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Queuing Models for Sizing and Structuring Rental Fleets

Author

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  • Felix Papier

    (Department of Supply Chain Management and Management Science, University of Cologne, Albertus-Magnus-Platz, 50923 Cologne, Germany)

  • Ulrich W. Thonemann

    (Department of Supply Chain Management and Management Science, University of Cologne, Albertus-Magnus-Platz, 50923 Cologne, Germany)

Abstract

This paper has been motivated by a fleet optimization problem faced by one of the leading European cargo rail companies. The company operates a fleet of more than 100,000 rail cars and annually invests significant sums of money into new cars. Because the price tag of a new car is over 50,000 euros, planning such a fleet is an important activity at the company. In this paper, we develop and solve analytical models for fleet planning. We first describe the rental process and show how it can be modeled as a queuing loss system. We then develop a profit function and derive several structural results, such as the concavity of the profit function in the fleet size. Building on these structural results, we show how the fleet size can be optimized, how the fleet structure (i.e., the types of cars being used) can be optimized, and how a joint fleet of owned and leased cars can be optimized. Because some of the optimal methods are difficult to implement, we also develop and test an approximation that is easy to implement. To illustrate our findings and to validate our approach, we provide numerical results that are based on data of the company that motivated our research.

Suggested Citation

  • Felix Papier & Ulrich W. Thonemann, 2008. "Queuing Models for Sizing and Structuring Rental Fleets," Transportation Science, INFORMS, vol. 42(3), pages 302-317, August.
    • Handle: RePEc:inm:ortrsc:v:42:y:2008:i:3:p:302-317
    DOI: 10.1287/trsc.1070.0225
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    References listed on IDEAS

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    1. George J. Beaujon & Mark A. Turnquist, 1991. "A Model for Fleet Sizing and Vehicle Allocation," Transportation Science, INFORMS, vol. 25(1), pages 19-45, February.
    2. Warren B. Powell, 1986. "A Stochastic Model of the Dynamic Vehicle Allocation Problem," Transportation Science, INFORMS, vol. 20(2), pages 117-129, May.
    3. Warren B. Powell & Tassio A. Carvalho, 1998. "Dynamic Control of Logistics Queueing Networks for Large-Scale Fleet Management," Transportation Science, INFORMS, vol. 32(2), pages 90-109, May.
    4. Hau L. Lee, 1996. "Effective Inventory and Service Management Through Product and Process Redesign," Operations Research, INFORMS, vol. 44(1), pages 151-159, February.
    5. Gregory A. Godfrey & Warren B. Powell, 2002. "An Adaptive Dynamic Programming Algorithm for Dynamic Fleet Management, I: Single Period Travel Times," Transportation Science, INFORMS, vol. 36(1), pages 21-39, February.
    6. List, George F. & Wood, Bryan & Nozick, Linda K. & Turnquist, Mark A. & Jones, Dean A. & Kjeldgaard, Edwin A. & Lawton, Craig R., 2003. "Robust optimization for fleet planning under uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 39(3), pages 209-227, May.
    7. Sergei V. Savin & Morris A. Cohen & Noah Gans & Ziv Katalan, 2005. "Capacity Management in Rental Businesses with Two Customer Bases," Operations Research, INFORMS, vol. 53(4), pages 617-631, August.
    8. Bojovic, Nebojsa J., 2002. "A general system theory approach to rail freight car fleet sizing," European Journal of Operational Research, Elsevier, vol. 136(1), pages 136-172, January.
    9. William C. Jordan & Mark A. Turnquist, 1983. "A Stochastic, Dynamic Network Model for Railroad Car Distribution," Transportation Science, INFORMS, vol. 17(2), pages 123-145, May.
    10. M. Tainiter, 1964. "Some Stochastic Inventory Models for Rental Situations," Management Science, INFORMS, vol. 11(2), pages 316-326, November.
    11. Yafeng Du & Randolph Hall, 1997. "Fleet Sizing and Empty Equipment Redistribution for Center-Terminal Transportation Networks," Management Science, INFORMS, vol. 43(2), pages 145-157, February.
    12. Ernest Koenigsberg & Richard C. Lam, 1976. "Cyclic Queue Models of Fleet Operations," Operations Research, INFORMS, vol. 24(3), pages 516-529, June.
    13. Ward Whitt, 1991. "The Pointwise Stationary Approximation for Mt/Mt/s Queues Is Asymptotically Correct As the Rates Increase," Management Science, INFORMS, vol. 37(3), pages 307-314, March.
    14. Hanif D. Sherali & Cihan H. Tuncbilek, 1997. "Static and Dynamic Time-Space Strategic Models and Algorithms for Multilevel Rail-Car Fleet Management," Management Science, INFORMS, vol. 43(2), pages 235-250, February.
    15. Yigal Gerchak & David Mossman, 1992. "On the Effect of Demand Randomness on Inventories and Costs," Operations Research, INFORMS, vol. 40(4), pages 804-807, August.
    16. Huseyin Topaloglu & Warren Powell, 2007. "Incorporating Pricing Decisions into the Stochastic Dynamic Fleet Management Problem," Transportation Science, INFORMS, vol. 41(3), pages 281-301, August.
    17. Linos F. Frantzeskakis & Warren B. Powell, 1990. "A Successive Linear Approximation Procedure for Stochastic, Dynamic Vehicle Allocation Problems," Transportation Science, INFORMS, vol. 24(1), pages 40-57, February.
    18. Huseyin Topaloglu & Warren B. Powell, 2006. "Dynamic-Programming Approximations for Stochastic Time-Staged Integer Multicommodity-Flow Problems," INFORMS Journal on Computing, INFORMS, vol. 18(1), pages 31-42, February.
    19. Mark A. Turnquist & William C. Jordan, 1986. "Fleet Sizing under Production Cycles and Uncertain Travel Times," Transportation Science, INFORMS, vol. 20(4), pages 227-236, November.
    20. Kenneth R. Baker & Michael J. Magazine & Henry L. W. Nuttle, 1986. "The Effect of Commonality on Safety Stock in a Simple Inventory Model," Management Science, INFORMS, vol. 32(8), pages 982-988, August.
    21. G J King & H Topaloglu, 2007. "Incorporating the pricing decisions into the dynamic fleet management problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(8), pages 1065-1074, August.
    22. Peiling Wu & Joseph C. Hartman & George R. Wilson, 2005. "An Integrated Model and Solution Approach for Fleet Sizing with Heterogeneous Assets," Transportation Science, INFORMS, vol. 39(1), pages 87-103, February.
    23. Gregory A. Godfrey & Warren B. Powell, 2002. "An Adaptive Dynamic Programming Algorithm for Dynamic Fleet Management, II: Multiperiod Travel Times," Transportation Science, INFORMS, vol. 36(1), pages 40-54, February.
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    Cited by:

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    2. Frank, Laura & Klopfer, Antonia & Walther, Grit, 2024. "Designing corporate mobility as a service – Decision support and perspectives," Transportation Research Part A: Policy and Practice, Elsevier, vol. 182(C).
    3. Vanga, Ratnaji & Venkateswaran, Jayendran, 2020. "Fleet sizing of reusable articles under uncertain demand and turnaround times," European Journal of Operational Research, Elsevier, vol. 285(2), pages 566-582.
    4. Leonardo D. Epstein & Eduardo González & Abdón Sepúlveda, 2020. "Optimal size of a rental inventory with items available from a secondary source: a model with non-stationary probabilities," Annals of Operations Research, Springer, vol. 286(1), pages 371-390, March.
    5. Kallrath, J. & Klosterhalfen, S.T. & Walter, M. & Fischer, G. & Blackburn, R., 2017. "Payload-based fleet optimization for rail cars in the chemical industry," European Journal of Operational Research, Elsevier, vol. 259(1), pages 113-129.
    6. Van der Heide, G. & Roodbergen, K.J. & Van Foreest, N.D., 2021. "Cross docking for libraries with a depot," European Journal of Operational Research, Elsevier, vol. 290(2), pages 749-765.
    7. Mohamed Amjath & Laoucine Kerbache & James MacGregor Smith, 2024. "A Closed Queueing Networks Approach for an Optimal Heterogeneous Fleet Size of an Inter-Facility Bulk Material Transfer System," Logistics, MDPI, vol. 8(1), pages 1-38, March.
    8. José Carbajal & Alan Erera & Martin Savelsbergh, 2013. "Balancing fleet size and repositioning costs in LTL trucking," Annals of Operations Research, Springer, vol. 203(1), pages 235-254, March.
    9. Jonathan Turner & Soonhui Lee & Mark Daskin & Tito Homem-de-Mello & Karen Smilowitz, 2012. "Dynamic fleet scheduling with uncertain demand and customer flexibility," Computational Management Science, Springer, vol. 9(4), pages 459-481, November.
    10. Felix Papier & Ulrich W. Thonemann, 2010. "Capacity Rationing in Stochastic Rental Systems with Advance Demand Information," Operations Research, INFORMS, vol. 58(2), pages 274-288, April.
    11. Hyunjin Lee & Taesik Lee, 2021. "Demand modelling for emergency medical service system with multiple casualties cases: k-inflated mixture regression model," Flexible Services and Manufacturing Journal, Springer, vol. 33(4), pages 1090-1115, December.
    12. Pazour, Jennifer A. & Roy, Debjit, 2012. "Minimizing Customer Waiting Costs for Rental Vehicle Providers using Threshold Reservation Policies," IIMA Working Papers WP2012-12-05, Indian Institute of Management Ahmedabad, Research and Publication Department.
    13. Vincent W. Slaugh & Bahar Biller & Sridhar R. Tayur, 2016. "Managing Rentals with Usage-Based Loss," Manufacturing & Service Operations Management, INFORMS, vol. 18(3), pages 429-444, July.
    14. Asteris, Michael & Collins, Alan & Jones, Dylan F., 2012. "Container port infrastructure in north-west Europe: Policy-level modeling," Journal of Policy Modeling, Elsevier, vol. 34(2), pages 312-324.

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