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Beam search heuristics for the single machine scheduling problem with linear earliness and quadratic tardiness costs

Author

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  • Jorge M. S. Valente

    (LIAAD, Faculdade de Economia, Universidade do Porto, Portugal)

Abstract

In this paper, we consider the single machine scheduling problem with linear earliness and quadratic tardiness costs, and no machine idle time. We present heuristic algorithms based on the beam search technique. These algorithms include classic beam search procedures, as well as the filtered and recovering variants. Several dispatching rules are considered as evaluation functions, in order to analyse the effect of different rules on the effectiveness of the beam search algorithms. The computational results show that using better rules indeed improves the performance of the beam search heuristics. The detailed, filtered and recovering beam search procedures outperform the best existing heuristic. The best results are given by the recovering and detailed variants, which provide objective function values that are quite close to the optimum. For small to medium size instances, either of these procedures can be used. For larger instances, however, the detailed beam search algorithm requires excessive computation times, and the recovering beam search procedure then becomes the heuristic of choice.

Suggested Citation

  • Jorge M. S. Valente, 2007. "Beam search heuristics for the single machine scheduling problem with linear earliness and quadratic tardiness costs," FEP Working Papers 250, Universidade do Porto, Faculdade de Economia do Porto.
  • Handle: RePEc:por:fepwps:250
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    References listed on IDEAS

    as
    1. Jorge M. S. Valente, 2006. "Heuristics for the single machine scheduling problem with early and quadratic tardy penalties," FEP Working Papers 234, Universidade do Porto, Faculdade de Economia do Porto.
    2. Hoogeveen, Han, 2005. "Multicriteria scheduling," European Journal of Operational Research, Elsevier, vol. 167(3), pages 592-623, December.
    3. Sabuncuoglu, I. & Bayiz, M., 1999. "Job shop scheduling with beam search," European Journal of Operational Research, Elsevier, vol. 118(2), pages 390-412, October.
    4. Ghirardi, M. & Potts, C. N., 2005. "Makespan minimization for scheduling unrelated parallel machines: A recovering beam search approach," European Journal of Operational Research, Elsevier, vol. 165(2), pages 457-467, September.
    5. F Della Croce & V T'kindt, 2002. "A Recovering Beam Search algorithm for the one-machine dynamic total completion time scheduling problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(11), pages 1275-1280, November.
    6. Esteve, B. & Aubijoux, C. & Chartier, A. & T'kindt, V., 2006. "A recovering beam search algorithm for the single machine Just-in-Time scheduling problem," European Journal of Operational Research, Elsevier, vol. 172(3), pages 798-813, August.
    7. John J. Kanet & V. Sridharan, 2000. "Scheduling with Inserted Idle Time: Problem Taxonomy and Literature Review," Operations Research, INFORMS, vol. 48(1), pages 99-110, February.
    8. Su, Ling-Huey & Chang, Pei-Chann, 1998. "A heuristic to minimize a quadratic function of job lateness on a single machine," International Journal of Production Economics, Elsevier, vol. 55(2), pages 169-175, July.
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    Cited by:

    1. Jorge M. S. Valente & José Fernando Gonçalves, 2008. "A genetic algorithm approach for the single machine scheduling problem with linear earliness and quadratic tardiness penalties," FEP Working Papers 264, Universidade do Porto, Faculdade de Economia do Porto.

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    Keywords

    scheduling; single machine; linear earliness; quadratic tardiness; beam search; heuristics;
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