决策依赖不确定性下疫苗接种点选址的分布式鲁棒优化

Distributionally Robust Optimization of Vacination Site Location Problem under Decision-dependent Uncertainty

考虑到居民接种疫苗的意愿往往会受到接种点选址决策的影响,提出一种新的应对接种需求具有决策依赖不确定性的疫苗接种点选址方法。首先,构造了基于矩信息的决策依赖模糊集对接种需求分布进行建模,将每个随机接种需求的均值和方差表示为选址决策的分段线性函数。其次,在每个需求点引入最低接种量,提出了需求不确定下接种点选址的分布式鲁棒优化模型。最后,运用鲁棒对等理论提出并证明了两个命题,结合McCormick包络法,将该模型重构为混合整数线性规划模型。算例测试和灵敏度分析结果表明,本文模型可以实现经济效益与社会效益的平衡,从而为不确定环境下疫苗接种点的合理布局提供决策支持。

Considering that residents'willingness to receive vaccines is often influenced by vaccination site location decisions,a new method was proposed to address the vaccination needs with decision-dependent uncertainty.Firstly,a decision-dependent fuzzy set based on moment information was constructed to model the distribution of vaccination demands,and the mean and variance of each random vaccination demand were expressed as a piecewise linear function of location decision.Secondly,the minimum vaccination amount was introduced at each demand point,and a distributionally robust optimization model was proposed for vaccination site location under uncertain demand.Finally,two propositions were proposed and proved by using the robust equivalence theory.Combined with McCormick envelope method,the model was reformulated into a mixed integer linear programming model.The results of testing and sensitivity analysis indicate that this model can achieve a balance between economic and social benefits,thereby providing decision support for the reasonable layout of vaccination sites in uncertain environments.