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Scheduling in multi-scenario environment with an agreeable condition on job processing times

Author

Listed:
  • Miri Gilenson

    (Ben-Gurion University of the Negev)

  • Dvir Shabtay

    (Ben-Gurion University of the Negev)

  • Liron Yedidsion

    (Amazon Research, Amazon)

  • Rohit Malshe

    (Amazon Research, Amazon)

Abstract

In the literature on multi-scenario scheduling problems, it is assumed that (i) each scenario defines a different possible realization of the job’s parameters; and (ii) the value of each parameter is arbitrary for any job in any scenario. Under these assumptions many multi-scenario scheduling problems have been proven to be $$\mathcal {NP}$$ NP -hard. We study a special case of this set of problems, in which there is an agreeable condition between scenarios on the processing-time parameters. Accordingly, the processing time of job $$J_{j}$$ J j under scenario $$s_{i}$$ s i is at most its value under scenario $$s_{i+1}$$ s i + 1 , for $$i=1,\ldots q-1$$ i = 1 , … q - 1 , where q is the number of different possible scenarios. We focus on three classical scheduling problems for which the single-scenario case is solvable in polynomial time, while the multi-scenario case is $$\mathcal {NP}$$ NP -hard, even when there are only two scenarios. The three scheduling problems consist of minimizing either the total completion time or the number of tardy jobs on a single machine, and minimizing the makespan in a two-machine flow-shop system. We show that the multi-scenario version of all three problems remains $$\mathcal {NP}$$ NP -hard even when processing times are agreeable and there are only two scenarios. We also show that for a more specific structure of job processing times two out of the three problems become easy to solve, while the complexity status of the third remains open for future research.

Suggested Citation

  • Miri Gilenson & Dvir Shabtay & Liron Yedidsion & Rohit Malshe, 2021. "Scheduling in multi-scenario environment with an agreeable condition on job processing times," Annals of Operations Research, Springer, vol. 307(1), pages 153-173, December.
  • Handle: RePEc:spr:annopr:v:307:y:2021:i:1:d:10.1007_s10479-021-04316-5
    DOI: 10.1007/s10479-021-04316-5
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    References listed on IDEAS

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