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The multi-item capacitated lot-sizing problem with setup times and shortage costs

Abstract : We address a multi-item capacitated lot-sizing problem with setup times and shortage costs that arises in real-world production planning problems. Demand cannot be backlogged, but can be totally or partially lost. The problem is NP-hard. A mixed integer mathematical formulation is presented. Our approach in this paper is to propose some classes of valid inequalities based on a generalization of Miller et al. [A.J. Miller, G.L. Nemhauser, M.W.P. Savelsbergh, On the polyhedral structure of a multi-item production planning model with setup times, Mathematical Programming 94 (2003) 375–405] and Marchand and Wolsey [H. Marchand, L.A. Wolsey, The 0–1 knapsack problem with a single continuous variable, Mathematical Programming 85 (1999) 15–33] results. We also describe fast combinatorial separation algorithms for these new inequalities. We use them in a branch-and-cut framework to solve the problem. Some experimental results showing the effectiveness of the approach are reported.
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https://hal.archives-ouvertes.fr/hal-00506261
Contributor : Nabil Absi <>
Submitted on : Tuesday, July 27, 2010 - 2:56:14 PM
Last modification on : Wednesday, June 24, 2020 - 4:19:21 PM
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Nabil Absi, Safia Kedad-Sidhoum. The multi-item capacitated lot-sizing problem with setup times and shortage costs. European Journal of Operational Research, Elsevier, 2008, 185 (3), pp.1351-1374. ⟨10.1016/j.ejor.2006.01.053⟩. ⟨hal-00506261⟩

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