IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v193y2022i1d10.1007_s10957-022-02025-y.html
   My bibliography  Save this article

A Stochastic Nash Equilibrium Problem for Medical Supply Competition

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-022-02025-y
    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/s10957-022-02025-y?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. 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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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).
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. A. Maugeri & F. Raciti, 2010. "Remarks on infinite dimensional duality," Journal of Global Optimization, Springer, vol. 46(4), pages 581-588, April.
    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.
    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. Elena Molho & Domenico Scopelliti, 2023. "On the study of multistage stochastic vector quasi-variational problems," Journal of Global Optimization, Springer, vol. 86(4), pages 931-952, August.
    2. Domenico Scopelliti, 2022. "On a Class of Multistage Stochastic Hierarchical Problems," Mathematics, MDPI, vol. 10(21), pages 1-13, October.

    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. Jie Jiang & Shengjie Li, 2021. "Regularized Sample Average Approximation Approach for Two-Stage Stochastic Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 650-671, August.
    2. Francesca Faraci & Baasansuren Jadamba & Fabio Raciti, 2016. "On Stochastic Variational Inequalities with Mean Value Constraints," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 675-693, November.
    3. Hu, Shaolong & Han, Chuanfeng & Dong, Zhijie Sasha & Meng, Lingpeng, 2019. "A multi-stage stochastic programming model for relief distribution considering the state of road network," Transportation Research Part B: Methodological, Elsevier, vol. 123(C), pages 64-87.
    4. Gabriella Colajanni & Patrizia Daniele & Daniele Sciacca, 2022. "On the Provision of Services With UAVs in Disaster Scenarios: A Two-Stage Stochastic Approach," SN Operations Research Forum, Springer, vol. 3(1), pages 1-30, March.
    5. Can Li & Ignacio E. Grossmann, 2019. "A finite $$\epsilon $$ϵ-convergence algorithm for two-stage stochastic convex nonlinear programs with mixed-binary first and second-stage variables," Journal of Global Optimization, Springer, vol. 75(4), pages 921-947, December.
    6. Nur Banu Demir & Serhat Gul & Melih Çelik, 2021. "A stochastic programming approach for chemotherapy appointment scheduling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 68(1), pages 112-133, February.
    7. Baasansuren Jadamba & Fabio Raciti, 2015. "On the Modeling of Some Environmental Games with Uncertain Data," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 959-968, December.
    8. Baloch, Gohram & Gzara, Fatma & Elhedhli, Samir, 2023. "Risk-based allocation of COVID-19 personal protective equipment under supply shortages," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1085-1100.
    9. 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).
    10. Shao, Jianfang & Fan, Yu & Wang, Xihui & Liang, Changyong & Liang, Liang, 2023. "Designing a new framework agreement in humanitarian logistics based on deprivation cost functions," International Journal of Production Economics, Elsevier, vol. 256(C).
    11. Kar, Biswajit & Jenamani, Mamata, 2024. "Optimal multimodal multi-echelon vaccine distribution network design for low and medium-income countries with manufacturing infrastructure during healthcare emergencies," International Journal of Production Economics, Elsevier, vol. 273(C).
    12. Mehdi Alizadeh & Mir Saman Pishvaee & Hamed Jahani & Mohammad Mahdi Paydar & Ahmad Makui, 2023. "Viable healthcare supply chain network design for a pandemic," Annals of Operations Research, Springer, vol. 328(1), pages 35-73, September.
    13. Aarti Singh & Ratri Parida, 2022. "Decision-Making Models for Healthcare Supply Chain Disruptions: Review and Insights for Post-pandemic Era," International Journal of Global Business and Competitiveness, Springer, vol. 17(2), pages 130-141, December.
    14. Baasansuren Jadamba & Massimo Pappalardo & Fabio Raciti, 2018. "Efficiency and Vulnerability Analysis for Congested Networks with Random Data," Journal of Optimization Theory and Applications, Springer, vol. 177(2), pages 563-583, May.
    15. Escudero, Laureano F. & Garín, M. Araceli & Monge, Juan F. & Unzueta, Aitziber, 2020. "Some matheuristic algorithms for multistage stochastic optimization models with endogenous uncertainty and risk management," European Journal of Operational Research, Elsevier, vol. 285(3), pages 988-1001.
    16. Aldrighetti, Riccardo & Battini, Daria & Ivanov, Dmitry & Zennaro, Ilenia, 2021. "Costs of resilience and disruptions in supply chain network design models: A review and future research directions," International Journal of Production Economics, Elsevier, vol. 235(C).
    17. Zhang, Ying & Qi, Mingyao & Miao, Lixin & Liu, Erchao, 2014. "Hybrid metaheuristic solutions to inventory location routing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 70(C), pages 305-323.
    18. Lee, Jinkyu & Bae, Sanghyeon & Kim, Woo Chang & Lee, Yongjae, 2023. "Value function gradient learning for large-scale multistage stochastic programming problems," European Journal of Operational Research, Elsevier, vol. 308(1), pages 321-335.
    19. Cailin Wang & Jidong Wu & Xin He & Mengqi Ye & Wenhui Liu & Rumei Tang, 2018. "Emerging Trends and New Developments in Disaster Research after the 2008 Wenchuan Earthquake," IJERPH, MDPI, vol. 16(1), pages 1-19, December.
    20. Muhammad Rahies Khan & Amir Manzoor, 2021. "Application and Impact of New Technologies in the Supply Chain Management During COVID-19 Pandemic: A Systematic Literature Review," International Journal of Economics & Business Administration (IJEBA), International Journal of Economics & Business Administration (IJEBA), vol. 0(2), pages 277-292.

    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:joptap:v:193:y:2022:i:1:d:10.1007_s10957-022-02025-y. 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.