Stabilized Branch-and-cut-and-price for the Generalized Assignment Problem * Alexandre Pigatti, Marcus Poggi de Arag˜ao Departamento de Inform´atica, PUC do Rio de Janeiro {apigatti, poggi}@inf.puc-rio.br Eduardo Uchoa Departamento de Engenharia de Produ¸c˜ ao, Universidade Federal Fluminense uchoa@producao.uff.br October, 2004 Abstract The Generalized Assignment Problem (GAP) is a classic scheduling problem with many applications. We propose a branch-and-cut-and- price for that problem featuring a stabilization mechanism to accelerate column generation convergence. We also propose ellipsoidal cuts, a new way of transforming the exact algorithm into a powerful heuristic, in the same spirit of the cuts recently proposed by Fischetti and Lodi. The improved solutions found by this heuristic can, in turn, help the task of the exact algorithm. The resulting algorithms showed a very good performance and were able to solve three among the last five open instances from the OR-Library. 1 Introduction The Generalized Assigment Problem (GAP) is defined as follows. Let I = {1, ..., m} be a set of machines and J = {1, ..., n} a set of tasks. Each machine i ∈ I has a capacity b i . Each task j ∈ J when assigned to machine j ∈ J consumes a ij units of capacity and implies in a cost of c ij units. One searches for an assignment of every task to one of the machines, respecting the machine capacities and minimizing the total cost. This classical NP- hard problem has many applications in industrial scheduling. Some recent applications of the GAP in other contexts include the allocation of patients to medical flies in the US army [10] and in the operation of the international spatial telescope ROSAT [7]. * The results in this article were already presented in [8] 1