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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

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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  • Marius Posta & Jacques Ferland & Philippe Michelon, 2012. "An exact method with variable fixing for solving the generalized assignment problem," Computational Optimization and Applications, Springer, vol. 52(3), pages 629-644, July.
    • Handle: RePEc:spr:coopap:v:52:y:2012:i:3:p:629-644
    DOI: 10.1007/s10589-011-9432-0
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    References listed on IDEAS

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    1. 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.
    2. Robert M. Nauss, 2003. "Solving the Generalized Assignment Problem: An Optimizing and Heuristic Approach," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 249-266, August.
    3. Yagiura, Mutsunori & Ibaraki, Toshihide & Glover, Fred, 2006. "A path relinking approach with ejection chains for the generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 169(2), pages 548-569, March.
    4. Mutsunori Yagiura & Toshihide Ibaraki & Fred Glover, 2004. "An Ejection Chain Approach for the Generalized Assignment Problem," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 133-151, May.
    5. Martin Savelsbergh, 1997. "A Branch-and-Price Algorithm for the Generalized Assignment Problem," Operations Research, INFORMS, vol. 45(6), pages 831-841, December.
    6. 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.
    7. Alper Atamtürk & Martin Savelsbergh, 2005. "Integer-Programming Software Systems," Annals of Operations Research, Springer, vol. 140(1), pages 67-124, November.
    8. David Pisinger, 1997. "A Minimal Algorithm for the 0-1 Knapsack Problem," Operations Research, INFORMS, vol. 45(5), pages 758-767, October.
    9. 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.
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    Cited by:

    1. Mikhail A. Bragin & Peter B. Luh & Joseph H. Yan & Nanpeng Yu & Gary A. Stern, 2015. "Convergence of the Surrogate Lagrangian Relaxation Method," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 173-201, January.
    2. Francisco Castillo-Zunino & Pinar Keskinocak, 2021. "Bi-criteria multiple knapsack problem with grouped items," Journal of Heuristics, Springer, vol. 27(5), pages 747-789, October.
    3. Stefka Fidanova & Krassimir Todorov Atanassov, 2021. "ACO with Intuitionistic Fuzzy Pheromone Updating Applied on Multiple-Constraint Knapsack Problem," Mathematics, MDPI, vol. 9(13), pages 1-7, June.
    4. Ruslan Sadykov & François Vanderbeck & Artur Pessoa & Issam Tahiri & Eduardo Uchoa, 2019. "Primal Heuristics for Branch and Price: The Assets of Diving Methods," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 251-267, April.

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