A set partitioning heuristic for the generalized assignment problem

This paper discusses a heuristic for the generalized assignment problem (GAP). The objective of GAP is to minimize the costs of assigning J jobs to M capacity constrained machines, such that each job is assigned to exactly one machine. The problem is known to be NP-Hard, and it is hard from a computational point of view as well. The heuristic proposed here is based on column generation techniques, and yields both upper and lower bounds. On a set of relatively hard test problems the heuristic is able to find solutions that are on average within 0.13% from optimality.