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

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  • Marius Posta

    ()

  • Jacques Ferland

    ()

  • Philippe Michelon

    ()

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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. Copyright Springer Science+Business Media, LLC 2012

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    File URL: http://hdl.handle.net/10.1007/s10589-011-9432-0
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    Bibliographic Info

    Article provided by Springer in its journal Computational Optimization and Applications.

    Volume (Year): 52 (2012)
    Issue (Month): 3 (July)
    Pages: 629-644

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    Handle: RePEc:spr:coopap:v:52:y:2012:i:3:p:629-644

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    Web page: http://www.springer.com/math/journal/10589

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    Related research

    Keywords: Integer programming; Generalized assignment problem; Branch and bound; Lagrangian relaxation; Dynamic programming;

    References

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    1. Haddadi, Salim & Ouzia, Hacene, 2004. "Effective algorithm and heuristic for the generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 153(1), pages 184-190, February.
    2. Pasquale Avella & Maurizio Boccia & Igor Vasilyev, 2010. "A computational study of exact knapsack separation for the generalized assignment problem," Computational Optimization and Applications, Springer, vol. 45(3), pages 543-555, April.
    3. Diaz, Juan A. & Fernandez, Elena, 2001. "A Tabu search heuristic for the generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 132(1), pages 22-38, July.
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