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A proof for the longest‐job‐first policy in one‐machine scheduling

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  • T. C. E. Cheng
  • H. G. Kahlbacher

Abstract

We consider a one‐machine scheduling problem with earliness and tardiness penalties. All jobs are assigned a common due date and the objective is to minimize the total penalty due to job earliness and tardiness. We are interested in finding the optimal combination of the common due‐date value and the job sequence. Despite the fact that this problem in general is very hard to solve, we prove that there exists at least a common property for all optimal solutions: The first job in an optimal sequence is one of the longest jobs. We also prove that this property holds for a general class of unimodal penalty functions.

Suggested Citation

  • T. C. E. Cheng & H. G. Kahlbacher, 1991. "A proof for the longest‐job‐first policy in one‐machine scheduling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(5), pages 715-720, October.
    • Handle: RePEc:wly:navres:v:38:y:1991:i:5:p:715-720
    DOI: 10.1002/1520-6750(199110)38:53.0.CO;2-6
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    References listed on IDEAS

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    1. S. S. Panwalkar & M. L. Smith & A. Seidmann, 1982. "Common Due Date Assignment to Minimize Total Penalty for the One Machine Scheduling Problem," Operations Research, INFORMS, vol. 30(2), pages 391-399, April.
    2. 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.
    3. Kenneth R. Baker & Gary D. Scudder, 1990. "Sequencing with Earliness and Tardiness Penalties: A Review," Operations Research, INFORMS, vol. 38(1), pages 22-36, February.
    4. 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.
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