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

TL;DR

This paper develops MILP-based approximation methods for non-stationary stochastic lot-sizing problems under (s,Q) policies, enabling efficient near-optimal solutions for complex, time-varying inventory control scenarios.

Contribution

It introduces mixed integer non-linear programming heuristics with piecewise-linear cost approximations for non-stationary stochastic lot-sizing under (s,Q) policies, a novel approach in this context.

Findings

Efficient computation of near-optimal policy parameters.

Applicable to a broad class of non-stationary inventory problems.

Demonstrated effectiveness through numerical experiments.

Abstract

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 reorder points are allowed to vary with time and we consider order quantities either to be a series of time-dependent constants or a fixed value; this leads to two variants of the policy: the (st,Qt) and the (st,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 piecewise-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.