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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.
摘要：
在本文中,我们研究了在自然灾害引起的紧急情况下医疗机构对医疗用品的竞争。特别是,我们在随机环境中建立了两阶段采购计划模型。我们考虑一项事前政策，每个医疗机构都力求从第一阶段开始将医疗物品的购买成本和运输时间降至最低，和追索决策程序，以优化预期的总成本和对先前计划的惩罚，以应对每个灾难场景。因此，每个机构都处理一个两阶段随机规划模型，该模型考虑了第一阶段未满足的需求，以及随之而来的惩罚。然后，机构同时解决自己的随机优化问题，并达到由随机纳什均衡概念支配的稳定状态。此外，我们将问题表述为变分不等式；描述了离散和一般概率分布的情况。我们还提出了一种使用无限维对偶性工具的替代公式。最后,我们讨论了一些应用渐进对冲算法的数值插图。
