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Optimal sharing of surgical costs in the presence of queues

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  • Paula González
  • Carmen Herrero

Abstract

We deal with a cost-allocation problem arising from sharing a medical service in the presence of queues. We use a standard queuing theory model in a context of several medical procedures, a certain demand for treatment and a maximum average waiting-time guaranteed by the government. We show that the sharing of an operating-theatre to treat patients of different medical disciplines leads to a cost reduction. We then compute an optimal fee per procedure for the use of the operating theatre, based on the Shapley value. Afterwards, considering the recovery time, we characterize the conditions under which the co-operation among treatments has a positive impact on the post-operative costs. Finally, a numerical example, constructed on the basis of real data, is provided to highlight the main features of our model. Copyright Springer-Verlag 2004

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:59:y:2004:i:3:p:435-446
    DOI: 10.1007/s001860400350
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    Cited by:

    1. Atay, Ata & Trudeau, Christian, 2024. "Queueing games with an endogenous number of machines," Games and Economic Behavior, Elsevier, vol. 144(C), pages 104-125.
    2. Stefano Moretti & Fioravante Patrone, 2008. "Transversality of the Shapley value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 1-41, July.
    3. Álvarez, Xana & Gómez-Rúa, María & Vidal-Puga, Juan, 2019. "Risk prevention of land flood: A cooperative game theory approach," MPRA Paper 91515, University Library of Munich, Germany.
    4. Haizhen Mou, 2012. "The political economy of public health expenditure and wait times in a public‐private mixed health care system," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 45(4), pages 1640-1666, November.
    5. Lee, Hyun-Rok & Lee, Taesik, 2024. "Reward function design method to achieve system-level objectives in ambulance diversion problem," European Journal of Operational Research, Elsevier, vol. 317(3), pages 1003-1014.
    6. 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.
    7. Shoshana Anily & Moshe Haviv, 2010. "Cooperation in Service Systems," Operations Research, INFORMS, vol. 58(3), pages 660-673, June.
    8. Michael Samudra & Carla Van Riet & Erik Demeulemeester & Brecht Cardoen & Nancy Vansteenkiste & Frank E. Rademakers, 2016. "Scheduling operating rooms: achievements, challenges and pitfalls," Journal of Scheduling, Springer, vol. 19(5), pages 493-525, October.
    9. Avishai Mandelbaum & Petar Momčilović & Yulia Tseytlin, 2012. "On Fair Routing from Emergency Departments to Hospital Wards: QED Queues with Heterogeneous Servers," Management Science, INFORMS, vol. 58(7), pages 1273-1291, July.

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    More about this item

    Keywords

    Surgical waiting-lists; Queueing theory; Cost-sharing game; C44; C71; H51;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • H51 - Public Economics - - National Government Expenditures and Related Policies - - - Government Expenditures and Health

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