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A branch-and-price algorithm for the variable size bin packing problem with minimum filling constraint

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Abstract

In this paper we consider a variation of the bin packing problem in which bins of different types have different costs and capacities. Furthermore, each bin has to be filled at least to a certain level, which depends on its type. We present a set partitioning formulation and an exact optimization algorithm which exploits column generation and specialized heuristics. We compare our algorithm with the general purpose solver ILOG CPLEX, running on two compact ILP formulations and we report on experimental results on instances we have generated from data-sets for the variable size bin packing problem.

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Authors and Affiliations

  1. Dipartimento di Tecnologie dell’Informazione, Università degli Studi di Milano, Via Bramante 65, 26013, Crema, Italy

    Andrea Bettinelli, Alberto Ceselli & Giovanni Righini

Authors
  1. Andrea Bettinelli
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  2. Alberto Ceselli
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  3. Giovanni Righini
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Correspondence to Giovanni Righini.

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Bettinelli, A., Ceselli, A. & Righini, G. A branch-and-price algorithm for the variable size bin packing problem with minimum filling constraint. Ann Oper Res 179, 221–241 (2010). https://doi.org/10.1007/s10479-008-0452-9

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  • DOI: https://doi.org/10.1007/s10479-008-0452-9

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