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Scheduling with time-dependent discrepancy times

Author

Listed:
  • Florian Jaehn

    (University of Augsburg)

  • Helmut A. Sedding

    (University of Augsburg)

Abstract

In time-dependent scheduling, various processing time functions are studied, yet absolute value functions have surprisingly been omitted from the discussion. Such a processing time function increases linearly with a job’s discrepancy from its ideal midtime. The objective is to find a schedule that minimizes the makespan, introducing the discrepancy time minimization problem. This single-machine scheduling problem with time-dependent processing times is motivated by optimization of walking times on a car assembly line. Its decision version is NP hard, as we show by reduction of the even–odd partition problem. For the variant with known start time, we develop several heuristics. Further insights form lower bounds and dominance rules for a branch-and-bound search. Numerical experiments show the performance of our algorithms on problem instances of up to 60 jobs. For the variant with common ideal midtime and flexible start time, we present a polynomial-time algorithm.

Suggested Citation

  • Florian Jaehn & Helmut A. Sedding, 2016. "Scheduling with time-dependent discrepancy times," Journal of Scheduling, Springer, vol. 19(6), pages 737-757, December.
    • Handle: RePEc:spr:jsched:v:19:y:2016:i:6:d:10.1007_s10951-016-0472-2
    DOI: 10.1007/s10951-016-0472-2
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    References listed on IDEAS

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    Cited by:

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    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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