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New Bounds for the Identical Parallel Processor Weighted Flow Time Problem

Author

Listed:
  • Scott Webster

    (School of Business, University of Wisconsin-Madison, Madison, Wisconsin 53706)

Abstract

In 1964, Eastman, Even, and Isaacs (EEI) presented a polynomial time lower bound for the NP-hard problem of scheduling n jobs on m available and identical processors to minimize weighted flow time. A general bound, of which the EEI bound is a special case, is proposed. Four new bounds for the identical processor problem are given. All of the new bounds can be applied to problems with variable processor ready times. The EEI bound is limited to problems where all processors are initially available at the same time. Two of the four new bounds are shown to dominate the EEI bound. The two other bounds are found to be effective for a particular problem class. Two polynomial time lower bounds for problems with nonidentical processors are introduced. One bound is applicable to the uniform processor problem, the other bound can be applied to the general processor problem. No bounds have previously been proposed for these problems.

Suggested Citation

  • Scott Webster, 1992. "New Bounds for the Identical Parallel Processor Weighted Flow Time Problem," Management Science, INFORMS, vol. 38(1), pages 124-136, January.
    • Handle: RePEc:inm:ormnsc:v:38:y:1992:i:1:p:124-136
    DOI: 10.1287/mnsc.38.1.124
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    Citations

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    Cited by:

    1. J. M. van den Akker & J. A. Hoogeveen & S. L. van de Velde, 1999. "Parallel Machine Scheduling by Column Generation," Operations Research, INFORMS, vol. 47(6), pages 862-872, December.
    2. Zhi-Long Chen & Warren B. Powell, 1999. "Solving Parallel Machine Scheduling Problems by Column Generation," INFORMS Journal on Computing, INFORMS, vol. 11(1), pages 78-94, February.
    3. Rabia Nessah & Chengbin Chu, 2010. "Infinite split scheduling: a new lower bound of total weighted completion time on parallel machines with job release dates and unavailability periods," Annals of Operations Research, Springer, vol. 181(1), pages 359-375, December.
    4. Xiangtong Qi, 2005. "A logistics scheduling model: Inventory cost reduction by batching," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(4), pages 312-320, June.
    5. Arthur Kramer & Anand Subramanian, 2019. "A unified heuristic and an annotated bibliography for a large class of earliness–tardiness scheduling problems," Journal of Scheduling, Springer, vol. 22(1), pages 21-57, February.
    6. Daniel Kowalczyk & Roel Leus, 2018. "A Branch-and-Price Algorithm for Parallel Machine Scheduling Using ZDDs and Generic Branching," INFORMS Journal on Computing, INFORMS, vol. 30(4), pages 768-782, November.
    7. Webster, S. T., 1996. "A general lower bound for the makespan problem," European Journal of Operational Research, Elsevier, vol. 89(3), pages 516-524, March.
    8. Webster, Scott, 1995. "Weighted flow time bounds for scheduling identical processors," European Journal of Operational Research, Elsevier, vol. 80(1), pages 103-111, January.
    9. Dunstall, Simon & Wirth, Andrew, 2005. "A comparison of branch-and-bound algorithms for a family scheduling problem with identical parallel machines," European Journal of Operational Research, Elsevier, vol. 167(2), pages 283-296, December.

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