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

•We present a mathematical programming model to compute (s, S) policies parameters.•We introduce a mixed-integer linear programming reformulation.•Our reformulation can be solved by existing off-the-shelf solvers.•We discuss a computationally efficient binary search heuristic.•We observe average opt...

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Bibliographic Details
Published in:European journal of operational research Vol. 271; no. 2; pp. 490 - 500
Main Authors: Xiang, Mengyuan, Rossi, Roberto, Martin-Barragan, Belen, Tarim, S. Armagan
Format: Journal Article
Language:English
Published: Elsevier B.V 01.12.2018
Subjects:
(s, S) policy
Binary search
Inventory
Mixed integer programming
Stochastic lot-sizing
Binary search
Mixed integer programming
(s, S) policy
Stochastic lot-sizing
Inventory
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:•We present a mathematical programming model to compute (s, S) policies parameters.•We introduce a mixed-integer linear programming reformulation.•Our reformulation can be solved by existing off-the-shelf solvers.•We discuss a computationally efficient binary search heuristic.•We observe average optimality gaps of 0.3%, and reasonable computational times. 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 optimization 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.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2018.05.030