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Single machine parallel-batch scheduling under time-of-use electricity prices: New formulations and optimisation approaches

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  • Tian, Zheng
  • Zheng, Li

Abstract

Electricity costs account for a relatively large proportion of total production costs in many energy-intensive manufacturing industries. And energy-efficient scheduling is getting increasing attention from researchers owing to its wide real-world applications and computational challenges. In this study, the single-machine parallel-batch scheduling problem with non-identical job sizes under time-of-use electricity prices is investigated. The objective is to minimise the total energy consumption cost such that the makespan does not exceed a given deadline. First, an improved time-slot-indexed formulation is proposed to eliminate symmetric solutions. Subsequently, a new set partition-based formulation is developed. To the best of our knowledge, there is no exact algorithm for this problem, except for some formulations solved by off-the-shelf solvers. To address this problem, a branch-and-price algorithm is developed with a novel and efficient branching rule. In addition, a column-generation-based heuristic is proposed to solve larger-scale instances. Extensive numerical experiments show that the efficiency of the branch-and-price algorithm is significantly better than that of off-the-shelf solvers, and many instances with up to 100 jobs could be solved to optimality within a 20-minute computational time limit for the first time. The column-generation-based heuristic can efficiently provide better solutions than existing heuristics (2.75% average gap in three minutes on instances with 100 jobs and 3.12% average gap in ten minutes on instances with 200 jobs).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:312:y:2024:i:2:p:512-524
    DOI: 10.1016/j.ejor.2023.07.012
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    1. Gahm, Christian & Denz, Florian & Dirr, Martin & Tuma, Axel, 2016. "Energy-efficient scheduling in manufacturing companies: A review and research framework," European Journal of Operational Research, Elsevier, vol. 248(3), pages 744-757.
    2. Sung, C. S. & Choung, Y. I., 2000. "Minimizing makespan on a single burn-in oven in semiconductor manufacturing," European Journal of Operational Research, Elsevier, vol. 120(3), pages 559-574, February.
    3. Catanzaro, Daniele & Pesenti, Raffaele & Ronco, Roberto, 2023. "Job scheduling under Time-of-Use energy tariffs for sustainable manufacturing: a survey," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1091-1109.
    4. Eglese, R. W., 1990. "Simulated annealing: A tool for operational research," European Journal of Operational Research, Elsevier, vol. 46(3), pages 271-281, June.
    5. Masmoudi, Oussama & Delorme, Xavier & Gianessi, Paolo, 2019. "Job-shop scheduling problem with energy consideration," International Journal of Production Economics, Elsevier, vol. 216(C), pages 12-22.
    6. Muter, İbrahim, 2020. "Exact algorithms to minimize makespan on single and parallel batch processing machines," European Journal of Operational Research, Elsevier, vol. 285(2), pages 470-483.
    7. Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser & Martin W. P. Savelsbergh & Pamela H. Vance, 1998. "Branch-and-Price: Column Generation for Solving Huge Integer Programs," Operations Research, INFORMS, vol. 46(3), pages 316-329, June.
    8. Peng Wu & Junheng Cheng & Feng Chu, 2021. "Large-scale energy-conscious bi-objective single-machine batch scheduling under time-of-use electricity tariffs via effective iterative heuristics," Annals of Operations Research, Springer, vol. 296(1), pages 471-494, January.
    9. Fowler, John W. & Mönch, Lars, 2022. "A survey of scheduling with parallel batch (p-batch) processing," European Journal of Operational Research, Elsevier, vol. 298(1), pages 1-24.
    10. Melouk, Sharif & Damodaran, Purushothaman & Chang, Ping-Yu, 2004. "Minimizing makespan for single machine batch processing with non-identical job sizes using simulated annealing," International Journal of Production Economics, Elsevier, vol. 87(2), pages 141-147, January.
    11. Ozturk, Onur, 2020. "A truncated column generation algorithm for the parallel batch scheduling problem to minimize total flow time," European Journal of Operational Research, Elsevier, vol. 286(2), pages 432-443.
    12. Luo, Hao & Du, Bing & Huang, George Q. & Chen, Huaping & Li, Xiaolin, 2013. "Hybrid flow shop scheduling considering machine electricity consumption cost," International Journal of Production Economics, Elsevier, vol. 146(2), pages 423-439.
    13. Kan Fang & Nelson A. Uhan & Fu Zhao & John W. Sutherland, 2016. "Scheduling on a single machine under time-of-use electricity tariffs," Annals of Operations Research, Springer, vol. 238(1), pages 199-227, March.
    14. Kan Fang & Nelson Uhan & Fu Zhao & John Sutherland, 2016. "Scheduling on a single machine under time-of-use electricity tariffs," Annals of Operations Research, Springer, vol. 238(1), pages 199-227, March.
    15. Renan Spencer Trindade & Olinto César Bassi de Araújo & Marcia Helena Costa Fampa & Felipe Martins Müller, 2018. "Modelling and symmetry breaking in scheduling problems on batch processing machines," International Journal of Production Research, Taylor & Francis Journals, vol. 56(22), pages 7031-7048, November.
    16. 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.
    17. A. Alfieri & A. Druetto & A. Grosso & F. Salassa, 2021. "Column generation for minimizing total completion time in a parallel-batching environment," Journal of Scheduling, Springer, vol. 24(6), pages 569-588, December.
    18. Onur Ozturk, 2020. "A bi-criteria optimization model for medical device sterilization," Annals of Operations Research, Springer, vol. 293(2), pages 809-831, October.
    19. Husseinzadeh Kashan, Ali & Ozturk, Onur, 2022. "Improved MILP formulation equipped with valid inequalities for scheduling a batch processing machine with non-identical job sizes," Omega, Elsevier, vol. 112(C).
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