A computational study of exact knapsack separation for the generalized assignment problem

A computational study of exact knapsack separation for the generalized assignment problem

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Article ID: iaor20103236
Volume: 45
Issue: 3
Start Page Number: 543
End Page Number: 555
Publication Date: Apr 2010
Journal: Computational Optimization and Applications
Authors: , ,
Keywords: combinatorial optimization
Abstract:

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.

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