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Model and Algorithm for a Two-Machine Group Scheduling Problem with Setup and Transportation Time

Author

Listed:
  • Yu Ni

    (School of Economics and Management, University of Science and Technology Beijing, No. 30, Xueyuan Road, Haidian District, Beijing 100083, China)

  • Shufen Dai

    (School of Economics and Management, University of Science and Technology Beijing, No. 30, Xueyuan Road, Haidian District, Beijing 100083, China)

  • Shuaipeng Yuan

    (School of Economics and Management, University of Science and Technology Beijing, No. 30, Xueyuan Road, Haidian District, Beijing 100083, China)

  • Bailin Wang

    (School of Economics and Management, University of Science and Technology Beijing, No. 30, Xueyuan Road, Haidian District, Beijing 100083, China)

  • Zhuolun Zhang

    (School of Economics and Management, University of Science and Technology Beijing, No. 30, Xueyuan Road, Haidian District, Beijing 100083, China)

Abstract

This paper investigates a two-machine group scheduling problem with sequence-independent setup times and round-trip transportation times, which is derived from the production management requirements of modern steel manufacturing enterprises. The objective is to minimize the makespan. Addressing limitations in prior studies, we consider a critical but largely ignored transportation method, namely round-trip transportation, and restricted transporter capacity between machines. To solve this problem, a mixed-integer programming model is first developed. Then, the problem complexity is analyzed for situations with both single and unlimited transporters. For the NP-hard case of a single transporter, we design an efficient two-stage heuristic algorithm with proven acceptable solution quality bounds. Extensive computational experiments based on steel plant data demonstrate the effectiveness of our approach in providing near-optimal solutions, and the maximum deviation between our algorithm and the optimal solution is 1.38%. This research can provide an operable optimization method that is valuable for group scheduling and transportation scheduling.

Suggested Citation

  • Yu Ni & Shufen Dai & Shuaipeng Yuan & Bailin Wang & Zhuolun Zhang, 2024. "Model and Algorithm for a Two-Machine Group Scheduling Problem with Setup and Transportation Time," Mathematics, MDPI, vol. 12(6), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:6:p:888-:d:1358833
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    References listed on IDEAS

    as
    1. Tian, Zheng & Zheng, Li, 2024. "Single machine parallel-batch scheduling under time-of-use electricity prices: New formulations and optimisation approaches," European Journal of Operational Research, Elsevier, vol. 312(2), pages 512-524.
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