Two-stage absolute semi-deviation mean-risk stochastic programming: An application to the supply chain replenishment problem

Abstract

Abstract Conventionally, two-stage stochastic programs have been devised to minimize the expectation of recourse actions. However, in the presence of high data variability, the solutions from expected value models may not be robust, and hence weighted risk measures are introduced in the objective function. In this study, we consider a two-stage stochastic program with mean absolute semi-deviation (MASD) as a risk measure for an application in supply chain planning. Models with MASD lack block-angular structures; thus, they are not suitable for traditional decomposition algorithms and pose computational challenges. We therefore propose a heuristic procedure based on the expected excess risk measure for solving the model. Specifically, we propose a heuristic for a generic replenishment problem in supply chains with MASD risk measures. We evaluate the robustness of the MASD model solutions by comparing the fill rate for replenishment plans with the optimal solutions from deterministic and expected value models, and we demonstrate the efficacy of the heuristic based on extensive computational experiments.