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Mathematical models and an effective exact algorithm for unrelated parallel machine scheduling with family setup times and machine cost

Author

Listed:
  • Kai Li

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

  • Fulong Xie

    (Hefei University of Technology)

  • Jianfu Chen

    (Hefei University of Technology)

  • Wei Xiao

    (Hohai University)

  • Tao Zhou

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

Abstract

This paper investigates unrelated parallel machine scheduling problems, considering machine- and sequence-dependent family setup times and machine usage costs to minimise the sum of the total weighted completion time and the total machine usage cost. The machine usage cost consists of a fixed cost and a variable cost proportional to the processing times of jobs. These features align with numerous real-world applications that include machine usage costs, for example, rental fees when customers rent machines via a cloud manufacturing platform. To address the problem, five integer programming models are developed from different perspectives. Afterwards, a modified branch-and-price algorithm (B&P) based on the set-partitioning model is proposed. To enhance the performance of B&P, we introduce two dynamic programming algorithms and a heuristic pricing algorithm, and the initial solution is generated by an improved variable neighbourhood search algorithm. Extensive experimental results show that the proposed B&P outperforms state-of-the-art mathematical models and algorithms. Notably, B&P can optimally solve instances with up to 10 machines, 100 jobs, and 12 families within half an hour. Interestingly, experimental results also show that the B&P performs significantly better when total completion time is dominated by the total variable cost of machine usage.

Suggested Citation

  • Kai Li & Fulong Xie & Jianfu Chen & Wei Xiao & Tao Zhou, 2025. "Mathematical models and an effective exact algorithm for unrelated parallel machine scheduling with family setup times and machine cost," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 47(1), pages 129-176, March.
    • Handle: RePEc:spr:orspec:v:47:y:2025:i:1:d:10.1007_s00291-024-00778-8
    DOI: 10.1007/s00291-024-00778-8
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    References listed on IDEAS

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