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On the tractability of hard scheduling problems with generalized due-dates with respect to the number of different due-dates

Author

Listed:
  • Gur Mosheiov

    (The Hebrew University)

  • Daniel Oron

    (The University of Sydney Business School)

  • Dvir Shabtay

    (Ben-Gurion University of the Negev)

Abstract

We study two $$\mathcal {NP}$$ NP -hard single-machine scheduling problems with generalized due-dates. In such problems, due-dates are associated with positions in the job sequence rather than with jobs. Accordingly, the job that is assigned to position j in the job processing order (job sequence), is assigned with a predefined due-date, $$\delta _{j}$$ δ j . In the first problem, the objective consists of finding a job schedule that minimizes the maximal absolute lateness, while in the second problem, we aim to maximize the weighted number of jobs completed exactly at their due-date. Both problems are known to be strongly $$\mathcal {NP}$$ NP -hard when the instance includes an arbitrary number of different due-dates. Our objective is to study the tractability of both problems with respect to the number of different due-dates in the instance, $$\nu _{d}$$ ν d . We show that both problems remain $$ \mathcal {NP}$$ NP -hard even when $$\nu _{d}=2$$ ν d = 2 , and are solvable in pseudo-polynomial time when the value of $$\nu _{d}$$ ν d is upper bounded by a constant. To complement our results, we show that both problems are fixed parameterized tractable (FPT) when we combine the two parameters of number of different due-dates ( $$\nu _{d}$$ ν d ) and number of different processing times ( $$\nu _{p}$$ ν p ).

Suggested Citation

  • Gur Mosheiov & Daniel Oron & Dvir Shabtay, 2022. "On the tractability of hard scheduling problems with generalized due-dates with respect to the number of different due-dates," Journal of Scheduling, Springer, vol. 25(5), pages 577-587, October.
  • Handle: RePEc:spr:jsched:v:25:y:2022:i:5:d:10.1007_s10951-022-00743-9
    DOI: 10.1007/s10951-022-00743-9
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    References listed on IDEAS

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    Cited by:

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