Dantzig-Wolfe and Lagrangian decompositions in integer linear programming (Q1758875)

Summary: 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.