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A Two-Machine Learning Date Flow-Shop Scheduling Problem with Heuristics and Population-Based GA to Minimize the Makespan

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Listed:
  • Jian-You Xu

    (College of Information Science and Engineering, Northeastern University, Shenyang 110819, China)

  • Win-Chin Lin

    (Department of Statistics, Feng Chia University, Taichung 40724, Taiwan)

  • Yu-Wei Chang

    (Department of Statistics, Feng Chia University, Taichung 40724, Taiwan)

  • Yu-Hsiang Chung

    (Department of Industrial Engineering Automation Operation Intelligence, Micron Memory Taiwan Co., Ltd., Taichung 42152, Taiwan
    Department of Industrial Engineering and Management, Chin-Yi University of Technology, Taichung 411030, Taiwan)

  • Juin-Han Chen

    (Department of Industrial Engineering and Management, Cheng Shiu University, Kaohsiung City 83347, Taiwan)

  • Chin-Chia Wu

    (Department of Statistics, Feng Chia University, Taichung 40724, Taiwan)

Abstract

This paper delves into the scheduling of the two-machine flow-shop problem with step-learning, a scenario in which job processing times decrease if they commence after their learning dates. The objective is to optimize resource allocation and task sequencing to ensure efficient time utilization and timely completion of all jobs, also known as the makespan. The identified problem is established as NP-hard due to its reduction to a single machine for a common learning date. To address this complexity, this paper introduces an initial integer programming model, followed by the development of a branch-and-bound algorithm augmented with two lemmas and a lower bound to attain an exact optimal solution. Additionally, this paper proposes four straightforward heuristics inspired by the Johnson rule, along with their enhanced counterparts. Furthermore, a population-based genetic algorithm is formulated to offer approximate solutions. The performance of all proposed methods is rigorously evaluated through numerical experimental studies.

Suggested Citation

  • Jian-You Xu & Win-Chin Lin & Yu-Wei Chang & Yu-Hsiang Chung & Juin-Han Chen & Chin-Chia Wu, 2023. "A Two-Machine Learning Date Flow-Shop Scheduling Problem with Heuristics and Population-Based GA to Minimize the Makespan," Mathematics, MDPI, vol. 11(19), pages 1-21, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4060-:d:1247161
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    References listed on IDEAS

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