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Single-machine and parallel-machine serial-batching scheduling problems with position-based learning effect and linear setup time

Author

Listed:
  • Jun Pei

    (Hefei University of Technology
    University of Florida
    Key Laboratory of Process Optimization and Intelligent Decision-Making of Ministry of Education)

  • Bayi Cheng

    (Hefei University of Technology
    Key Laboratory of Process Optimization and Intelligent Decision-Making of Ministry of Education)

  • Xinbao Liu

    (Hefei University of Technology
    Key Laboratory of Process Optimization and Intelligent Decision-Making of Ministry of Education)

  • Panos M. Pardalos

    (University of Florida)

  • Min Kong

    (Hefei University of Technology
    Key Laboratory of Process Optimization and Intelligent Decision-Making of Ministry of Education)

Abstract

This paper introduces the serial batching scheduling problems with position-based learning effect, where the actual job processing time is a function of its position. Two scheduling problems respectively for single-machine and parallel-machine are studied, and in each problem the objectives of minimizing maximum earliness and total number of tardy jobs are both considered respectively. In the proposed scheduling models, all jobs are first partitioned into serial batches, and then all batches are processed on the serial-batching machine. We take some practical production features into consideration, i.e., setup time before processing each batch increases with the time, regarded as time-dependent setup time, and we formalize it as a linear function of its starting time. Under the single-machine scheduling setting, structural properties are derived for the problems with the objectives of minimizing maximum earliness and number of tardy jobs respectively, based on which optimization algorithms are developed to solve them. Under the parallel-machine scheduling setting, a hybrid VNS–GSA algorithm combining variable neighborhood search (VNS) and gravitational search algorithm (GSA) is proposed to solve the problems with these two objectives respectively, and the effectiveness and efficiency of the proposed VNS–GSA are demonstrated and compared with the algorithms of GSA, VNS, and simulated annealing (SA). This paper demonstrates that the consideration of different objectives leads to various optimal decisions on jobs assignment, jobs batching, and batches sequencing, which generates a new insight to investigate batching scheduling problems with learning effect under single-machine and parallel-machine settings.

Suggested Citation

  • Jun Pei & Bayi Cheng & Xinbao Liu & Panos M. Pardalos & Min Kong, 2019. "Single-machine and parallel-machine serial-batching scheduling problems with position-based learning effect and linear setup time," Annals of Operations Research, Springer, vol. 272(1), pages 217-241, January.
    • Handle: RePEc:spr:annopr:v:272:y:2019:i:1:d:10.1007_s10479-017-2481-8
    DOI: 10.1007/s10479-017-2481-8
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    References listed on IDEAS

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    4. Yang, Fan & Davari, Morteza & Wei, Wenchao & Hermans, Ben & Leus, Roel, 2022. "Scheduling a single parallel-batching machine with non-identical job sizes and incompatible job families," European Journal of Operational Research, Elsevier, vol. 303(2), pages 602-615.
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    9. Wang, Xiong & Ferreira, Fernando A.F. & Chang, Ching-Ter, 2022. "Multi-objective competency-based approach to project scheduling and staff assignment: Case study of an internal audit project," Socio-Economic Planning Sciences, Elsevier, vol. 81(C).
    10. Jun Pei & Qingru Song & Baoyu Liao & Xinbao Liu & Panos M. Pardalos, 2021. "Parallel-machine serial-batching scheduling with release times under the effects of position-dependent learning and time-dependent deterioration," Annals of Operations Research, Springer, vol. 298(1), pages 407-444, March.
    11. Chen, Ke & Cheng, T.C.E. & Huang, Hailiang & Ji, Min & Yao, Danli, 2023. "Single-machine scheduling with autonomous and induced learning to minimize total weighted number of tardy jobs," European Journal of Operational Research, Elsevier, vol. 309(1), pages 24-34.
    12. Jun-Ho Lee & Hyun-Jung Kim, 2021. "A heuristic algorithm for identical parallel machine scheduling: splitting jobs, sequence-dependent setup times, and limited setup operators," Flexible Services and Manufacturing Journal, Springer, vol. 33(4), pages 992-1026, December.
    13. Zhe Zhang & Xiaoling Song & Huijun Huang & Yong Yin & Benjamin Lev, 2022. "Scheduling problem in seru production system considering DeJong’s learning effect and job splitting," Annals of Operations Research, Springer, vol. 312(2), pages 1119-1141, May.

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