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Preemptive Scheduling of Uniform Machines by Ordinary Network Flow Techniques

Author

Listed:
  • A. Federgruen

    (Graduate School of Business, Columbia University, New York, New York 10027)

  • H. Groenevelt

    (Graduate School of Management, University of Rochester, Rochester, New York 14627)

Abstract

We consider the problem of scheduling n jobs, each with a specific processing requirement, release time and due date on m uniform parallel machines. It is shown that a feasible schedule can be obtained by determining the maximum flow in a network, thus permitting the use of standard network flow codes. Using a specialized maximum flow procedure, the complexity reduces to O(tn 3 ) operations when t is the number of distinct machine types. Previous algorithms solve the feasibility problem in O((m + log n)(m 2 n 3 + n 4 )) operations. In addition to the feasibility problem, we describe algorithms for the maximum lateness criterion. Here we develop a bound which compares even more favorably to the best previous bound. We also show how other criteria with respect to the amount of work completed on each job prior to its due date or the amount of work scheduled in each of a sequence of periods can be optimized by similar path augmenting techniques.

Suggested Citation

  • A. Federgruen & H. Groenevelt, 1986. "Preemptive Scheduling of Uniform Machines by Ordinary Network Flow Techniques," Management Science, INFORMS, vol. 32(3), pages 341-349, March.
    • Handle: RePEc:inm:ormnsc:v:32:y:1986:i:3:p:341-349
    DOI: 10.1287/mnsc.32.3.341
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    Citations

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    Cited by:

    1. Akiyoshi Shioura & Natalia V. Shakhlevich & Vitaly A. Strusevich, 2016. "Application of Submodular Optimization to Single Machine Scheduling with Controllable Processing Times Subject to Release Dates and Deadlines," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 148-161, February.
    2. Shioura, Akiyoshi & Shakhlevich, Natalia V. & Strusevich, Vitaly A., 2018. "Preemptive models of scheduling with controllable processing times and of scheduling with imprecise computation: A review of solution approaches," European Journal of Operational Research, Elsevier, vol. 266(3), pages 795-818.
    3. Rubing Chen & Jinjiang Yuan & C.T. Ng & T.C.E. Cheng, 2019. "Single‐machine scheduling with deadlines to minimize the total weighted late work," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(7), pages 582-595, October.
    4. Akiyoshi Shioura & Natalia V. Shakhlevich & Vitaly A. Strusevich, 2020. "Scheduling problems with controllable processing times and a common deadline to minimize maximum compression cost," Journal of Global Optimization, Springer, vol. 76(3), pages 471-490, March.
    5. S. Thomas McCormick, 1999. "Fast Algorithms for Parametric Scheduling Come From Extensions to Parametric Maximum Flow," Operations Research, INFORMS, vol. 47(5), pages 744-756, October.
    6. Sedeño-Noda, A. & de Pablo, D. Alcaide López & González-Martín, C., 2009. "A network flow-based method to solve performance cost and makespan open-shop scheduling problems with time-windows," European Journal of Operational Research, Elsevier, vol. 196(1), pages 140-154, July.
    7. Guinet, Alain, 2001. "Multi-site planning: A transshipment problem," International Journal of Production Economics, Elsevier, vol. 74(1-3), pages 21-32, December.
    8. Sedeno-Noda, A. & Alcaide, D. & Gonzalez-Martin, C., 2006. "Network flow approaches to pre-emptive open-shop scheduling problems with time-windows," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1501-1518, November.
    9. Bornstein, Claudio Thomas & Alcoforado, Luciane Ferreira & Maculan, Nelson, 2005. "A graph-oriented approach for the minimization of the number of late jobs for the parallel machines scheduling problem," European Journal of Operational Research, Elsevier, vol. 165(3), pages 649-656, September.
    10. C N Potts & V A Strusevich, 2009. "Fifty years of scheduling: a survey of milestones," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 41-68, May.

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