmuous time representation. Batch sizing and scheduling of numerous recipes and products on several packaging lines are considered in the model. Overnight production and, hence, the necessity for identifying two different shelf life values for the same batch is also included in the model formulation. Numerical experiments show that near-optimal solutions can be obtained within a reasonable computational time. Finally, the proposed MILP model can be adapted to cover specific features arising in other fresh food industries.

1. Introduction Production planning of yogurt is certainly one of the most challenging tasks in the dairy industry as the planner has to cope with e.g. an extraordinary high number of products and variants as well as with sequence-dependent set-up times and costs on capital-intensive processing equipment. One important distinctive factor to consider in fresh food production planning is shelf life. Shelf life restrictions directly infiuence wastage, inventory levels and out-of-stock rates in the retail

68

outlets. Furthermore, consumers tend to buy the product with the longest possible shelf life. The possibility to offer a longer shelf life than its competitors constitutes a pivotal competitive advantage for fresh food producers. Hence, the consideration of shelf life is crucial for production planning systems in the dairy or other fresh food industries. The remainder of this paper is organized as follows. A short literature review of research of scheduling in make-and-pack production as well as on production planning for perishable products is given in Section 2. An introduction into the production of yogurt is provided in Section 3. In the main part of this paper (see Section 4), a MILP model is presented that integrates shelf life into production planning and scheduling. The model is numerically validated in Section 5. Finally, an outlook is given on its applicability in other fresh food industries.

2. Literature Review Batch production in the chemical industry can be taken as a reference for the production of yogurt as both must consider numerous variants, which are based on few product types or recipes. In literature, this production environment is named "make and pack production" (e.g. Neuhaus et al., 2002; Mendez and Cerda, 2002). Major issues of operational production planning are lot sizing and scheduling, which can be performed in one single or two separate planning steps. As set-ups in yogurt production are sequence-dependent, the exact set-up costs and times can only be determined after the sequencing of the orders. Moreover, as sequencing depends on lot sizing, both tasks must be performed simultaneously (c.f Sikora et al., 1996). Neuhaus et al. (2002) present an approach that simultaneously considers lot sizing and scheduling based on the block-planning principle. By integrating several variants of a product type or recipe into a "block", the complexity of the model can be significantly reduced without being unrealistic. For the determination of the sequence of batches within a block, a "natural" sequence of batches often exists, for example from the lower taste to the stronger or from the brighter color to the darker. With regard to the consideration of shelf life in production planning, two different avenues can be distinguished. A vast body of literature exists on inventory management for perishable products, which covers food products as well as the behavior of radioactive materials, photographic film, prescription drugs, or blood conserves, Nahmias (1982) and Raafat (1991) give comprehensive literature overviews and an analysis of proposed inventory models for perishables. The major drawback of all perishable inventory models is that production issues are almost completely neglected although the shelf life of products is actually determined by their time of production. In addition, production capacities, sequence-dependent set-up times, or production on multiple units or lines are not reflected. Considering the integration of shelf life into production planning and scheduling, most re-

69

search is concerned with adding a shelf life constraint to the Economic Lot Scheduling Problem. Soman et al. (2004) provide a review of the major contributions. Shortcomings of this model type include the constant demand rate assumption, the single facility consideration and the neglect of sequence-dependent setup times.

3. Production of Yogurt The production of yogurt consists of five major steps. First, the raw milk is collected from the farms by tanker trucks and stored in silos in the dairy factory. Second, the raw milk is subject to a number of preparatory treatments, which include its standardization (in many cases with milk powder), its heating in a plate heat exchanger, its concentration in an evaporator and its homogenization. Third, the raw milk is transformed into yogurt during the fermentation process by adding starter cultures. For stured yogurt, the fermentation is performed in tanks while set yogurt is fermented in the packaging after filling. This research, however, focuses on stirred yogurt. In fermentation, the recipe complexity is still relatively low compared to the packaging step. Fourth, the yogurt is flavored with fruits and other ingredients and filled into the retail containers on capital-intensive filling and packaging lines. This flavoring and packaging step has to cope with a high number of product variants, which is caused by the vast variety of packaging materials and tastes. In packaging, sequence dependent set-up times occur; nonetheless in many cases a natural sequence exists that can help to avoid extensive setup times (e.g. the brighter color before the darker). Fifth, the packed products are stored and delivered to the retail outlets.

4. Model Formulation The presented MILP-model aims at generating a weekly plan for the production of yogurt and focuses particularly on the filling and packaging stage. It is based on the block planning approach; all products that can be filled on the same packaging line and that are based on the same recipe are part of the same block. The model applies a combination of a continuous and a discrete time representation. Start and end times of batches on the packaging lines are reflected by continuous variables, while a discrete time grid is used for shelf life considerations. The planning horizon covers one week from Monday to Friday, including the possibility to use overtime capacity on Sunday before and on Saturday after the planning week. The demand to be covered also includes Monday and Tuesday of the following week.

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Indices, sets j,k eJ I eL s eS p eP as d sD a S r €R J ^J(r) I eLR(r) I eLJ(j) deD(s) s eS(d) Data revj varcj Slj

B capi steri cli berij lossr cloSSr djd Cl

mb psj fir fc crj

OSi

adj fdp Idp bpj

final products lines days production days demand days recipes, blocks products based on recipe r lines that can process recipe r lines that can process product^ demand days (to meet the demand of these days, lots produced on day s can be considered) days (the lots produced on these days can be considered to meet the demand of demand day d) revenue for selling one unit of producty variable costs for the production of one unit of producty shelf life of producty in days sufficiently large number capacity of line /, in units per day time for sterilizing line / time for cleaning line / maximum additional benefit for meeting the maximum shelf life of producty, in € per unit cleaning loss of fermented plain yogurt of recipe r, in kg cost for the cleaning loss of plain yogurt of recipe r, in € per kg demand of producty on demand day d mventory of producty, produced on day s costs of utilization of line / on a weekday, in € per day minimum batch size to be processed, in kg packaging size of producty, in kg per unit fermentation time for recipe r, in hours fermentation capacity, in kg-hours per day minimum remaining shelf life of producty required by the customer (in % of maximum shelf life) quarantine time of producty overtime supplement for weekend production on line /, in € per day percentage of plain yogurt contained in one unit of producty start of the first possible production day within the week (Sunday) start of the last possible production day within the week (Saturday) position of producty in the corresponding block

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Decision variables Srpi ^ {0,1} =1, if recipe r is produced on production day/? on line / (0, otherwise) Cjpi ^ {0,1} =1, if product y is produced until the end of production day p-7 and at the beginning of day/? (0, otherwise) Xjpi e {0;s >fdp; p e P: p=s

(5a)

deD(s)

j eJ;s

eS

(5b)

deD{s)

djd

j eJ; d eD

= SES(d):s+qj mb'S

Z ^'jpl . \jeJ{r)

rpl

J

r eR;p

eP:p < Idp; I

LR(r)

(7b)

eP:p = Idp; I e LR(r)

(7c)

E

(

B>mh'S r Fermentation capacity r

ER;P

rpl

\

3 S Z^./-/'V«4 A+IS "^.^-Iq

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r €R;j eJ(r);p

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