Approximations for non-stationary stochastic lot-sizing under (s,Q)-type policy

This paper addresses the single-item single-stocking location non-stationary stochastic lot-sizing problem under a reorder point – order quantity control strategy. The reorder points and order quantities are chosen at the beginning of the planning horizon. The re-order points are allowed to vary with time and we consider order quantities either to bea series of time-dependent constants or a fixed value; this leads to two variants of the policy: the (s t , Q t ) and the (s t , Q) policies, respectively. For both policies, we present stochastic dynamic programs (SDP) to determine optimal policy parameters and introduce mixed integer non-linear programming (MINLP) heuristics that leverage piece wise-linear approximations of the cost function. Numerical experiments demonstrate that our solution method efficiently computes near-optimal parameters for a broad class of problem instances.