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

• Published in: European journal of operational research Vol. 298; no. 2; pp. 573 - 584
• Main Authors: Ma, Xiyuan, Rossi, Roberto, Archibald, Thomas Welsh
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 16.04.2022
• Subjects: ([formula omitted]) Policy; Inventory; Non-stationary demand; Stochastic lot-sizing; Non-stationary demand; Stochastic lot-sizing; Inventory; (s,Q) Policy
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2021.06.013

•We model the nonstationary stochastic lot-sizing problem under an (s,Q) policy.•We investigate the optimal policy under the static-dynamic uncertainty strategy.•We prove an (st,Qt) policy is optimal for static order quantities.•We develop a MILP based heuristic algorithm to obtain near-optimal policy parameter.•We evaluate the performance of (st,Qt) and (st,Q) policies found via the heuristic. 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.