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Resource Pooling and Cost Allocation Among Independent Service Providers

Author

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  • Frank Karsten

    (School of Industrial Engineering, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands)

  • Marco Slikker

    (School of Industrial Engineering, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands)

  • Geert-Jan van Houtum

    (School of Industrial Engineering, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands)

Abstract

We study a situation where several independent service providers collaborate by complete pooling of their resources and customer streams into a joint service system. These service providers may represent such diverse organizations as hospitals that pool beds or maintenance firms that pool repairmen. We model the service systems as Erlang delay systems ( M/M/s queues) that face a fixed cost rate per server and homogeneous delay costs for waiting customers. We examine rules to fairly allocate the collective costs of the pooled system amongst the participants by applying concepts from cooperative game theory. We consider both the case where players’ numbers of servers are exogenously given and the scenario where any coalition picks an optimal number of servers. By exploiting new analytical properties of the continuous extension of the classic Erlang delay function, we provide sufficient conditions for the games under consideration to possess a core allocation (i.e., an allocation that gives no group of players an incentive to split off and form a separate pool) and to admit a population monotonic allocation scheme (whereby adding extra players does not make anyone worse off). This is not guaranteed in general, as illustrated via examples.

Suggested Citation

  • Frank Karsten & Marco Slikker & Geert-Jan van Houtum, 2015. "Resource Pooling and Cost Allocation Among Independent Service Providers," Operations Research, INFORMS, vol. 63(2), pages 476-488, April.
    • Handle: RePEc:inm:oropre:v:63:y:2015:i:2:p:476-488
    DOI: 10.1287/opre.2015.1360
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    Cited by:

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    4. Loe Schlicher & Marco Slikker & Willem van Jaarsveld & Geert-Jan van Houtum, 2020. "Core Nonemptiness of Stratified Pooling Games: A Structured Markov Decision Process Approach," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1445-1465, November.
    5. Judith Timmer & Werner Scheinhardt, 2018. "Customer and Cost Sharing in a Jackson Network," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-10, September.
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    7. Bendel, Dan & Haviv, Moshe, 2018. "Cooperation and sharing costs in a tandem queueing network," European Journal of Operational Research, Elsevier, vol. 271(3), pages 926-933.
    8. Lotty E. Westerink‐Duijzer & Loe P. J. Schlicher & Marieke Musegaas, 2020. "Core Allocations for Cooperation Problems in Vaccination," Production and Operations Management, Production and Operations Management Society, vol. 29(7), pages 1720-1737, July.
    9. Schlicher, L. & Dietzenbacher, Bas & Musegaas, Marieke, 2023. "Stable streaming platforms: a cooperative game approach," Research Memorandum 001, Maastricht University, Graduate School of Business and Economics (GSBE).
    10. Westerink-Duijzer, L.E. & Schlicher, L.P.J. & Musegaas, M., 2019. "Fair allocations for cooperation problems in vaccination," Econometric Institute Research Papers EI2019-06, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    11. Frank Karsten & Marco Slikker & Peter Borm, 2017. "Cost allocation rules for elastic single‐attribute situations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(4), pages 271-286, June.
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    13. Luo, Chunlin & Zhou, Xiaoyang & Lev, Benjamin, 2022. "Core, shapley value, nucleolus and nash bargaining solution: A Survey of recent developments and applications in operations management," Omega, Elsevier, vol. 110(C).
    14. Schlicher, L.P.J. & Musegaas, M. & Westerink-Duijzer, L.E., 2019. "Resource location games," Econometric Institute Research Papers EI2019-05, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    15. van Oorschot, K.E. & Wang, Yan & Akkermans, Henk, 2018. "Throbbing between two lives : Resource pooling in service supply chains," Other publications TiSEM ca35c4c6-4bec-4d57-aa61-3, Tilburg University, School of Economics and Management.
    16. Loe Schlicher & Marco Slikker & Geert‐Jan van Houtum, 2017. "Probabilistic resource pooling games," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(7), pages 531-546, October.
    17. Wang, Yong & Peng, Shouguo & Zhou, Xuesong & Mahmoudi, Monirehalsadat & Zhen, Lu, 2020. "Green logistics location-routing problem with eco-packages," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 143(C).
    18. Ulaş Özen & Marco Slikker & Greys Sošić, 2022. "On the core of m$m$‐attribute games," Production and Operations Management, Production and Operations Management Society, vol. 31(4), pages 1770-1787, April.
    19. Vahdani, Behnam & Mohammadi, Mehrdad & Thevenin, Simon & Meyer, Patrick & Dolgui, Alexandre, 2023. "Production-sharing of critical resources with dynamic demand under pandemic situation: The COVID-19 pandemic," Omega, Elsevier, vol. 120(C).

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