A Study of Lagrangian Relaxation and Dantzig-Wolfe Decompositions for the Generalized Assignment Problem

This article presents a comparative study of two mathematical methods for data reduction, namely Lagrangian Relaxation (LR) and Dantzig-Wolfe Decompositions (DWD) in Integer Linear Programming (ILP). The analysis is performed on the classical Generalized Assignment Problem (GAP). To this end, we have used the general-purpose MIP solver. However, the experimentation is done on a widely used GAP benchmark of large and complex instances. The two methods have been evaluated from the standpoint of solution quality and the time required to find it.