Computing non-stationary (s,S) policies using mixed integer linear programming

This paper addresses the single-item single-stocking location non-stationary stochastic lot sizing problem under the (s; S) control policy. We first present a mixed integer non-linear programming (MINLP) formulation for determining near-optimal (s; S) policy parameters. To tackle larger instances, we then combine the previously introduced MINLP model and a binary search approach. These models can be reformulated as mixed integer linear programming (MILP) models which can be easily implemented and solved by using off-the-shelf optimisation software. Computational experiments demonstrate that optimality gaps of these models are less than 0:3% of the optimal policy cost and computational times are reasonable.