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Maximum lateness minimization in one-dimensional bin packing

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  • Arbib, Claudio
  • Marinelli, Fabrizio

Abstract

In the One-dimensional Bin Packing problem (1-BP) items of different lengths must be assigned to a minimum number of bins of unit length. Regarding each item as a job that requires unit time and some resource amount, and each bin as the total (discrete) resource available per time unit, the 1-BP objective is the minimization of the makespan Cmax=maxj{Cj}. We here generalize the problem to the case in which each item j is due by some date dj: our objective is to minimize a convex combination of Cmax and Lmax=maxj{Cj−dj}. For this problem we propose a time-indexed Mixed Integer Linear Programming formulation. The formulation can be decomposed and solved by column generation relegating single-bin packing to a pricing problem to be solved dynamically. We use bounds to (individual terms of) the objective function to address the oddity of activation constraints. In this way, we get very good gaps for instances that are considered difficult for the 1-BP.

Suggested Citation

  • Arbib, Claudio & Marinelli, Fabrizio, 2017. "Maximum lateness minimization in one-dimensional bin packing," Omega, Elsevier, vol. 68(C), pages 76-84.
    • Handle: RePEc:eee:jomega:v:68:y:2017:i:c:p:76-84
    DOI: 10.1016/j.omega.2016.06.003
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    Cited by:

    1. Arbib, Claudio & Felici, Giovanni & Servilio, Mara, 2019. "Common operation scheduling with general processing times: A branch-and-cut algorithm to minimize the weighted number of tardy jobs," Omega, Elsevier, vol. 84(C), pages 18-30.
    2. Parreño, F. & Alvarez-Valdes, R., 2021. "Mathematical models for a cutting problem in the glass manufacturing industry," Omega, Elsevier, vol. 103(C).
    3. Polyakovskiy, Sergey & M’Hallah, Rym, 2021. "Just-in-time two-dimensional bin packing," Omega, Elsevier, vol. 102(C).
    4. Zhang, Hongbin & Yang, Yu & Wu, Feng, 2024. "Scheduling a set of jobs with convex piecewise linear cost functions on a single-batch-processing machine," Omega, Elsevier, vol. 122(C).
    5. Polyakovskiy, Sergey & M’Hallah, Rym, 2018. "A hybrid feasibility constraints-guided search to the two-dimensional bin packing problem with due dates," European Journal of Operational Research, Elsevier, vol. 266(3), pages 819-839.

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