Polyhedral and Lagrangian approaches for lot sizing with production time windows and setup times

Authors:
Nadjib Brahimi;Stéphane Dauzere-Peres;Laurence A. Wolsey
Affiliations:
Department of Industrial Engineering and Management, College of Engineering, University of Sharjah, P.O. Box 27272 Sharjah, United Arab Emirates;Centre Microélectronique de Provence, Ecole des Mines de Saint-Etienne - Site Georges Charpak, 880 avenue de Minet, F-13541 Gardanne, France;CORE, Center for Operations Research and Econometrics, Université Catholique de Louvain, 34 Voie du Roman Pays, 1348 Louvain-la-Neuve, Belgium
Venue:
Computers and Operations Research
Year:
2010

Citing 16
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Abstract

In this paper, we solve the capacitated multi item lot-sizing problem with non-customer specific production time windows and setup times using two approaches: (i) using a Lagrangian relaxation-based heuristic and (ii) using reformulations and a commercial software. The results of the two approaches are analyzed and compared based on randomly generated data sets. The results show that the first approach finds feasible solution more rapidly but a steady state is reached very quickly. On the other hand the second approach quickly finds good lower bounds and finds good feasible solutions if more CPU time is allowed. It turns out that, for a wide variety of instances varying in size and other parameters, we can obtain feasible solutions within 1-5% of optimal within 10s and also obtain solutions that are guaranteed within 1-2% of optimal within 60-120s.