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Capacitated Multi-Item Lot-Sizing Problems with Time Windows

IRCCyN—Ecole des Mines de Nantes, UMR CNRS 6597, La Chantrerie, BP 20722, F-44307 Nantes Cedex 3, France
Ecole des Mines de Saint-Etienne, CMP Georges Charpak, Avenue des Anémones—Quartier Saint-Pierre, F-13541 Gardanne, France
IRCCyN—IUT de Nantes, UMR CNRS 6597, 2, Avenue du Professeur Jean Rouxel, BP 539, F-44475 Carquefou, France
nadjib.brahimi{at}emn.fr
dauzere-peres{at}emse.fr
najib.najid{at}iut-nantes.univ-nantes.fr

This research concerns a new family of capacitated multi-item lot-sizing problems, namely, lot-sizing problems with time windows. Two classes of the problem are analyzed and solved using different Lagrangian heuristics. Capacity constraints and a subset of time window constraints are relaxed resulting in particular single-item time window problems that are solved in polynomial time. Other relaxations leading to the classical Wagner-Whitin problem are also tested. Several smoothing heuristics are implemented and tested, and their results are compared. The gaps between lower and upper bounds for most problems are very small (less than 1%). Moreover, the proposed algorithms are robust and do not seem to be too affected when different parameters of the problem are varied.

Subject classifications: production/scheduling, approximations/heuristic: Lagrangian heuristics; production/scheduling, planning: capacitated multi-item lot sizing; programming, integer, relaxation/subgradient: Lagrangian relaxations.
History: Received June 2004; revision received September 2005; accepted September 2005.