The generalized assignment problem: valid inequalities and facets
Mathematical Programming: Series A and B
(1,k)-configuration facets for the generalized assignment problem
Mathematical Programming: Series A and B
A genetic algorithm for the generalised assignment problem
Computers and Operations Research
Solving the Generalized Assignment Problem: An Optimizing and Heuristic Approach
INFORMS Journal on Computing
An Ejection Chain Approach for the Generalized Assignment Problem
INFORMS Journal on Computing
A convex-analysis perspective on disjunctive cuts
Mathematical Programming: Series A and B
A family of inequalities for the generalized assignment polytope
Operations Research Letters
A Lagrangian heuristic for sprint planning in agile software development
Computers and Operations Research
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The Generalized Assignment Problem is a well-known NP-hard combinatorial optimization problem which consists of minimizing the assignment costs of a set of jobs to a set of machines satisfying capacity constraints. Most of the existing algorithms are of a Branch-and-Price type, with lower bounds computed through 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, whose core is 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 several previously unsolved instances.