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On Single-Machine Scheduling with Precedence Relations and Linear or Discounted Costs

Author

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  • K. D. Glazebrook

    (University of Newcastle upon Tyne, Newcastle upon Tyne, England)

  • J. C. Gittins

    (University of Oxford, Oxford, England)

Abstract

Some results of Sidney (Sidney, J. B. 1975. Decomposition algorithms for single machine sequencing with precedence relations and deferral costs. Opns. Res. 23 283–298.) concerning order-constrained deterministic scheduling with linear costs are extended to the more complex discounted costs case. Further, certain order-constrained stochastic scheduling problems are shown to have optimal strategies which are nonpreemptive. When this is so, results for the deterministic case may be utilized to obtain these optimal strategies. The models discussed are of interest in computer and job-shop scheduling and research planning.

Suggested Citation

  • K. D. Glazebrook & J. C. Gittins, 1981. "On Single-Machine Scheduling with Precedence Relations and Linear or Discounted Costs," Operations Research, INFORMS, vol. 29(1), pages 161-173, February.
    • Handle: RePEc:inm:oropre:v:29:y:1981:i:1:p:161-173
    DOI: 10.1287/opre.29.1.161
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    Cited by:

    1. Kevin D. Glazebrook, 1987. "Evaluating the effects of machine breakdowns in stochastic scheduling problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(3), pages 319-335, June.
    2. S. E. Pilnick & K. D. Glazebrook & D. P. Gaver, 1991. "Optimal sequential replenishment of ships during combat," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(5), pages 637-668, October.
    3. K. D. Glazebrook, 1992. "Single‐machine scheduling of stochastic jobs subject to deterioration or delay," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(5), pages 613-633, August.
    4. K. D. Glazebrook, 1995. "A suboptimality bound for permutation policies in single machine stochastic scheduling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(6), pages 993-1005, September.

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