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Scheduling jobs with a V-shaped time-dependent processing time

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  • Helmut A. Sedding

    (Ulm University
    ZHAW Zurich University of Applied Sciences)

Abstract

In the field of time-dependent scheduling, a job’s processing time is specified by a function of its start time. While monotonic processing time functions are well-known in the literature, this paper introduces non-monotonic functions with a convex, piecewise-linear V-shape similar to the absolute value function. They are minimum at an ideal start time, which is the same for all given jobs. Then, the processing time equals the job’s basic processing time. Earlier or later, it increases linearly with slopes that can be asymmetric and job-specific. The objective is to sequence the given jobs on a single machine and minimize the makespan. This is motivated by production planning of moving car assembly lines, in particular, to sequence a worker’s assembly operations such that the time-dependent walking times to gather materials from the line-side is minimized. This paper characterizes the problem’s computational complexity in several angles. NP-hardness is observed even if the two slopes are the same for all jobs. A fully polynomial time approximation scheme is devised for the more generic case of agreeable ratios of basic processing time and slopes. In the most generic case with job-specific slopes, several polynomial cases are identified.

Suggested Citation

  • Helmut A. Sedding, 2020. "Scheduling jobs with a V-shaped time-dependent processing time," Journal of Scheduling, Springer, vol. 23(6), pages 751-768, December.
    • Handle: RePEc:spr:jsched:v:23:y:2020:i:6:d:10.1007_s10951-020-00665-4
    DOI: 10.1007/s10951-020-00665-4
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    1. E. L. Lawler & J. M. Moore, 1969. "A Functional Equation and its Application to Resource Allocation and Sequencing Problems," Management Science, INFORMS, vol. 16(1), pages 77-84, September.
    2. Vitaly A. Strusevich & Kabir Rustogi, 2017. "Scheduling with Time-Changing Effects and Rate-Modifying Activities," International Series in Operations Research and Management Science, Springer, number 978-3-319-39574-6, December.
    3. Nicholas G. Hall & Wieslaw Kubiak & Suresh P. Sethi, 1991. "Earliness–Tardiness Scheduling Problems, II: Deviation of Completion Times About a Restrictive Common Due Date," Operations Research, INFORMS, vol. 39(5), pages 847-856, October.
    4. Jacek Blazewicz & Klaus H. Ecker & Erwin Pesch & Günter Schmidt & Malgorzata Sterna & Jan Weglarz, 2019. "Handbook on Scheduling," International Handbooks on Information Systems, Springer, edition 2, number 978-3-319-99849-7, November.
    5. B Alidaee & N K Womer, 1999. "Scheduling with time dependent processing times: Review and extensions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(7), pages 711-720, July.
    6. Nicholas G. Hall & Marc E. Posner, 1991. "Earliness-Tardiness Scheduling Problems, I: Weighted Deviation of Completion Times About a Common Due Date," Operations Research, INFORMS, vol. 39(5), pages 836-846, October.
    7. Florian Jaehn & Helmut A. Sedding, 2016. "Scheduling with time-dependent discrepancy times," Journal of Scheduling, Springer, vol. 19(6), pages 737-757, December.
    8. Wayne E. Smith, 1956. "Various optimizers for single‐stage production," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 59-66, March.
    9. Hoogeveen, J. A. & van de Velde, S. L., 1991. "Scheduling around a small common due date," European Journal of Operational Research, Elsevier, vol. 55(2), pages 237-242, November.
    10. Sid Browne & Uri Yechiali, 1990. "Scheduling Deteriorating Jobs on a Single Processor," Operations Research, INFORMS, vol. 38(3), pages 495-498, June.
    11. Wieslaw Kubiak & Steef van de Velde, 1998. "Scheduling deteriorating jobs to minimize makespan," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(5), pages 511-523, August.
    12. Helmut A. Sedding, 2020. "Line side placement for shorter assembly line worker paths," IISE Transactions, Taylor & Francis Journals, vol. 52(2), pages 181-198, February.
    13. Gerhard J. Woeginger, 2000. "When Does a Dynamic Programming Formulation Guarantee the Existence of a Fully Polynomial Time Approximation Scheme (FPTAS)?," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 57-74, February.
    14. 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.
    15. Michael R. Garey & Robert E. Tarjan & Gordon T. Wilfong, 1988. "One-Processor Scheduling with Symmetric Earliness and Tardiness Penalties," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 330-348, May.
    16. Vitaly A. Strusevich & Kabir Rustogi, 2017. "Scheduling with Rate-Modifying Activities," International Series in Operations Research & Management Science, in: Scheduling with Time-Changing Effects and Rate-Modifying Activities, chapter 0, pages 317-331, Springer.
    17. T.C. Edwin Cheng & Qing Ding & Mikhail Y. Kovalyov & Aleksander Bachman & Adam Janiak, 2003. "Scheduling jobs with piecewise linear decreasing processing times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(6), pages 531-554, September.
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