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Weighted-Tardiness Scheduling on Parallel Machines with Proportional Weights

Author

Listed:
  • Esther M. Arkin

    (Cornell University, Ithaca, New York)

  • Robin O. Roundy

    (Cornell University, Ithaca, New York)

Abstract

In this paper, we address the problem of scheduling a number of jobs on a bank of parallel machines to minimize the total weighted tardiness, under the assumption that the weight of each job is proportional to its processing time. The version of the problem that has general weights has been shown to be strongly NP-complete. We prove this version of the problem to be NP-complete, and give a pseudopolynomial time algorithm for solving it. We study a family of simple sequencing rules in which the jobs are sequenced in increasing order of γ i = d i − θ p i , where d i is the due date of job i , p i its processing time, w i its weight, and 0 ≤ θ ≤ 1. This family of sequencing rules generalizes the earliest due date sequencing rule. We obtain bounds on the ratio [ C γ · C * ]/[Σ i w i p i ], where C γ and C * are the costs of the heuristic and optimal schedules, respectively. The denominator is the cost of having each job be late by its own processing time. It is intended to measure what is or is not a large deviation from optimality, in absolute rather than relative terms, for the problem at hand. We also report on the results of computational experiments.

Suggested Citation

  • Esther M. Arkin & Robin O. Roundy, 1991. "Weighted-Tardiness Scheduling on Parallel Machines with Proportional Weights," Operations Research, INFORMS, vol. 39(1), pages 64-81, February.
    • Handle: RePEc:inm:oropre:v:39:y:1991:i:1:p:64-81
    DOI: 10.1287/opre.39.1.64
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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. Chen, Jeng-Fung & Wu, Tai-Hsi, 2006. "Total tardiness minimization on unrelated parallel machine scheduling with auxiliary equipment constraints," Omega, Elsevier, vol. 34(1), pages 81-89, January.
    3. Alidaee, Bahram & Dragan, Irinel, 1997. "A note on minimizing the weighted sum of tardy and early completion penalties in a single machine: A case of small common due date," European Journal of Operational Research, Elsevier, vol. 96(3), pages 559-563, February.
    4. Lee, Young Hoon & Pinedo, Michael, 1997. "Scheduling jobs on parallel machines with sequence-dependent setup times," European Journal of Operational Research, Elsevier, vol. 100(3), pages 464-474, August.
    5. Alves de Queiroz, Thiago & Iori, Manuel & Kramer, Arthur & Kuo, Yong-Hong, 2023. "Dynamic scheduling of patients in emergency departments," European Journal of Operational Research, Elsevier, vol. 310(1), pages 100-116.
    6. Cheng, T. C. E. & Ng, C. T. & Yuan, J. J. & Liu, Z. H., 2005. "Single machine scheduling to minimize total weighted tardiness," European Journal of Operational Research, Elsevier, vol. 165(2), pages 423-443, September.
    7. 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.
    8. Shim, Sang-Oh & Kim, Yeong-Dae, 2007. "Scheduling on parallel identical machines to minimize total tardiness," European Journal of Operational Research, Elsevier, vol. 177(1), pages 135-146, February.
    9. Azizoglu, Meral & Kirca, Omer, 1998. "Tardiness minimization on parallel machines," International Journal of Production Economics, Elsevier, vol. 55(2), pages 163-168, July.
    10. Yalaoui, Farouk & Chu, Chengbin, 2002. "Parallel machine scheduling to minimize total tardiness," International Journal of Production Economics, Elsevier, vol. 76(3), pages 265-279, April.

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