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Three notes on scheduling unit-length jobs with precedence constraints to minimize the total completion time

Author

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  • Tianyu Wang

    (Beihang University)

  • Odile Bellenguez

    (LS2N, La Chantrerie)

Abstract

In this paper, we provide three notes on scheduling unit-length jobs with precedence constraints to minimize the total completion time. First, we propose an exact algorithm for in-trees, of which the complexity depends mainly on the graph height, i.e., the length of the longest chain of the precedence graph. We show that this work improves the algorithm in the literature both theoretically and experimentally. Second, we close the open problem for level-orders by showing how it is polynomially solvable. Third, we prove that preemptive scheduling in-trees is strongly NP-hard with arbitrary number of machines, of which the complexity was also open.

Suggested Citation

  • Tianyu Wang & Odile Bellenguez, 2021. "Three notes on scheduling unit-length jobs with precedence constraints to minimize the total completion time," Journal of Scheduling, Springer, vol. 24(6), pages 649-662, December.
    • Handle: RePEc:spr:jsched:v:24:y:2021:i:6:d:10.1007_s10951-021-00702-w
    DOI: 10.1007/s10951-021-00702-w
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    References listed on IDEAS

    as
    1. Tianyu Wang & Odile Bellenguez-Morineau, 2019. "A complexity analysis of parallel scheduling unit-time jobs with in-tree precedence constraints while minimizing the mean flow time," Journal of Scheduling, Springer, vol. 22(6), pages 709-714, December.
    2. Bo Chen & Ed Coffman & Dariusz Dereniowski & Wiesław Kubiak, 2016. "Normal-form preemption sequences for an open problem in scheduling theory," Journal of Scheduling, Springer, vol. 19(6), pages 701-728, December.
    3. D. Prot & O. Bellenguez-Morineau, 2018. "A survey on how the structure of precedence constraints may change the complexity class of scheduling problems," Journal of Scheduling, Springer, vol. 21(1), pages 3-16, February.
    4. Tianyu Wang & Odile Bellenguez-Morineau, 2019. "The Complexity of Parallel Machine Scheduling of Unit-Processing-Time Jobs under Level-Order Precedence Constraints," Journal of Scheduling, Springer, vol. 22(3), pages 263-269, June.
    5. T. C. Hu, 1961. "Parallel Sequencing and Assembly Line Problems," Operations Research, INFORMS, vol. 9(6), pages 841-848, December.
    Full references (including those not matched with items on IDEAS)

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