A Stochastic Nash Equilibrium Problem for Medical Supply Competition

Georgia Fargetta (), Antonino Maugeri () and Laura Scrimali ()
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Georgia Fargetta: University of Catania
Antonino Maugeri: University of Catania
Laura Scrimali: University of Catania

Journal of Optimization Theory and Applications, 2022, vol. 193, issue 1, No 17, 354-380

Abstract: 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.

Keywords: Stochastic programming problem; Variational inequality; Duality; Medical Supplies; 49J40; 90C46; 90B15 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-022-02025-y

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