An exact method with variable fixing for solving the generalized assignment problem

We propose a simple and very effective algorithm for solving the generalized assignment problem exactly. Our contribution is twofold: we reformulate the optimization problem into a sequence of decision problems, and we solve these effectively using variable-fixing rules. The decision problems are solved by a simple depth-first lagrangian branch-and-bound method, improved by the variable-fixing rules which help prune the search tree. These rules rely on lagrangian relative costs which we compute using an existing but little-known dynamic programming algorithm.