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A Branch-and-Price Algorithm for the Multilevel Generalized Assignment Problem

Author

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  • Alberto Ceselli

    (Dipartimento di Tecnologie dell’Informazione, Università degli Studi di Milano, via Bramante 65, 26013, Crema, Italy)

  • Giovanni Righini

    (Dipartimento di Tecnologie dell’Informazione, Università degli Studi di Milano, via Bramante 65, 26013, Crema, Italy)

Abstract

The multilevel generalized assignment problem (MGAP) is a variation of the generalized assignment problem, in which agents can execute tasks at different efficiency levels with different costs. We present a branch-and-price algorithm that is the first exact algorithm for the MGAP. It is based on a decomposition into a master problem with set-partitioning constraints and a pricing subproblem that is a multiple-choice knapsack problem. We report on our computational experience with randomly generated instances with different numbers of agents, tasks, and levels; and with different correlations between cost and resource consumption for each agent-task-level assignment. Experimental results show that our algorithm is able to solve instances larger than those of the maximum size considered in the literature to proven optimality.

Suggested Citation

  • Alberto Ceselli & Giovanni Righini, 2006. "A Branch-and-Price Algorithm for the Multilevel Generalized Assignment Problem," Operations Research, INFORMS, vol. 54(6), pages 1172-1184, December.
    • Handle: RePEc:inm:oropre:v:54:y:2006:i:6:p:1172-1184
    DOI: 10.1287/opre.1060.0323
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    References listed on IDEAS

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    Cited by:

    1. Tibor Szkaliczki, 2025. "Solution Methods for the Multiple-Choice Knapsack Problem and Their Applications," Mathematics, MDPI, vol. 13(7), pages 1-35, March.
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    3. Han-Lin Li & Yao-Huei Huang & Shu-Cherng Fang, 2013. "A Logarithmic Method for Reducing Binary Variables and Inequality Constraints in Solving Task Assignment Problems," INFORMS Journal on Computing, INFORMS, vol. 25(4), pages 643-653, November.
    4. Lu, Yiping & Chen, Danny Z., 2021. "A new exact algorithm for the Weapon-Target Assignment problem," Omega, Elsevier, vol. 98(C).

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