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

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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.

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Authors and Affiliations

  1. Département d’Informatique et de Recherche Opérationelle, Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montréal, Québec, H3C 3J7, Canada

    Marius Posta & Jacques A. Ferland

  2. Laboratoire d’Informatique d’Avignon, Université d’Avignon et des Pays du Vaucluse, 84911, Avignon, Cedex 9, France

    Philippe Michelon

Authors
  1. Marius Posta
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  2. Jacques A. Ferland
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  3. Philippe Michelon
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Correspondence to Marius Posta.

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Posta, M., Ferland, J.A. & Michelon, P. An exact method with variable fixing for solving the generalized assignment problem. Comput Optim Appl 52, 629–644 (2012). https://doi.org/10.1007/s10589-011-9432-0

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  • DOI: https://doi.org/10.1007/s10589-011-9432-0

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