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A single machine scheduling problem with two-dimensional vector packing constraints

Author

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  • Billaut, Jean-Charles
  • Della Croce, Federico
  • Grosso, Andrea

Abstract

We consider a scheduling problem where jobs consume a perishable resource stored in vials. It leads to a new scheduling problem, with two-dimensional jobs, one dimension for the duration and one dimension for the consumption. Jobs have to be finished before a given due date, and the objective is to schedule the jobs on a single machine so that the maximum lateness does not exceed a given threshold and the number of vials required for processing all the jobs is minimized. We propose a two-step approach embedding a Recovering Beam Search algorithm to get a good-quality initial solution reachable in short time and a more time consuming matheuristic algorithm. Computational experiments are performed on the benchmark instances available for the two-dimensional vector packing problem integrated with additional due dates to take into account the maximum lateness constraints. The computational results show very good performances of the proposed approach that remains effective also on the original two-dimensional vector packing instances without due dates where 7 new bounds are obtained.

Suggested Citation

  • Billaut, Jean-Charles & Della Croce, Federico & Grosso, Andrea, 2015. "A single machine scheduling problem with two-dimensional vector packing constraints," European Journal of Operational Research, Elsevier, vol. 243(1), pages 75-81.
    • Handle: RePEc:eee:ejores:v:243:y:2015:i:1:p:75-81
    DOI: 10.1016/j.ejor.2014.11.036
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    References listed on IDEAS

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    Cited by:

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    2. Fanjul-Peyro, Luis & Perea, Federico & Ruiz, Rubén, 2017. "Models and matheuristics for the unrelated parallel machine scheduling problem with additional resources," European Journal of Operational Research, Elsevier, vol. 260(2), pages 482-493.
    3. Emine Akyol Ozer & Tugba Sarac, 2019. "MIP models and a matheuristic algorithm for an identical parallel machine scheduling problem under multiple copies of shared resources constraints," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 94-124, April.
    4. Framinan, Jose M. & Perez-Gonzalez, Paz, 2018. "Order scheduling with tardiness objective: Improved approximate solutions," European Journal of Operational Research, Elsevier, vol. 266(3), pages 840-850.
    5. Marco Ghirardi & Fabio Salassa, 2022. "A simple and effective algorithm for the maximum happy vertices problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 181-193, April.
    6. Bentao Su & Naiming Xie, 2020. "Single workgroup scheduling problem with variable processing personnel," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(2), pages 671-684, June.

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