MIP-based heuristics for multi-item capacitated lot-sizing problem with setup times and shortage costs

• Published in: R.A.I.R.O. Recherche opérationnelle Vol. 41; no. 2; pp. 171 - 192
• Main Authors: Absi, Nabil, Kedad-Sidhoum, Safia
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Paris EDP Sciences 01.04.2007
• Subjects: 90B30; 90C59; Applied sciences; Computer Science; Exact sciences and technology; heuristic; Inventory control, production control. Distribution; Lot-sizing; Mathematical programming; mixed integer programming; Operational research and scientific management; Operational research. Management science; Operations Research; production planning; safety stock deficit; setup time; shortage cost; Backorder; Partition; Lot-sizing; safety stock deficit; Sensitivity analysis; 90B30,90C59; Mixed integer programming; heuristic; Lot sizing; Safety stock; Real time; shortage cost; Optimization; Production management; Shortage; Multi item management; Production planning; Heuristic method; NP hard problem; Setup time; heuristic Mathematics Subject Classification 90B30; setup time; mixed integer programming; 90C59; production planning
• ISSN: 0399-0559; 1290-3868; 1290-3868
• DOI: 10.1051/ro:2007014

We address a multi-item capacitated lot-sizing problem with setup times that arises in real-world production planning contexts. Demand cannot be backlogged, but can be totally or partially lost. Safety stock is an objective to reach rather than an industrial constraint to respect. The problem is NP-hard. We propose mixed integer programming heuristics based on a planning horizon decomposition strategy to find a feasible solution. The planning horizon is partitioned into several sub-horizons over which a freezing or a relaxation strategy is applied. Some experimental results showing the effectiveness of the approach on real-world instances are presented. A sensitivity analysis on the parameters of the heuristics is reported.