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The parallel machine min‐max weighted absolute lateness scheduling problem

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  • Chung‐Lun Li
  • T. C. E. Cheng

Abstract

Given a set of jobs, a processing time and a weight for each job, several parallel and identical machines, and a common due date that is not too early to constrain the scheduling decision, we want to find an optimal job schedule so as to minimize the maximum weighted absolute lateness. We show that this problem is NP‐complete even for the single‐machine case, and is strongly NP‐complete for the general case. We present a polynomial time heuristic for this problem and analyze its worst‐case performance. Empirical testing of the heuristic is reported, and the results suggest that the performance is asymptotically optimal as the number of jobs tends to infinity. © 1994 John Wiley & Sons, Inc.

Suggested Citation

  • Chung‐Lun Li & T. C. E. Cheng, 1994. "The parallel machine min‐max weighted absolute lateness scheduling problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(1), pages 33-46, February.
    • Handle: RePEc:wly:navres:v:41:y:1994:i:1:p:33-46
    DOI: 10.1002/1520-6750(199402)41:13.0.CO;2-S
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    References listed on IDEAS

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    5. Cheng, T. C. E. & Gupta, M. C., 1989. "Survey of scheduling research involving due date determination decisions," European Journal of Operational Research, Elsevier, vol. 38(2), pages 156-166, January.
    6. John J. Kanet, 1981. "Minimizing the average deviation of job completion times about a common due date," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 28(4), pages 643-651, December.
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    8. Nicholas G. Hall & Wieslaw Kubiak & Suresh P. Sethi, 1991. "Earliness–Tardiness Scheduling Problems, II: Deviation of Completion Times About a Restrictive Common Due Date," Operations Research, INFORMS, vol. 39(5), pages 847-856, October.
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    Cited by:

    1. Nasini, Stefano & Nessah, Rabia, 2022. "A multi-machine scheduling solution for homogeneous processing: Asymptotic approximation and applications," International Journal of Production Economics, Elsevier, vol. 251(C).

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