Title: Dantzig-Wolfe and Lagrangian decompositions in integer linear programming

Authors: L. Létocart; A. Nagih; N. Touati-Moungla

Addresses: LIPN, UMR 7030 CNRS, Institut Galilée – Université Paris 13, 99 avenue Jean-Baptiste Clément, 93430 Villetaneuse, France. ' LITA, Université Paul Verlaine, Ile du Saulcy, 57045 Metz Cedex 1, France. ' LIX, École polytechnique, 91128 Palaiseau Cedex, France

Abstract: We propose in this paper a new Dantzig-Wolfe master model based on Lagrangian Decomposition (LD). We establish the relationship with classical Dantzig-Wolfe decomposition master problem and propose an alternative proof of the dominance of LD on Lagrangian Relaxation (LR) dual bound. As illustration, we give the corresponding models and numerical results for two standard mathematical programs: the 0-1 bidimensional knapsack problem and the generalised assignment problem.

Keywords: Dantzig-Wolfe decomposition; column generation; Lagrangian relaxation; Lagrangian decomposition; 0-1 bidimensional knapsack problem; generalised assignment problem; modelling.

DOI: 10.1504/IJMOR.2012.046686

International Journal of Mathematics in Operational Research, 2012 Vol.4 No.3, pp.247 - 262

Published online: 02 May 2012 *

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