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A computational study of exact knapsack separation for the generalized assignment problem

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Abstract

The Generalized Assignment Problem is a well-known NP-hard combinatorial optimization problem which consists of minimizing the assignment costs of a set of jobs to a set of machines satisfying capacity constraints. Most of the existing algorithms are of a Branch-and-Price type, with lower bounds computed through Dantzig–Wolfe reformulation and column generation.

In this paper we propose a cutting plane algorithm working in the space of the variables of the basic formulation, whose core is an exact separation procedure for the knapsack polytopes induced by the capacity constraints. We show that an efficient implementation of the exact separation procedure allows to deal with large-scale instances and to solve to optimality several previously unsolved instances.

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Authors and Affiliations

  1. RCOST—Research Center on Software Technology, Università del Sannio, Viale Traiano, 82100, Benevento, Italy

    Pasquale Avella & Maurizio Boccia

  2. Institute of System Dynamics and Control Theory, Siberian Branch of Russian Academy of Sciences, Lermontov Srt., 134, 664033, Irkutsk, Russia

    Igor Vasilyev

Authors
  1. Pasquale Avella
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  2. Maurizio Boccia
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  3. Igor Vasilyev
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Correspondence to Igor Vasilyev.

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Avella, P., Boccia, M. & Vasilyev, I. A computational study of exact knapsack separation for the generalized assignment problem. Comput Optim Appl 45, 543–555 (2010). https://doi.org/10.1007/s10589-008-9183-8

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  • DOI: https://doi.org/10.1007/s10589-008-9183-8

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