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

ABSI Nabil (absi***at***emse.fr)
Kedad-Sidhoum Safia (safia.kedad-sidhoum***at***lip6.fr)

Abstract: 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. A mixed integer mathematical formulation is presented. 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.

Keywords: Lot-sizing, setup times, shortage costs, safety stock deficit, production planning, mixed integer programming, heuristics

Category 1: Applications -- OR and Management Sciences

Citation: Working paper - LIP6 - September 2005 Accepted (RAIRO-OR) in 2006, Available online on http://dx.doi.org/10.1051/ro:2007014

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Entry Submitted: 11/17/2005
Entry Accepted: 11/17/2005
Entry Last Modified: 07/18/2007

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