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A Stochastic Nash Equilibrium Problem for Medical Supply Competition

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  • Georgia Fargetta

    (University of Catania)

  • Antonino Maugeri

    (University of Catania)

  • Laura Scrimali

    (University of Catania)

Abstract

In this paper, we study the competition of healthcare institutions for medical supplies in emergencies caused by natural disasters. In particular, we develop a two-stage procurement planning model in a random environment. We consider a pre-event policy, in which each healthcare institution seeks to minimize the purchasing cost of medical items and the transportation time from the first stage, and a recourse decision process to optimize the expected overall costs and the penalty for the prior plan, in response to each disaster scenario. Thus, each institution deals with a two-stage stochastic programming model that takes into account the unmet demand at the first stage, and the consequent penalty. Then, the institutions simultaneously solve their own stochastic optimization problems and reach a stable state governed by the stochastic Nash equilibrium concept. Moreover, we formulate the problem as a variational inequality; both the discrete and the general probability distribution cases are described. We also present an alternative formulation using infinite-dimensional duality tools. Finally, we discuss some numerical illustrations applying the progressive hedging algorithm.

Suggested Citation

  • Georgia Fargetta & Antonino Maugeri & Laura Scrimali, 2022. "A Stochastic Nash Equilibrium Problem for Medical Supply Competition," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 354-380, June.
    • Handle: RePEc:spr:joptap:v:193:y:2022:i:1:d:10.1007_s10957-022-02025-y
    DOI: 10.1007/s10957-022-02025-y
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    References listed on IDEAS

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    1. Mete, Huseyin Onur & Zabinsky, Zelda B., 2010. "Stochastic optimization of medical supply location and distribution in disaster management," International Journal of Production Economics, Elsevier, vol. 126(1), pages 76-84, July.
    2. Salarpour, Mojtaba & Nagurney, Anna, 2021. "A multicountry, multicommodity stochastic game theory network model of competition for medical supplies inspired by the Covid-19 pandemic," International Journal of Production Economics, Elsevier, vol. 236(C).
    3. Georgia Fargetta & Laura Scrimali, 2021. "Optimal Emergency Evacuation with Uncertainty," Springer Optimization and Its Applications, in: Ioannis N. Parasidis & Efthimios Providas & Themistocles M. Rassias (ed.), Mathematical Analysis in Interdisciplinary Research, pages 261-279, Springer.
    4. B. Jadamba & F. Raciti, 2015. "Variational Inequality Approach to Stochastic Nash Equilibrium Problems with an Application to Cournot Oligopoly," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 1050-1070, June.
    5. Patrizia Daniele & Sofia Giuffrè, 2015. "Random Variational Inequalities and the Random Traffic Equilibrium Problem," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 363-381, October.
    6. Semih Atakan & Suvrajeet Sen, 2018. "A Progressive Hedging based branch-and-bound algorithm for mixed-integer stochastic programs," Computational Management Science, Springer, vol. 15(3), pages 501-540, October.
    7. Joachim Gwinner & Fabio Raciti, 2012. "Some equilibrium problems under uncertainty and random variational inequalities," Annals of Operations Research, Springer, vol. 200(1), pages 299-319, November.
    8. R. T. Rockafellar & Roger J.-B. Wets, 1991. "Scenarios and Policy Aggregation in Optimization Under Uncertainty," Mathematics of Operations Research, INFORMS, vol. 16(1), pages 119-147, February.
    9. A. Maugeri & F. Raciti, 2010. "Remarks on infinite dimensional duality," Journal of Global Optimization, Springer, vol. 46(4), pages 581-588, April.
    10. Anna Nagurney & Mojtaba Salarpour & June Dong & Pritha Dutta, 2021. "Competition for Medical Supplies Under Stochastic Demand in the Covid-19 Pandemic: A Generalized Nash Equilibrium Framework," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Panos M. Pardalos (ed.), Nonlinear Analysis and Global Optimization, pages 331-356, Springer.
    11. Min Li & Chao Zhang, 2020. "Two-Stage Stochastic Variational Inequality Arising from Stochastic Programming," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 324-343, July.
    12. Anna Nagurney & Mojtaba Salarpour & June Dong & Ladimer S. Nagurney, 2020. "A Stochastic Disaster Relief Game Theory Network Model," SN Operations Research Forum, Springer, vol. 1(2), pages 1-33, June.
    13. Riccardo Aldrighetti & Ilenia Zennaro & Serena Finco & Daria Battini, 2019. "Healthcare Supply Chain Simulation with Disruption Considerations: A Case Study from Northern Italy," Global Journal of Flexible Systems Management, Springer;Global Institute of Flexible Systems Management, vol. 20(1), pages 81-102, December.
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    2. Domenico Scopelliti, 2022. "On a Class of Multistage Stochastic Hierarchical Problems," Mathematics, MDPI, vol. 10(21), pages 1-13, October.

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