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Improved Bounds on Relaxations of a Parallel Machine Scheduling Problem

Author

Listed:
  • Cynthia A. Phillips

    (Sandia National Labs)

  • Andreas S. Schulz

    (Technical University of Berlin)

  • David B. Shmoys

    (Cornell University)

  • Cliff Stein

    (Dartmouth College)

  • Joel Wein

    (Polytechnic University)

Abstract

We consider the problem of scheduling n jobs withrelease dates on m identical parallel machines to minimize the average completion time of the jobs. We prove that the ratio of the average completion time of the optimal nonpreemptive schedule to that of the optimal preemptive schedule is at most 7/3, improving a bound of $$(3 - \frac{1}{m})$$ Shmoys and Wein.

Suggested Citation

  • Cynthia A. Phillips & Andreas S. Schulz & David B. Shmoys & Cliff Stein & Joel Wein, 1998. "Improved Bounds on Relaxations of a Parallel Machine Scheduling Problem," Journal of Combinatorial Optimization, Springer, vol. 1(4), pages 413-426, December.
    • Handle: RePEc:spr:jcomop:v:1:y:1998:i:4:d:10.1023_a:1009750913529
    DOI: 10.1023/A:1009750913529
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    References listed on IDEAS

    as
    1. Robert McNaughton, 1959. "Scheduling with Deadlines and Loss Functions," Management Science, INFORMS, vol. 6(1), pages 1-12, October.
    2. Leslie A. Hall & Andreas S. Schulz & David B. Shmoys & Joel Wein, 1997. "Scheduling to Minimize Average Completion Time: Off-Line and On-Line Approximation Algorithms," Mathematics of Operations Research, INFORMS, vol. 22(3), pages 513-544, August.
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    Cited by:

    1. Yalaoui, F. & Chu, C., 2006. "New exact method to solve the Pm/rj/[summation operator]Cj schedule problem," International Journal of Production Economics, Elsevier, vol. 100(1), pages 168-179, March.
    2. Martin W. P. Savelsbergh & R. N. Uma & Joel Wein, 2005. "An Experimental Study of LP-Based Approximation Algorithms for Scheduling Problems," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 123-136, February.

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