IDEAS home Printed from https://ideas.repec.org/a/spr/orspec/v40y2018i1d10.1007_s00291-017-0499-6.html
   My bibliography  Save this article

Pooling of critical, low-utilization resources with unavailability

Author

Listed:
  • Loe Schlicher

    (Eindhoven University of Technology)

  • Marco Slikker

    (Eindhoven University of Technology)

  • Geert-Jan Houtum

    (Eindhoven University of Technology)

Abstract

We consider an environment in which several independent service providers can collaborate by pooling their critical, low-utilization resources that are subject to unavailability. We examine the allocation of the joint profit for such a pooled situation by studying an associated cooperative game. For this game, we will prove non-emptiness of the core, present a population monotonic allocation scheme and show convexity under some conditions. Moreover, four allocation rules will be introduced and we will investigate whether they satisfy monotonicity to availability, monotonicity to profit, situation symmetry and game symmetry. Finally, we will also investigate whether the payoff vectors resulting from those allocation rules are members of the core.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:orspec:v:40:y:2018:i:1:d:10.1007_s00291-017-0499-6
    DOI: 10.1007/s00291-017-0499-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00291-017-0499-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00291-017-0499-6?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Heuvel, Wilco van den & Borm, Peter & Hamers, Herbert, 2007. "Economic lot-sizing games," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1117-1130, January.
    2. Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 139-199, December.
    3. Behzad Hezarkhani & Marco Slikker & Tom Woensel, 2016. "A competitive solution for cooperative truckload delivery," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 51-80, January.
    4. Muto, S. & Nakayama, M. & Potters, J.A.M. & Tijs, S.H., 1988. "On big boss games," Other publications TiSEM 488a314a-179c-4628-91e6-7, Tilburg University, School of Economics and Management.
    5. 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.
    6. 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.
    7. Ulac{s} Özen & Jan Fransoo & Henk Norde & Marco Slikker, 2008. "Cooperation Between Multiple Newsvendors with Warehouses," Manufacturing & Service Operations Management, INFORMS, vol. 10(2), pages 311-324, February.
    8. 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.
    9. Jun Li & Xiaoqiang Cai & Yinlian Zeng, 2016. "Cost allocation for less-than-truckload collaboration among perishable product retailers," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 81-117, January.
    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. 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.
    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.

    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. 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.
    2. Hezarkhani, Behzad & Slikker, Marco & Van Woensel, Tom, 2018. "Collaborative replenishment in the presence of intermediaries," European Journal of Operational Research, Elsevier, vol. 266(1), pages 135-146.
    3. 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.
    4. Luis A. Guardiola & Ana Meca & Justo Puerto, 2022. "The effect of consolidated periods in heterogeneous lot-sizing games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 380-404, July.
    5. 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.
    6. Li, Jun & Feng, Hairong & Zeng, Yinlian, 2014. "Inventory games with permissible delay in payments," European Journal of Operational Research, Elsevier, vol. 234(3), pages 694-700.
    7. 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.
    8. Bouchery, Yann & Hezarkhani, Behzad & Stauffer, Gautier, 2022. "Coalition formation and cost sharing for truck platooning," Transportation Research Part B: Methodological, Elsevier, vol. 165(C), pages 15-34.
    9. J. Drechsel & A. Kimms, 2010. "The subcoalition-perfect core of cooperative games," Annals of Operations Research, Springer, vol. 181(1), pages 591-601, December.
    10. Rodica Branzei & Dinko Dimitrov & Stef Tijs, 2008. "Convex Games Versus Clan Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 363-372.
    11. 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.
    12. Xin Chen & Jiawei Zhang, 2009. "A Stochastic Programming Duality Approach to Inventory Centralization Games," Operations Research, INFORMS, vol. 57(4), pages 840-851, August.
    13. Stefano Moretti & Henk Norde, 2022. "Some new results on generalized additive games," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(1), pages 87-118, March.
    14. Hamers, H.J.M. & Miquel, S. & Norde, H.W., 2011. "Monotonic Stable Solutions for Minimum Coloring Games," Other publications TiSEM efae8d09-83e6-4fe4-9623-e, Tilburg University, School of Economics and Management.
    15. Brânzei, R. & Scotti, F. & Tijs, S.H. & Torre, A., 2002. "Discretization of Information Collecting Situations and Continuity of Compensation Rules," Discussion Paper 2002-18, Tilburg University, Center for Economic Research.
    16. Özen, Ulas & Norde, Henk & Slikker, Marco, 2011. "On the convexity of newsvendor games," International Journal of Production Economics, Elsevier, vol. 133(1), pages 35-42, September.
    17. Brânzei, R. & Tijs, S.H. & Timmer, J.B., 2000. "Collecting Information to improve Decision-Making," Other publications TiSEM 74fa171d-2799-4747-9c2e-7, Tilburg University, School of Economics and Management.
    18. Endre Bjørndal & Herbert Hamers & Maurice Koster, 2004. "Cost allocation in a bank ATM network," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(3), pages 405-418, July.
    19. 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.
    20. Ana Meca, 2007. "A core-allocation family for generalized holding cost games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(3), pages 499-517, June.

    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:spr:orspec:v:40:y:2018:i:1:d:10.1007_s00291-017-0499-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.