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Structural properties of time-dependent scheduling problems with the lp norm objective

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  • Gawiejnowicz, Stanisław
  • Kurc, Wiesław

Abstract

We consider general properties which describe the structure of schedules for a single machine scheduling problem with linearly deteriorating jobs and the objective to minimize the lp norm. Applying a matrix formulation of the problem, we show that it has unique solutions and for p≥1 it possesses a kind of convexity. We also express the time complexity of the problem as a function of index p of the lp norm and prove that there exist thresholds p∞ and p1 such that p∞1, while symmetricity of the schedules may hold only for some p≥1.

Suggested Citation

  • Gawiejnowicz, Stanisław & Kurc, Wiesław, 2015. "Structural properties of time-dependent scheduling problems with the lp norm objective," Omega, Elsevier, vol. 57(PB), pages 196-202.
    • Handle: RePEc:eee:jomega:v:57:y:2015:i:pb:p:196-202
    DOI: 10.1016/j.omega.2015.04.015
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    References listed on IDEAS

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    9. Min Ji & Chou-Jung Hsu & Dar-Li Yang, 2013. "Single-machine scheduling with deteriorating jobs and aging effects under an optional maintenance activity consideration," Journal of Combinatorial Optimization, Springer, vol. 26(3), pages 437-447, October.
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    Cited by:

    1. 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.
    2. Stanisław Gawiejnowicz, 2020. "A review of four decades of time-dependent scheduling: main results, new topics, and open problems," Journal of Scheduling, Springer, vol. 23(1), pages 3-47, February.

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