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Computational Optimization and Applications

, Volume 52, Issue 3, pp 629–644 | Cite as

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

  • Marius PostaEmail author
  • Jacques A. Ferland
  • Philippe Michelon
Article

Abstract

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

Keywords

Integer programming Generalized assignment problem Branch and bound Lagrangian relaxation Dynamic programming 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Marius Posta
    • 1
    Email author
  • Jacques A. Ferland
    • 1
  • Philippe Michelon
    • 2
  1. 1.Département d’Informatique et de Recherche OpérationelleUniversité de MontréalMontréalCanada
  2. 2.Laboratoire d’Informatique d’AvignonUniversité d’Avignon et des Pays du VaucluseAvignon, Cedex 9France

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