Periodic Review Multiperiod Inventory Control Under a Mean–Variance Optimization Objective

We study in this correspondence paper a solution scheme which solves a periodic review multiperiod inventory problem under a mean-variance (MV) framework. We first investigate a primal inventory problem with an MV objective function. Owing to the nonseparable nature of variance, we construct an auxiliary problem which is separable. By solving the auxiliary problem, we identify the conditions under which the solutions of the primal and auxiliary problems converge. Hence, we propose the algorithm and show that a base-stock policy is optimal.