IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v63y2015i2p476-488.html

Resource Pooling and Cost Allocation Among Independent Service Providers

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.2015.1360
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.2015.1360?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. Cruijssen, Frans & Cools, Martine & Dullaert, Wout, 2007. "Horizontal cooperation in logistics: Opportunities and impediments," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 43(2), pages 129-142, March.
    2. Norde, Henk & Reijnierse, Hans, 2002. "A dual description of the class of games with a population monotonic allocation scheme," Games and Economic Behavior, Elsevier, vol. 41(2), pages 322-343, November.
    3. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Benjaafar, Saifallah, 1995. "Performance bounds for the effectiveness of pooling in multi-processing systems," European Journal of Operational Research, Elsevier, vol. 87(2), pages 375-388, December.
    5. Garcia-Sanz, M.D. & Fernandez, F.R. & Fiestras-Janeiro, M.G. & Garcia-Jurado, I. & Puerto, J., 2008. "Cooperation in Markovian queueing models," European Journal of Operational Research, Elsevier, vol. 188(2), pages 485-495, July.
    6. Shoshana Anily & Moshe Haviv, 2014. "Subadditive and Homogeneous of Degree One Games Are Totally Balanced," Operations Research, INFORMS, vol. 62(4), pages 788-793, August.
    7. A. J. E. M. Janssen & J. S. H. van Leeuwaarden & Bert Zwart, 2011. "Refining Square-Root Safety Staffing by Expanding Erlang C," Operations Research, INFORMS, vol. 59(6), pages 1512-1522, December.
    8. Ward Whitt, 1999. "Partitioning Customers into Service Groups," Management Science, INFORMS, vol. 45(11), pages 1579-1592, November.
    9. Paula González & Carmen Herrero, 2004. "Optimal sharing of surgical costs in the presence of queues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(3), pages 435-446, July.
    10. 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.
    11. Yimin Yu & Saif Benjaafar & Yigal Gerchak, 2015. "Capacity Sharing and Cost Allocation among Independent Firms with Congestion," Production and Operations Management, Production and Operations Management Society, vol. 24(8), pages 1285-1310, August.
    12. Shoshana Anily & Moshe Haviv, 2010. "Cooperation in Service Systems," Operations Research, INFORMS, vol. 58(3), pages 660-673, June.
    13. Chris Snijders, 1995. "Axiomatization of the Nucleolus," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 189-196, February.
    14. M. E. Dyer & L. G. Proll, 1977. "Note--On the Validity of Marginal Analysis for Allocating Servers in M/M/c Queues," Management Science, INFORMS, vol. 23(9), pages 1019-1022, May.
    15. Joel M. Calabrese, 1992. "Optimal Workload Allocation in Open Networks of Multiserver Queues," Management Science, INFORMS, vol. 38(12), pages 1792-1802, December.
    16. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
    17. Sem Borst & Avi Mandelbaum & Martin I. Reiman, 2004. "Dimensioning Large Call Centers," Operations Research, INFORMS, vol. 52(1), pages 17-34, February.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Hanlin Liu & Yimin Yu & Saif Benjaafar & Huihui Wang, 2022. "Price-Directed Cost Sharing and Demand Allocation Among Service Providers with Multiple Demand Sources and Multiple Facilities," Manufacturing & Service Operations Management, INFORMS, vol. 24(1), pages 647-663, January.
    3. 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.
    4. Hanlin Liu & Yimin Yu, 2022. "Incentives for Shared Services: Multiserver Queueing Systems with Priorities," Manufacturing & Service Operations Management, INFORMS, vol. 24(3), pages 1751-1759, May.
    5. Slikker, Marco & Norde, Henk, 2011. "The monoclus of a coalitional game," Games and Economic Behavior, Elsevier, vol. 71(2), pages 420-435, March.
    6. Groote Schaarsberg, M. & Borm, P.E.M. & Hamers, H.J.M. & Reijnierse, J.H., 2012. "Interactive Purchasing Situations," Other publications TiSEM 963efbbe-7dbf-43ba-948c-1, Tilburg University, School of Economics and Management.
    7. Oualid Jouini & Yves Dallery & Rabie Nait-Abdallah, 2008. "Analysis of the Impact of Team-Based Organizations in Call Center Management," Management Science, INFORMS, vol. 54(2), pages 400-414, February.
    8. 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.
    9. Tamás Solymosi, 2024. "Assignment games with population monotonic allocation schemes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 62(1), pages 67-88, February.
    10. Andradóttir, Sigrún & Ayhan, Hayriye & Down, Douglas G., 2017. "Resource pooling in the presence of failures: Efficiency versus risk," European Journal of Operational Research, Elsevier, vol. 256(1), pages 230-241.
    11. Lijun Gao & Jun Li & Yinlian Zeng, 2024. "Patient referral strategy and cost sharing for a medical consortium," 4OR, Springer, vol. 22(2), pages 253-281, June.
    12. Nur Sunar & Yichen Tu & Serhan Ziya, 2021. "Pooled vs. Dedicated Queues when Customers Are Delay-Sensitive," Management Science, INFORMS, vol. 67(6), pages 3785-3802, June.
    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. Slikker, M. & Norde, H.W., 2008. "The Monoclus of a Coalitional Game," Other publications TiSEM 8b2bae34-674a-4632-a64e-9, Tilburg University, School of Economics and Management.
    15. Josep M. Izquierdo & Jesús Montes & Carlos Rafels, 2024. "Population Lorenz-monotonic allocation schemes for TU-games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 63(2), pages 417-436, September.
    16. 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.
    17. Izquierdo, Josep M. & Rafels, Carles, 2001. "Average Monotonic Cooperative Games," Games and Economic Behavior, Elsevier, vol. 36(2), pages 174-192, August.
    18. Brânzei, R. & Tijs, S.H. & Timmer, J.B., 2000. "Cooperative Games arising from Information Sharing Situations," Discussion Paper 2000-42, Tilburg University, Center for Economic Research.
    19. Rodríguez-Pereira, Jessica & Cherkesly, Marilène & Rancourt, Marie-Ève & Laporte, Gilbert, 2026. "A comparison of cost-sharing models in horizontal cooperative routing," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 207(C).
    20. van Schijndel, M.J.M. & Braat, J.J.M., 2012. "Vehicle Planning in Cross Chain Control Centers," Discussion Paper 2012-058, Tilburg University, Center for Economic Research.

    More about this item

    Keywords

    ;
    ;
    ;

    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:inm:oropre:v:63:y:2015:i:2:p:476-488. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.