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Parallel machine scheduling with minimum number of tardy jobs: Approximation and exponential algorithms

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  • Della Croce, Federico
  • T’kindt, Vincent
  • Ploton, Olivier

Abstract

We consider the solution of some NP-hard parallel machine scheduling problems involving the minimization of the weighted or unweighted number of tardy jobs. We first show that these problems cannot be approximated in polynomial time. Then we propose exponential-time approximation algorithms and fixed parameter tractable exact algorithms to solve them.

Suggested Citation

  • Della Croce, Federico & T’kindt, Vincent & Ploton, Olivier, 2021. "Parallel machine scheduling with minimum number of tardy jobs: Approximation and exponential algorithms," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    • Handle: RePEc:eee:apmaco:v:397:y:2021:i:c:s0096300320308419
    DOI: 10.1016/j.amc.2020.125888
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    References listed on IDEAS

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    1. Lei Shang & Christophe Lenté & Mathieu Liedloff & Vincent T’Kindt, 2018. "Exact exponential algorithms for 3-machine flowshop scheduling problems," Journal of Scheduling, Springer, vol. 21(2), pages 227-233, April.
    2. 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.
    3. Stanisław Gawiejnowicz & Wiesław Kurc, 2020. "New results for an open time-dependent scheduling problem," Journal of Scheduling, Springer, vol. 23(6), pages 733-744, December.
    4. Lin, Yixun & Wang, Xiumei, 2007. "Necessary and sufficient conditions of optimality for some classical scheduling problems," European Journal of Operational Research, Elsevier, vol. 176(2), pages 809-818, January.
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    Cited by:

    1. Julio Mar-Ortiz & Alex J. Ruiz Torres & Belarmino Adenso-Díaz, 2022. "Scheduling in parallel machines with two objectives: analysis of factors that influence the Pareto frontier," Operational Research, Springer, vol. 22(4), pages 4585-4605, September.
    2. Vincent T’kindt & Federico Della Croce & Mathieu Liedloff, 2022. "Moderate exponential-time algorithms for scheduling problems," 4OR, Springer, vol. 20(4), pages 533-566, December.

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