The Pennsylvania State University The Graduate School College of Engineering FLEET PLANNING IN THE CAR RENTAL BUSINESS A Dissertation in Industrial Engineering and Operations Research by Gen-Han Wu © 2010 Gen-Han Wu Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy May 2010 The dissertation of Gen-Han Wu was reviewed and approved* by the following: Tom M. Cavalier Professor of Industrial Engineering Dissertation Advisor Chair of Committee A. Ravi Ravindran Professor of Industrial Engineering David A. Nembhard Associate Professor of Industrial Engineering Terry P. Harrison Professor of Supply Chain and Information System Paul Griffin Professor of Industrial Engineering Head of the Harold and Inge Marcus Department of Industrial and Manufacturing Engineering *Signatures are on file in the Graduate School. iii Abstract In the United States, consumption capacity in tourism is poised to grow significantly, and transportation is one of the essential elements in tourism. Airplanes and car rentals are the most typical modes of public travel. While air transport has earned significant scholarly attention and there exist abundant studies, fleet planning in the car rental business is discussed only minimally in operations research. Therefore, the purpose of this research is not only to build a thorough analytical framework for car rental fleet planning in different time phases, but also to develop practical algorithmic procedures. In long-term planning, pool segmentation and hub selection are studied. All rental locations are split into different pools and a hub is selected within each pool. The proposed clustering-based iterative algorithm offers a reliable clustering method to quickly find an initial solution with a small solution gap and an iterative method to gradually approach a near-optimum. In mid-term planning, inter-pool moves and asset replacement are distributed among different pools based on the change of seasonal demand. Numerical results have shown that the best-improvement descent local search with the structure of better neighbors has very good performance and can obtain a satisfactory solution in an extremely short time. In short-term planning, vehicle imbalance at different locations forces empty vehicles to be redistributed. Daily planning of demand allocation and empty flow redistribution is addressed in the same pool. Car upgrade policy and service level are also considered. A first- improvement descent local search is developed. Computing results demonstrate that the first- improvement descent local search not only obtains relatively good solutions in quite a short time but also solves very large scale integer programming problems easily. iv TABLE OF CONTENTS LIST OF FIGURES …..…………..…………………………………………………….viii LIST OF TABLES……………………..……………………………………………..…..xi ACKNOWLEDGEMENTS………………..………………………………….…….......xiv Chapter 1. INTRODUCTION……………………………………………………..…..1 1.1 Research Origin and Motivation……………………………………………......1 1.2 Research Purpose………………………………………………………...……..2 1.3 Problem Statement………………………………………………………...……3 1.4 Dissertation Framework………….…………………………………………......5 Chapter 2. CAR RENTAL BUSINESS PROFILE……………………………………7 2.1 History of the U.S. Car Rental Business………………..……………………...7 2.2 The U.S. Car Rental Market…………………………………………..………10 2.3 The Car Rental Software…………………………….......................................18 Chapter 3. LITERATURE REVIEW………………………………………..……….20 3.1 Car Rental Problems…………………………………………………….….…20 3.2 Fleet Planning Problems………………………………………………………27 3.2.1 Long-term: Pool Segmentation and Hub Selection…………………......28 3.2.2 Mid-term: Inter-pool Moves and Asset Replacement……………….…..32 3.2.3 Short-term: Demand Allocation and Empty Flow Redistribution…........33 Chapter 4. POOL SEGMENTATION AND HUB SELECTION……………………36 4.1 Problem Formulation……………………………………………………...…..36 4.2 Mathematical Model…………………………………………………………..38 4.3 Motivation………..…………………………………………………….….….40 4.4 Algorithm Procedure…………..………………………………………….…..45 v 4.4.1 Clustering Algorithm ………………………………………………...…47 4.4.1.1 Neighbor Factor ………………………………………………..47 4.4.1.2 Tabu List……………………………………………………..…47 4.4.1.3 Flow Chart……………………………………………….….….48 4.4.1.4 Detailed Procedure…………………………..…………….……50 4.4.1.5 Example……………………………………………………..….53 4.4.2 Enumeration Method…………………………………………………....72 4.4.3 Modified Prim Algorithm……………………………………………….73 4.5 Computing Results…………………………………………………………....74 4.5.1 Parameter Settings ……………………………………………………...74 4.5.2 Factor Levels…………………………………………………………....76 4.5.3 Experimental Platform…………………………………………………..78 4.5.4 Experimental Analysis…………………………………………………..78 4.5.4.1 Impact Analysis on Experimental Factors versus Algorithm Time.........................…...............................................................79 4.5.4.2 Impact Analysis on Locations in Practical Problem Size versus Algorithm Time...........................................................................84 4.5.4.3 Impact Analysis on Experimental Factors versus Solution Gap..............................................................................................84 4.5.4.4 Comparison of Computing Time between the Clustering-Based Iterative Algorithm and the Branch-and-Bound Method…........87 4.6 Concluding Remarks…………………………………………………………..93 Chapter 5. INTER-POOL MOVES AND ASSET REPLACEMENT………….……94 5.1 Problem Formulation……………………………………………………...…..94 5.2 Mathematical Model………………………………………………………......96 5.3 Motivation………………………………………………………………….....98 5.4 Algorithm Procedure………………………………………………………...102 5.4.1 Initial Solution…………………………………………………………102 5.4.2 The Structure of Better Neighbors…………………………………….105 5.4.3 Best-Improvement Descent Local Search……………………………..111 vi 5.5 Computing Results…………………………………………………………..114 5.5.1 Parameter Settings…………………………………………………..…114 5.5.2 Factor Levels……………….…………………………………………..117 5.5.3 Experimental Platform…………………………………………………118 5.5.4 Experimental Analysis…………………………………………………118 5.5.4.1 Impact Analysis on Experimental Factors versus Solution Gap ………………………………………………………………119 5.5.4.2 Impact Analysis on Experimental Factors versus Computing Time…………………………………………………………121 5.5.4.3 Impact Analysis on Large Scale Number of pools versus Computing Time………………………………………...…...126 5.6 Concluding Remarks……………………………………………………….129 Chapter 6. DEMAND ALLOCATION AND EMPTY FLOW REDISTRIBUTION… ………………………………………………………………………….131 6.1 Problem Formulation………………………………………………………...131 6.2 Mathematical Model…………………………………………………………133 6.3 Motivation…………………………………………………………………...135 6.4 Algorithm Procedure………………………………………………………...136 6.4.1 Initial Solution………………………………………………………….136 6.4.2 The Structure of Better Neighbors……………………………………..139 6.4.3 First-Improvement Descent Local Search……………………………...143 6.5 Computing Results……………………………………….…………………145 6.5.1 Parameter Settings…………………………………………………...…145 6.5.2 Factor Levels……………………………………………………………149 6.5.3 Experimental Platform………………………………………………….150 6.5.4 Experimental Analysis………………………………………………….150 6.5.4.1 Results for Small Scale Problems…………………………....150 6.5.4.2 Results for Large Scale Problems…………………………….154 6.6 Concluding Remarks…………………………………….…………………156 vii Chapter 7. Summary and Further Work…………………………………………….157 7.1 Summary……………………………………………………………………..157 7.2 Direction for Further Extensions and Research………………………...……160 REFERENCES……………………………………………………………………...161 Appendix A. Original Data on Experimental Factors versus Algorithm Time in Chapter 4………………………………………………………………………..…176 Appendix B. Tukey Tests on Four Factors versus Algorithm Time in Chapter 4……...182 Appendix C. Original Data on Experimental Factors versus Solution Gap in Chapter 4…………………………………………………………………………..187 Appendix D. Tukey Test on Three Factors versus Solution Gap in Chapter 4………...190 Appendix E. Original Data of Inter-pool Moves and Asset Replacement on Experimental Factors versus Solution Gap in Chapter 5………………………………..194 Appendix F. Tukey Tests of Inter-pool Moves and Asset Replacement on the Number of Car Ages/ Seasonal Periods versus Solution Gap in Chapter 5………….197 Appendix G. Tukey Tests of Inter-pool Moves and Asset Replacement on Three Factors versus Computing Time in Chapter 5…………………………..………..199 viii LIST OF FIGURES Figure 1.1: The problem of car rental operations…...…………………………………4 Figure 1.2: Overview of the research framework……...………………………………6 Figure 2.1: The U.S. car rental fleet size and market revenue……………………….10 Figure 2.2: The percentage of car fleet market share by rental companies…………..14 Figure 2.3: Market share of car rental revenue……………………………………….17 Figure 4.1: Network before pool segmentation……………………………………....37 Figure 4.2: Network after pool segmentation………………………………………...37 Figure 4.3: Example of an optimal solution with 60 facility locations………………40 Figure 4.4: The solution form of total cost incurred………………………………....41 Figure 4.5: Optimal value vs. different number of hubs……………………………..43 Figure 4.6: Fixing the pool region and re-selecting the hubs……………………...…44 Figure 4.7: Fixing the hubs and re-shaping the pool regions………………………...45 Figure 4.8: The clustering-based iterative algorithm …………………………….….46 Figure 4.9: The clustering algorithm(1/2)…………………………………………....48 Figure 4.10: The clustering algorithm(2/2)…………………………………………..49 Figure 4.11: Example of 14 locations with their demands and hub opening costs…..54 Figure 4.12: Node 11 is selected to be a hub…………………………………………59 Figure 4.13: Node 10 is selected to be a hub…………………………………………60 Figure 4.14: Node 12 is connected to hub 11 and node