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On scheduling with non-increasing time slot cost to minimize total weighted completion time

Author

Listed:
  • Yingchao Zhao

    (Caritas Institute of Higher Education)

  • Xiangtong Qi

    (Hong Kong University of Science and Technology)

  • Minming Li

    (City University of Hong Kong)

Abstract

This paper addresses a recent open scheduling problem which aims to minimize the summation of total weighted completion time and the total machine time slot cost. Focusing on the case of non-increasing time slot cost with non-preemptive jobs, we show that the problem can be solved in polynomial-time when the time slot cost decreases with certain patterns, including linearly decreasing, decreasing concave, and decreasing convex cases. Different methodologies are used for three cases. For the linearly decreasing case, we can classify all the jobs into three categories and schedule the job sets one by one. For the decreasing concave case, we calculate each job’s worst starting time and try to make them far away from their worst starting times. For the decreasing concave case, we calculate each job’s best starting time and let them start close to their best starting times. Finally, we show that the problem is NP-hard in the strong sense when the time slot cost decreases in an arbitrary way.

Suggested Citation

  • Yingchao Zhao & Xiangtong Qi & Minming Li, 2016. "On scheduling with non-increasing time slot cost to minimize total weighted completion time," Journal of Scheduling, Springer, vol. 19(6), pages 759-767, December.
    • Handle: RePEc:spr:jsched:v:19:y:2016:i:6:d:10.1007_s10951-015-0462-9
    DOI: 10.1007/s10951-015-0462-9
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    References listed on IDEAS

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    1. Tolga Aydinliyim & George L. Vairaktarakis, 2010. "Coordination of Outsourced Operations to Minimize Weighted Flow Time and Capacity Booking Costs," Manufacturing & Service Operations Management, INFORMS, vol. 12(2), pages 236-255, January.
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    Cited by:

    1. Markó Horváth & Tamás Kis, 2020. "Polyhedral results for position-based scheduling of chains on a single machine," Annals of Operations Research, Springer, vol. 284(1), pages 283-322, January.
    2. Michal Penn & Tal Raviv, 2021. "Complexity and algorithms for min cost and max profit scheduling under time-of-use electricity tariffs," Journal of Scheduling, Springer, vol. 24(1), pages 83-102, February.

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