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An exact algorithm for parallel machine scheduling with conflicts

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  • Daniel Kowalczyk

    (ORSTAT)

  • Roel Leus

    (ORSTAT)

Abstract

We consider an extension of classic parallel machine scheduling where a set of jobs is scheduled on identical parallel machines and an undirected conflict graph is part of the input. Each node in the graph represents a job, and an edge implies that its two jobs are conflicting, meaning that they cannot be scheduled on the same machine. The goal is to find an assignment of the jobs to the machines such that the maximum completion time (makespan) is minimized. We present an exact algorithm based on branch and price that combines methods from bin packing, scheduling, and graph coloring, with appropriate modifications. The algorithm has a good computational performance even for parallel machine scheduling without conflicting jobs.

Suggested Citation

  • Daniel Kowalczyk & Roel Leus, 2017. "An exact algorithm for parallel machine scheduling with conflicts," Journal of Scheduling, Springer, vol. 20(4), pages 355-372, August.
    • Handle: RePEc:spr:jsched:v:20:y:2017:i:4:d:10.1007_s10951-016-0482-0
    DOI: 10.1007/s10951-016-0482-0
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    2. Guopeng Song & Roel Leus, 2022. "Parallel Machine Scheduling Under Uncertainty: Models and Exact Algorithms," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3059-3079, November.
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    4. Ruslan Sadykov & François Vanderbeck & Artur Pessoa & Issam Tahiri & Eduardo Uchoa, 2019. "Primal Heuristics for Branch and Price: The Assets of Diving Methods," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 251-267, April.

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