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

Mengyuan Xiang, Roberto Rossi, Belen Martin-Barragan, S Armagan Tarim

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)490-500
JournalEuropean Journal of Operational Research
Issue number2
Early online date22 May 2018
Publication statusPublished - 1 Dec 2018


  • inventory
  • (s, S) policy
  • stochastic lot-sizing
  • mixed integer programming
  • binary search


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