IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v64y2017i7p531-546.html
   My bibliography  Save this article

Probabilistic resource pooling games

Author

Listed:
  • Loe Schlicher
  • Marco Slikker
  • Geert‐Jan van Houtum

Abstract

We study a setting with a single type of resource and with several players, each associated with a single resource (of this type). Unavailability of these resources comes unexpectedly and with player‐specific costs. Players can cooperate by reallocating the available resources to the ones that need the resources most and let those who suffer the least absorb all the costs. We address the cost savings allocation problem with concepts of cooperative game theory. In particular, we formulate a probabilistic resource pooling game and study them on various properties. We show that these games are not necessarily convex, do have non‐empty cores, and are totally balanced. The latter two are shown via an interesting relationship with Böhm‐Bawerk horse market games. Next, we present an intuitive class of allocation rules for which the resulting allocations are core members and study an allocation rule within this class of allocation rules with an appealing fairness property. Finally, we show that our results can be applied to a spare parts pooling situation.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:64:y:2017:i:7:p:531-546
    DOI: 10.1002/nav.21776
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.21776
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.21776?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. M. Guajardo & M. Rönnqvist, 2015. "Cost allocation in inventory pools of spare parts with service-differentiated demand classes," International Journal of Production Research, Taylor & Francis Journals, vol. 53(1), pages 220-237, January.
    2. Geert-Jan van Houtum & Bram Kranenburg, 2015. "Spare Parts Inventory Control under System Availability Constraints," International Series in Operations Research and Management Science, Springer, edition 127, number 978-1-4899-7609-3, September.
    3. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
    4. Albert Y. Ha, 1997. "Inventory Rationing in a Make-to-Stock Production System with Several Demand Classes and Lost Sales," Management Science, INFORMS, vol. 43(8), pages 1093-1103, August.
    5. Tijs, Stef & Borm, Peter & Lohmann, Edwin & Quant, Marieke, 2011. "An average lexicographic value for cooperative games," European Journal of Operational Research, Elsevier, vol. 213(1), pages 210-220, August.
    6. Wong, Hartanto & Oudheusden, Dirk Van & Cattrysse, Dirk, 2007. "Cost allocation in spare parts inventory pooling," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 43(4), pages 370-386, July.
    7. 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.
    8. Karsten, Frank & Basten, Rob J.I., 2014. "Pooling of spare parts between multiple users: How to share the benefits?," European Journal of Operational Research, Elsevier, vol. 233(1), pages 94-104.
    9. Shoshana Anily & Moshe Haviv, 2010. "Cooperation in Service Systems," Operations Research, INFORMS, vol. 58(3), pages 660-673, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Schlicher, Loe & Lurkin, Virginie, 2022. "Stable allocations for choice-based collaborative price setting," European Journal of Operational Research, Elsevier, vol. 302(3), pages 1242-1254.
    5. Zhanwen Shi & Erbao Cao & Kai Nie, 2023. "Capacity pooling games in crowdsourcing services," Electronic Commerce Research, Springer, vol. 23(2), pages 1007-1047, June.
    6. 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.
    7. 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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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).
    7. 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.
    8. Frank Karsten & Marco Slikker & Geert‐Jan van Houtum, 2012. "Inventory pooling games for expensive, low‐demand spare parts," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(5), pages 311-324, August.
    9. 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.
    10. 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.
    11. Miguel Ángel Mirás Calvo & Carmen Quinteiro Sandomingo & Estela Sánchez Rodríguez, 2020. "The boundary of the core of a balanced game: face games," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(2), pages 579-599, June.
    12. Shuo Zeng & Moshe Dror, 2019. "Serving many masters: an agent and his principals," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(1), pages 23-59, August.
    13. Mahdavi, Mojtaba & Olsen, Tava Lennon, 2021. "The dual-serving problem: What is the right choice of inventory strategy?," Omega, Elsevier, vol. 103(C).
    14. M Dror & B C Hartman, 2011. "Survey of cooperative inventory games and extensions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 565-580, April.
    15. Rogna, Marco, 2021. "The central core and the mid-central core as novel set-valued and point-valued solution concepts for transferable utility coalitional games," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 1-11.
    16. Loe Schlicher & Marco Slikker & Geert-Jan Houtum, 2018. "Pooling of critical, low-utilization resources with unavailability," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(1), pages 233-263, January.
    17. Mauricio Varas & Franco Basso & Paul Bosch & Juan Pablo Contreras & Raúl Pezoa, 2022. "A horizontal collaborative approach for planning the wine grape harvesting," Operational Research, Springer, vol. 22(5), pages 4965-4998, November.
    18. Luis A. Guardiola & Ana Meca & Justo Puerto, 2021. "Enforcing fair cooperation in production-inventory settings with heterogeneous agents," Annals of Operations Research, Springer, vol. 305(1), pages 59-80, October.
    19. Zheng, Meimei & Ye, Hongqing & Wang, Dong & Pan, Ershun, 2021. "Joint Optimization of Condition-Based Maintenance and Spare Parts Orders for Multi-Unit Systems with Dual Sourcing," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    20. Alarcón, F. & Alemany, M.M.E. & Ortiz, A., 2009. "Conceptual framework for the characterization of the order promising process in a collaborative selling network context," International Journal of Production Economics, Elsevier, vol. 120(1), pages 100-114, July.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:navres:v:64:y:2017:i:7:p:531-546. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.