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Study on Convex Resource Allocation Scheduling with a Time-Dependent Learning Effect

Author

Listed:
  • Yi-Chun Wang

    (School of Science, Shenyang Aerospace University, Shenyang 110136, China)

  • Ji-Bo Wang

    (School of Science, Shenyang Aerospace University, Shenyang 110136, China)

Abstract

In classical schedule problems, the actual processing time of a job is a fixed constant, but in the actual production process, the processing time of a job is affected by a variety of factors, two of which are the learning effect and resource allocation. In this paper, single-machine scheduling problems with resource allocation and a time-dependent learning effect are investigated. The actual processing time of a job depends on the sum of normal processing times of previous jobs and the allocation of non-renewable resources. With the convex resource consumption function, the goal is to determine the optimal schedule and optimal resource allocation. Three problems arising from two criteria (i.e., the total resource consumption cost and the scheduling cost) are studied. For some special cases of the problems, we prove that they can be solved in polynomial time. More generally, we propose some accurate and intelligent algorithms to solve these problems.

Suggested Citation

  • Yi-Chun Wang & Ji-Bo Wang, 2023. "Study on Convex Resource Allocation Scheduling with a Time-Dependent Learning Effect," Mathematics, MDPI, vol. 11(14), pages 1-20, July.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3179-:d:1198333
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    References listed on IDEAS

    as
    1. Yi-Chun Wang & Si-Han Wang & Ji-Bo Wang, 2023. "Resource Allocation Scheduling with Position-Dependent Weights and Generalized Earliness–Tardiness Cost," Mathematics, MDPI, vol. 11(1), pages 1-11, January.
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    Cited by:

    1. Zheng Liu & Ji-Bo Wang, 2024. "Single-Machine Scheduling with Simultaneous Learning Effects and Delivery Times," Mathematics, MDPI, vol. 12(16), pages 1-20, August.
    2. Xuyin Wang & Weiguo Liu, 2024. "Optimal Different Due-Date Assignment Scheduling with Group Technology and Resource Allocation," Mathematics, MDPI, vol. 12(3), pages 1-17, January.
    3. Ming-Hui Li & Dan-Yang Lv & Yuan-Yuan Lu & Ji-Bo Wang, 2024. "Scheduling with Group Technology, Resource Allocation, and Learning Effect Simultaneously," Mathematics, MDPI, vol. 12(7), pages 1-21, March.

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