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

Abstract

This paper addresses the single-item single-stocking location stochastic lot sizing problem under the $(s,S)$ 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 around $0.3\%$ of the optimal policy cost and computational times are reasonable.

References in corpus (2)

• A unified modeling approach for the static-dynamic uncertainty strategy in stochastic lot-sizing
• Piecewise linear approximations of the standard normal first order loss function

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• MILP Approximations for non-stationary stochastic lot-sizing under (s,Q)-type policy
• On the stochastic inventory problem under order capacity constraints
• A recursion-free functional approximation for the dynamic inventory problem