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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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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Klosterhalfen, S.T. & Kallrath, J. & Fischer, G., 2014. "Rail car fleet design: Optimization of structure and size," International Journal of Production Economics, Elsevier, vol. 157(C), pages 112-119.
    4. 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.
    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. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.

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