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Capacity rationing in rental systems with two customer classes and batch arrivals

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  • Papier, Felix
  • Thonemann, Ulrich W.

Abstract

Service differentiation is an emerging method to improve profit and to better serve high-priority customers. Such an approach has recently been introduced by one of Europe's leading rail cargo companies. Under this approach, customers can choose between classic and premium services. Premium service is priced above classic service and premium customers receive a service guarantee which classic customers do not receive. The company has to decide under which conditions it should ration its fleet capacity to classic customers in order to increase service of premium customers. We model such a situation as a batch-arrival queuing loss system. We describe the model, solve it optimally, and derive quantities of interest such as service probabilities. We further analyze it by performing numerical experiments based on the data from the company that motivated our research. We show that the potential of capacity rationing can be substantial in situations like the one we analyzed. We also derive conditions under which rationing is especially beneficial, such as under high unit fleet holding costs or in the presence of batch arrivals compared to single arrivals.

Suggested Citation

  • Papier, Felix & Thonemann, Ulrich W., 2011. "Capacity rationing in rental systems with two customer classes and batch arrivals," Omega, Elsevier, vol. 39(1), pages 73-85, January.
    • Handle: RePEc:eee:jomega:v:39:y:2011:i:1:p:73-85
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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. Banerjee, Pradeep K. & Turner, T. Rolf, 2012. "A flexible model for the pricing of perishable assets," Omega, Elsevier, vol. 40(5), pages 533-540.
    3. Saha, Kushal & Bhattacharya, Subir, 2021. "‘Buy online and pick up in-store’: Implications for the store inventory," European Journal of Operational Research, Elsevier, vol. 294(3), pages 906-921.
    4. ElHafsi, Mohsen & Fang, Jianxin & Hamouda, Essia, 2021. "Optimal production and inventory control of multi-class mixed backorder and lost sales demand class models," European Journal of Operational Research, Elsevier, vol. 291(1), pages 147-161.
    5. Pinto, Roberto, 2016. "Stock rationing under a profit satisficing objective," Omega, Elsevier, vol. 65(C), pages 55-68.
    6. Xufeng Yang & Wen Jiao & Juliang Zhang & Hong Yan, 2022. "Capacity management for a leasing system with different equipment and batch demands," Production and Operations Management, Production and Operations Management Society, vol. 31(7), pages 3004-3020, July.
    7. Belleh Fontem, 2022. "An optimal stopping policy for car rental businesses with purchasing customers," Annals of Operations Research, Springer, vol. 317(1), pages 47-76, October.
    8. Mohammad Firouz & Linda Li & Burcu B. Keskin, 2022. "Managing equipment rentals: Unreliable fleet, impatient customers, and finite commitment capacity," Production and Operations Management, Production and Operations Management Society, vol. 31(11), pages 3963-3981, November.

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