The Generalized Assignment Problem is a well-known NP-hard combinatorial optimization problem which consists of minimizing the assignment costs a set of jobs to a set of machines satisfying capacity constraints. Most of the existing algorithms are based on Branch-and-Price, with lower bounds computed by Dantzig-Wolfe reformulation and column generation. In this paper we propose a cutting plane algorithm, working in the space of the variables of the basic formulation, based on an exact separation procedure for the knapsack polytopes induced by the capacity constraints. We show that an efficient implementation of the exact separation procedure allows to deal with large-scale instances and to solve to optimality many previously unsolved instances.
Computational Optimization and Applications, 2008, DOI: 10.1007/s10589-008-9183-8