An MILP model for computing (s, S) policies with stochastic demand

In this paper, we present mixed integer linear programming (MILP) models to compute near optimal parameters for the nonstationary stochastic lot sizing problem under the (s, S) control policy. Our models are built based on piecewise linearization of first order loss functions. We discuss different variants of the stochastic lot sizing problem which include penalty cost scheme, alpha service level constraints, beta service level constraints and beta cycle service level constraints. These models also operate under lost sale settings. Our new MILP models favorably compare to existing approximation heuristics and exact methods in the literature: they are the first MILP heuristics to approximate (s, S) policy parameters, they perform efficiently under four measures of service quality, they work for generically distributed demand patterns as well , and they handle problems under lost sale settings. Our computational experiments demonstrate the effectiveness and versatility of our models.