Stochastic multiobjective problems with complementarity constraints and applications in healthcare management

We consider a class of stochastic multiobjective problems with complementarity constraints (SMOPCCs) in this paper. We derive the first-order optimality conditions including the Clarke/Mordukhovich/strong-type stationarity in the Pareto sense for the SMOPCC. Since these first-order optimality systems involve some unknown index sets, we reformulate them as nonlinear equations with simple constraints. Then, we introduce an asymptotic method to solve these constrained equations. Furthermore, we apply this methodology results to a patient allocation problem in healthcare management.