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Scheduling Jobs with Truncated Exponential Sum-of-Logarithm-Processing-Times Based and Position-based Learning Effects

Author

Listed:
  • Yuan-Yuan Lu

    (College of Mathematics, Jilin Normal University, Siping, Jilin 136000, P. R. China)

  • Fei Teng

    (College of Mathematics, Jilin Normal University, Siping, Jilin 136000, P. R. China)

  • Zhi-Xin Feng

    (College of Mathematics, Jilin Normal University, Siping, Jilin 136000, P. R. China)

Abstract

In this study, we consider a scheduling problem with truncated exponential sum-of-logarithm-processing-times based and position-based learning effects on a single machine. We prove that the shortest processing time (SPT) rule is optimal for the makespan minimization problem, the sum of the θth power of job completion times minimization problem, and the total lateness minimization problem, respectively. For the total weighted completion time minimization problem, the discounted total weighted completion time minimization problem, the maximum lateness minimization problem, we present heuristic algorithms (the worst-case bound of these heuristic algorithms are also given) according to the corresponding single machine scheduling problems without learning considerations. It also shows that the problems of minimizing the total tardiness, the total weighted completion time and the discounted total weighted completion time are polynomially solvable under some agreeable conditions on the problem parameters.

Suggested Citation

  • Yuan-Yuan Lu & Fei Teng & Zhi-Xin Feng, 2015. "Scheduling Jobs with Truncated Exponential Sum-of-Logarithm-Processing-Times Based and Position-based Learning Effects," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(04), pages 1-17.
    • Handle: RePEc:wsi:apjorx:v:32:y:2015:i:04:n:s0217595915500268
    DOI: 10.1142/S0217595915500268
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    Citations

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    Cited by:

    1. Zhusong Liu & Zhenyou Wang & Yuan-Yuan Lu, 2017. "A Bicriteria Approach for Single Machine Scheduling with Resource Allocation, Learning Effect and a Deteriorating Maintenance Activity," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(04), pages 1-16, August.
    2. Ji-Bo Wang & Bo Cui & Ping Ji & Wei-Wei Liu, 2021. "Research on single-machine scheduling with position-dependent weights and past-sequence-dependent delivery times," Journal of Combinatorial Optimization, Springer, vol. 41(2), pages 290-303, February.
    3. Qian, Jin & Lin, Hexiang & Kong, Yufeng & Wang, Yuansong, 2020. "Tri-criteria single machine scheduling model with release times and learning factor," Applied Mathematics and Computation, Elsevier, vol. 387(C).
    4. Hongyu He & Yanzhi Zhao & Xiaojun Ma & Yuan-Yuan Lu & Na Ren & Ji-Bo Wang, 2023. "Study on Scheduling Problems with Learning Effects and Past Sequence Delivery Times," Mathematics, MDPI, vol. 11(19), pages 1-19, September.

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