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Exponential-time algorithms for parallel machine scheduling problems

Author

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  • Olivier Ploton

    (Université de Tours)

  • Vincent T’kindt

    (Université de Tours)

Abstract

In this paper we consider the problem of scheduling a set of jobs on unrelated parallel machines in the presence of job release dates and deadlines, and we deal with the minimization of any general regular, either maximum or sum, objective function. We describe a generic exact exponential algorithm, solving a problem in two phases. In the first phase, given a threshold objective value, the algorithm counts the number of schedules whose objective value is at most the threshold. For this purpose, by using Inclusion-Exclusion, it solves multiple relaxed single-machine problems by means of dynamic programming. In the second phase, the algorithm uses this counting procedure to determine the optimal objective value and build, step by step, an explicit optimal schedule. The strength of this algorithm is to manage a wide class of parallel machine scheduling problems, and to achieve, on a theoretical point on view, moderate exponential time and pseudopolynomial space worst-case complexity bounds. While not the fastest in practice compared to specialized algorithms, this generic algorithm enhances the state-of-the-art theoretical worst-case complexity bounds of several particular parallel machine scheduling problems.

Suggested Citation

  • Olivier Ploton & Vincent T’kindt, 2022. "Exponential-time algorithms for parallel machine scheduling problems," Journal of Combinatorial Optimization, Springer, vol. 44(5), pages 3405-3418, December.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:5:d:10.1007_s10878-022-00901-x
    DOI: 10.1007/s10878-022-00901-x
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    References listed on IDEAS

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    1. E. L. Lawler, 1973. "Optimal Sequencing of a Single Machine Subject to Precedence Constraints," Management Science, INFORMS, vol. 19(5), pages 544-546, January.
    2. Han Hoogeveen & Petra Schuurman & Gerhard J. Woeginger, 2001. "Non-Approximability Results for Scheduling Problems with Minsum Criteria," INFORMS Journal on Computing, INFORMS, vol. 13(2), pages 157-168, May.
    3. Jacek Blazewicz & Klaus H. Ecker & Erwin Pesch & Günter Schmidt & Malgorzata Sterna & Jan Weglarz, 2019. "Handbook on Scheduling," International Handbooks on Information Systems, Springer, edition 2, number 978-3-319-99849-7, November.
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    Cited by:

    1. 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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