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Infinite split scheduling : a new lower bound of total weighted completion time on parallel machines with job release dates and unavailability periods

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  • R. Nessah

    (UMR CNRS 8179 - Université de Lille, Sciences et Technologies - CNRS - Centre National de la Recherche Scientifique)

  • C. Chu

Abstract

This paper addresses an identical parallel machine scheduling problem with job release dates and unavailability periods to minimize total weighted completion time. This problem is known to be NP-hard in the strong sense. We propose a new lower bound that can be computed in polynomial time. The test on more than 8 400 randomly generated instances shows a very significant improvement with respect to existing results for previously studied special cases: without unavailability constraints, unweighted version, or identical job release dates. For instance, the average improvement for the unweighted problem is as much as 20.43% for 2 machines, 53.03% for 7 machines and 66.70% for 15 machines. For some instances, the improvement can be even as much as 93%. Copyright Springer Science+Business Media, LLC 2010
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  • R. Nessah & C. Chu, 2010. "Infinite split scheduling : a new lower bound of total weighted completion time on parallel machines with job release dates and unavailability periods," Post-Print hal-00572976, HAL.
    • Handle: RePEc:hal:journl:hal-00572976
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    1. E. L. Lawler & J. M. Moore, 1969. "A Functional Equation and its Application to Resource Allocation and Sequencing Problems," Management Science, INFORMS, vol. 16(1), pages 77-84, September.
    2. Scott Webster, 1992. "New Bounds for the Identical Parallel Processor Weighted Flow Time Problem," Management Science, INFORMS, vol. 38(1), pages 124-136, January.
    3. 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.
    4. 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.
    5. Webster, Scott, 1995. "Weighted flow time bounds for scheduling identical processors," European Journal of Operational Research, Elsevier, vol. 80(1), pages 103-111, January.
    6. Webster, S. T., 1993. "A priority rule for minimizing weighted flow time in a class of parallel machine scheduling problems," European Journal of Operational Research, Elsevier, vol. 70(3), pages 327-334, November.
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    8. 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.
    9. R. Nessah & Farouk Yalaoui & C. Chu, 2008. "A branch and bound algorithm to minimize total weighted completion time on identical parallel machines with job release date," Post-Print hal-00580602, HAL.
    10. 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.
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    Cited by:

    1. Zhe Zhang & Xiaoling Song & Huijun Huang & Yong Yin & Benjamin Lev, 2022. "Scheduling problem in seru production system considering DeJong’s learning effect and job splitting," Annals of Operations Research, Springer, vol. 312(2), pages 1119-1141, May.

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