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Bounds for the Optimal Scheduling of n Jobs on m Processors

Author

Listed:
  • W. L. Eastman

    (Sperry Rand Research Center, Sudbury, Massachusetts)

  • S. Even

    (Sperry Rand Research Center, Sudbury, Massachusetts)

  • I. M. Isaacs

    (Sperry Rand Research Center, Sudbury, Massachusetts)

Abstract

The problem of scheduling n jobs on m identical processors has been introduced by R. McNaughton, but as yet no efficient algorithm has been found for determining an optimal sequencing of jobs. In this paper lower and upper bounds are given for the cost of an optimal schedule. Since the two bounds are not far apart, they may be helpful in practical scheduling problems. A procedure is described for obtaining a schedule which costs less than the given upper bound.

Suggested Citation

  • W. L. Eastman & S. Even & I. M. Isaacs, 1964. "Bounds for the Optimal Scheduling of n Jobs on m Processors," Management Science, INFORMS, vol. 11(2), pages 268-279, November.
    • Handle: RePEc:inm:ormnsc:v:11:y:1964:i:2:p:268-279
    DOI: 10.1287/mnsc.11.2.268
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    Citations

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    Cited by:

    1. Heydenreich, B. & Müller, R.J. & Uetz, M.J., 2006. "Decentralization and mechanism design for online machine scheduling," Research Memorandum 007, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    2. Megow, Nicole & Schulz, Andreas S., 2004. "Scheduling to Minimize Average Completion Time Revisited: Deterministic On-line Algorithms," Working papers 4435-03, Massachusetts Institute of Technology (MIT), Sloan School of Management.
    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. José R. Correa & Andreas S. Schulz, 2005. "Single-Machine Scheduling with Precedence Constraints," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 1005-1021, November.
    5. Birgit Heydenreich & Rudolf Müller & Marc Uetz, 2010. "Mechanism Design for Decentralized Online Machine Scheduling," Operations Research, INFORMS, vol. 58(2), pages 445-457, April.
    6. Andreas S. Schulz & Nelson A. Uhan, 2011. "Near-Optimal Solutions and Large Integrality Gaps for Almost All Instances of Single-Machine Precedence-Constrained Scheduling," Mathematics of Operations Research, INFORMS, vol. 36(1), pages 14-23, February.
    7. Lin Chen & Nicole Megow & Roman Rischke & Leen Stougie & José Verschae, 2021. "Optimal algorithms for scheduling under time-of-use tariffs," Annals of Operations Research, Springer, vol. 304(1), pages 85-107, September.
    8. Christoph Ambühl & Monaldo Mastrolilli & Nikolaus Mutsanas & Ola Svensson, 2011. "On the Approximability of Single-Machine Scheduling with Precedence Constraints," Mathematics of Operations Research, INFORMS, vol. 36(4), pages 653-669, November.
    9. Tzafestas, Spyros & Triantafyllakis, Alekos, 1993. "Deterministic scheduling in computing and manufacturing systems: a survey of models and algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(5), pages 397-434.
    10. Balireddi, Sindhura & Uhan, Nelson A., 2012. "Cost-sharing mechanisms for scheduling under general demand settings," European Journal of Operational Research, Elsevier, vol. 217(2), pages 270-277.
    11. Mehdi Rajabi Asadabadi, 2017. "A developed slope order index (SOI) for bottlenecks in projects and production lines," Computational Management Science, Springer, vol. 14(2), pages 281-291, April.
    12. Kramer, Arthur & Dell’Amico, Mauro & Iori, Manuel, 2019. "Enhanced arc-flow formulations to minimize weighted completion time on identical parallel machines," European Journal of Operational Research, Elsevier, vol. 275(1), pages 67-79.
    13. Itai Ashlagi & Shahar Dobzinski & Ron Lavi, 2012. "Optimal Lower Bounds for Anonymous Scheduling Mechanisms," Mathematics of Operations Research, INFORMS, vol. 37(2), pages 244-258, May.
    14. Bachtenkirch, David & Bock, Stefan, 2022. "Finding efficient make-to-order production and batch delivery schedules," European Journal of Operational Research, Elsevier, vol. 297(1), pages 133-152.
    15. Felipe T. Muñoz & Rodrigo Linfati, 2024. "Bounding the Price of Anarchy of Weighted Shortest Processing Time Policy on Uniform Parallel Machines," Mathematics, MDPI, vol. 12(14), pages 1-12, July.
    16. Azizoglu, Meral & Kirca, Omer, 1999. "On the minimization of total weighted flow time with identical and uniform parallel machines," European Journal of Operational Research, Elsevier, vol. 113(1), pages 91-100, February.
    17. Hui Liu & Maurice Queyranne & David Simchi‐Levi, 2005. "On the asymptotic optimality of algorithms for the flow shop problem with release dates," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(3), pages 232-242, April.
    18. José R. Correa & Martin Skutella & José Verschae, 2012. "The Power of Preemption on Unrelated Machines and Applications to Scheduling Orders," Mathematics of Operations Research, INFORMS, vol. 37(2), pages 379-398, May.
    19. Webster, Scott, 1995. "Weighted flow time bounds for scheduling identical processors," European Journal of Operational Research, Elsevier, vol. 80(1), pages 103-111, January.
    20. Nicole Megow & Marc Uetz & Tjark Vredeveld, 2006. "Models and Algorithms for Stochastic Online Scheduling," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 513-525, August.

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