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Beam search heuristics for quadratic earliness and tardiness scheduling


  • Jorge M. S. Valente

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


In this paper, we present beam search heuristics for the single machine scheduling problem with quadratic earliness and tardiness costs, and no machine idle time. These heuristics include classic beam search procedures, as well as filtered and recovering algorithms. We consider three dispatching heuristics as evaluation functions, in order to analyse the effect of different rules on the performance of the beam search procedures. The computational results show that using better dispatching heuristics improves the effectiveness of the beam search algorithms. The performance of the several heuristics is similar for instances with low variability. For high variability instances, however, the detailed, filtered and recovering beam search procedures clearly outperform the best existing heuristic. The detailed beam search algorithm performs quite well, and is recommended for small to medium size instances. For larger instances, however, this procedure requires excessive computation times, and the recovering beam search algorithm then becomes the heuristic of choice.

Suggested Citation

  • Jorge M. S. Valente, 2008. "Beam search heuristics for quadratic earliness and tardiness scheduling," FEP Working Papers 279, Universidade do Porto, Faculdade de Economia do Porto.
  • Handle: RePEc:por:fepwps:279

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    References listed on IDEAS

    1. Hoogeveen, Han, 2005. "Multicriteria scheduling," European Journal of Operational Research, Elsevier, vol. 167(3), pages 592-623, December.
    2. George Li, 1997. "Single machine earliness and tardiness scheduling," European Journal of Operational Research, Elsevier, vol. 96(3), pages 546-558, February.
    3. 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.
    4. Jorge M. S. Valente, 2007. "An exact approach for single machine scheduling with quadratic earliness and tardiness penalties," FEP Working Papers 238, Universidade do Porto, Faculdade de Economia do Porto.
    5. Schaller, Jeffrey, 2002. "Minimizing the sum of squares lateness on a single machine," European Journal of Operational Research, Elsevier, vol. 143(1), pages 64-79, November.
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    scheduling; heuristics; beam search; single machine; quadratic earliness; quadratic tardiness;

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