Rewards-Supply Aggregate Planning in the Management of Loyalty Reward Programs - A Stochastic Linear Programming Approach YUHENG CAO, B.I.B., M.Sc. A thesis submitted to the Faculty of Graduate and Postdoctoral Affairs in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Management Sprott School of Business Carleton University Ottawa, Ontario, Canada September 2011 ©2011YuhengCao All Rights Reserved Library and Archives Bibliotheque et 1*1 Canada Archives Canada Published Heritage Direction du Branch Patrimoine de I'edition 395 Wellington Street 395, rue Wellington OttawaONK1A0N4 Ottawa ON K1A 0N4 Canada Canada Your Tile Votre reference ISBN: 978-0-494-83243-1 Our file Notre reference ISBN: 978-0-494-83243-1 NOTICE: AVIS: The author has granted a non­ L'auteur a accorde une licence non exclusive exclusive license allowing Library and permettant a la Bibliotheque et Archives Archives Canada to reproduce, Canada de reproduire, publier, archiver, publish, archive, preserve, conserve, sauvegarder, conserver, transmettre au public communicate to the public by par telecommunication ou par I'lnternet, preter, telecommunication or on the Internet, distribuer et vendre des theses partout dans le loan, distribute and sell theses monde, a des fins commerciales ou autres, sur worldwide, for commercial or non­ support microforme, papier, electronique et/ou commercial purposes, in microform, autres formats. paper, electronic and/or any other formats. The author retains copyright L'auteur conserve la propriete du droit d'auteur ownership and moral rights in this et des droits moraux qui protege cette these. Ni thesis. Neither the thesis nor la these ni des extraits substantiels de celle-ci substantial extracts from it may be ne doivent etre imprimes ou autrement printed or otherwise reproduced reproduits sans son autorisation. without the author's permission. In compliance with the Canadian Conformement a la loi canadienne sur la Privacy Act some supporting forms protection de la vie privee, quelques may have been removed from this formulaires secondaires ont ete enleves de thesis. cette these. While these forms may be included Bien que ces formulaires aient inclus dans in the document page count, their la pagination, il n'y aura aucun contenu removal does not represent any loss manquant. of content from the thesis. 1*1 Canada Acknowledgements First of all, I would like to thank my supervisor Dr. Aaron L. Nsakanda for his patient guidance, valuable suggestions and enlightening comments during the period of my study in Carleton University. This dissertation owes a lot to his gentle, yet effective guidance. Without his help, this dissertation could not have been finished. His profound knowledge in management science definitely benefited me a lot. Working with him has always been an enjoyable and rewarding experience. I would like to thank all the members of my thesis committee: Dr. Vinod Kumar, Dr. Michael Armstrong, Dr. Akif A. Bulgak, and Dr. Yiqing Zhao with individually and collectively contributed to the thesis. Secondly, I would like to thank the Sprott School of Business, Carleton University, for providing financial support and necessary research facilities for this thesis. It would have been impossible for me to concentrate on my research without such financial support. Many thanks go to members and staff of the School of Business, who helped me during my studies at Carleton, in particular Melissa Doric, Greg Schmidt, and Jason Holtz. I would like to thank all of the great teachers and researchers I have encountered here at Carleton University, in particular Dr. Shaobo Ji, Dr. Roland Thomas, and Dr. Uma Kumar. Finally, I would like to thank my parents, whose love, support, and sacrifice made me what I am today. No words can properly express the love, gratitude, and admiration I have for them. 1 Abstract Loyalty reward programs (LRPs), initially developed as marketing programs to enhance customer retention, have now become an important part of customer-focused business strategies. One of the operational challenges faced by LRP managers is that of planning for the supply of rewards in a given period of time. We have developed three mathematical models for solving this problem under various settings. In each setting, the problem has been formulated as a two-stage stochastic linear programming model with recourse. A heuristic optimization procedure based on sample average approximation (SAA) is proposed for solving each of these models. We carried out extensive computational experiments to demonstrate the viability of the modeling and solution approaches for solving realistically sized (large-scale) problems as well as to evaluate the impacts of changes that internal dynamics and external uncertainties have on the performance of a loyalty reward program operating as a profit center. Findings from these computational studies have led to a number of managerial insights. Our results show that demand variability has negative impacts on LRP performance. As such, adopting an option contract provides good means for mitigation, especially when demand uncertainty is high. Our results have also shown that offering cooperative advertisement through bonus points is a double-edged sword. It may bring in higher LRP profitability, but it also results in higher liability. When demand variability is high, offering bonus points is not preferred in rewards-supply planning. Finally, our results indicate that budget tightness and liability control tightness have an impact on LRP performance to an extent that varies across different system settings. This research contributes to the literature in several ways: it synthesizes and extends the concept of supply chain management in the context of LRPs and it enhances the understanding of LRPs and rewards-supply planning problems through quantitative modeling and stochastic programming. Our findings will help LRP managers to understand the roles of cooperative advertising through bonus points and option contract in planning for the supply of rewards as well as to evaluate the impact of changes in the internal dynamics and external uncertainties on the performance of loyalty reward program operations. n Table of Contents Acknowledgements i Abstract ii List of Tables vi List of Figures viii List of Appendices ix Chapter 1 Introduction 1 1.1 Background and Research Motivation 1 1.2 Research Objectives 4 1.3 Outline of the Thesis 8 Chapter 2 Literature Review 9 2.1 Loyalty Reward Programs (LRPs) 9 2.1.1 Overview 9 2.1.2 Typology Framework for LRPs 12 2.1.3 Literature Review of LRPs 22 2.1.4 Summary 32 2.2 Supply Chain Contracts 35 2.2.1 Overview 35 2.2.2 Option Contracts 36 2.2.3 Summary 44 2.3 Cooperative Advertising 45 2.3.1 Overview 45 2.3.2 Cooperative Advertising and Budget Allocation 47 2.3.3 Cooperative Advertising in LRP Operations 50 2.3.4 Summary 51 Chapter 3 Research Framework and Mathematical Models 53 3.1 Loyalty Reward Programs - "Rewards-Points" Supply Chains 53 3.2 LRP Rewards - Supply Aggregate Planning Models 57 in 3.2.1 LRP Rewards - Supply Planning Problem without Bonus Points 58 3.2.1.1 Modeling Assumptions 58 3.2.1.2 Problem Description and Model Formulation 60 3.2.2 LRP Rewards - Supply Planning Problem with Bonus Points 66 3.2.2.1 Modeling Assumptions 67 3.2.2.2 Problem Description and Model Formulation 68 3.2.3 LRP Rewards - Supply Planning Problem with Option Contracts 73 3.2.3.1 Modeling Assumptions 73 3.2.3.2 Problem Description and Model Formulation 74 3.3 Summary 78 Chapter 4 Solution Methodology 79 4.1 Stochastic Programming and Its Implementation 79 4.1.1 Model Reformulation for Problem BP 82 4.1.2 Model Reformulation for Problem EP1 84 4.1.3 Model Reformulation for Problem EP2 85 4.2 Solution Procedure 87 4.2.1 Sample Average Approximation (SAA) Reformulation 89 4.2.1.1 SAA Model for Problem BP-2SLPR 90 4.2.1.2 SAA Model for Problem EP1-2SLPR 91 4.2.1.3 SAA Model for Problem EP2-2SLPR 92 4.2.2 SAA-based Heuristic Solution Procedure 94 4.2.3 Implementation Issues in the Solution Procedure 98 4.3 Summary 100 Chapter 5 Design of Numerical Studies 102 5.1 Procedure for Generating Testing Problems 102 5.2 Testing the Effectiveness of the Solution Methodology 106 5.2.1 Model Solvability 107 5.2.2 Quality of Stochastic Solutions 110 5.3 Testing the Impacts of Demand Variability 110 5.4 Testing the Impacts of Budget Tightness 113 5.5 Testing the Impacts of Liability Control Tightness 116 IV Chapter 6 Results and Analysis 120 6.1 Testing the Effectiveness of the Solution Methodology 120 6.1.1 Model Solvability 120 6.1.2 Quality of Stochastic Solutions 125 6.2 Testing the Impacts of Demand Variability 133 6.2.1 Under BP Setting 133 6.2.2 Under EP1 Setting 137 6.2.3 Under EP2 Setting 141 6.2.4 Comparison across BP, EP1, and EP2 Model Settings 146 6.2.5 Summary 147 6.3 Testing the Impacts of Budget Tightness 149 6.3.1 Under BP Setting 149 6.3.2 Under EP1 Setting 154 6.3.3 Under EP2 Setting 158 6.3.4 Comparison across BP, EP1, and EP2 Model Settings 162 6.3.5 Summary 175 6.4 Testing the Impacts of Liability Control 177 6.4.1 Under BP Setting 177 6.4.2 Under EP1 Setting 181 6.4.3 Under EP2 Setting 185 6.4.4 Comparison across BP, EP1, and EP2 Model Settings 191 6.4.5 More on Management Insights from Liability Control Analysis 197 6.4.6 Summary 200 Chapter 7 Conclusions and Future Research Directions 202 7.1 Findings and Implications 203 7.2 Limitations and Contributions 206 7.3 Future Research Directions 209 References 213 Appendices 222 v List of Tables Table 2.1