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Weighted Tardiness Single Machine Scheduling with Proportional Weights

Author

Listed:
  • Wlodzimierz Szwarc

    (School of Business Administration, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201)

  • John J. Liu

    (School of Business Administration, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201)

Abstract

This paper considers Arkin and Roundy's single machine weighted tardiness scheduling model with tardiness penalties proportional to the processing times. It presents a two-stage decomposition mechanism that proves to be powerful in solving the problem completely or reducing it to a much smaller problem. Three types of orderings of adjacent jobs are derived that play a crucial role in problem decomposition. The decomposition method solves 155 out of 320 test problems with job sizes ranging from 20 to 150. It reduces 163 unsolved problems to smaller subproblems with sizes not exceeding 25 jobs. The job sizes of the remaining two unsolved subproblems are 30 and 45.

Suggested Citation

  • Wlodzimierz Szwarc & John J. Liu, 1993. "Weighted Tardiness Single Machine Scheduling with Proportional Weights," Management Science, INFORMS, vol. 39(5), pages 626-632, May.
    • Handle: RePEc:inm:ormnsc:v:39:y:1993:i:5:p:626-632
    DOI: 10.1287/mnsc.39.5.626
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    Citations

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    Cited by:

    1. J. J. Kanet, 2007. "New Precedence Theorems for One-Machine Weighted Tardiness," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 579-588, August.
    2. Adenso-Diaz, Belarmino, 1996. "An SA/TS mixture algorithm for the scheduling tardiness problem," European Journal of Operational Research, Elsevier, vol. 88(3), pages 516-524, February.
    3. Sen, Tapan & Sulek, Joanne M. & Dileepan, Parthasarati, 2003. "Static scheduling research to minimize weighted and unweighted tardiness: A state-of-the-art survey," International Journal of Production Economics, Elsevier, vol. 83(1), pages 1-12, January.
    4. Akturk, M. Selim & Ozdemir, Deniz, 2001. "A new dominance rule to minimize total weighted tardiness with unequal release dates," European Journal of Operational Research, Elsevier, vol. 135(2), pages 394-412, December.
    5. Zhou, Hong & Cheung, Waiman & Leung, Lawrence C., 2009. "Minimizing weighted tardiness of job-shop scheduling using a hybrid genetic algorithm," European Journal of Operational Research, Elsevier, vol. 194(3), pages 637-649, May.

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