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Scheduling High Multiplicity Jobs on Parallel Multi-Purpose Machines with Setup Times and Machine Available Times

Author

Listed:
  • Caixia Jing

    (School of Economics and Management, Tiangong University, Tianjin 300387, P. R. China)

  • Wanzhen Huang

    (Department of Mathematical Sciences, Lakehead University, Ontario P7B 5E1, Canada)

  • Lei Zhang

    (School of Economics and Management, Tiangong University, Tianjin 300387, P. R. China)

  • Heng Zhang

    (College of Computer and Control Engineering, Nankai University, Tianjin 300071, P. R. China)

Abstract

In this paper, we consider the scheduling of high multiplicity jobs on parallel multi-purpose machines with setup times and machine available times, with the objective of minimizing makespan. High multiplicity means that jobs are partitioned into several groups and in each group all jobs are identical. Whenever there is a switch from processing a job of one group to a job of another group, a setup time is needed. Multi-purpose machine implies that each job can only be processed by a specific subset of all the machines, called processing set. A mixed integer programming is formulated for this NP-hard problem. A heuristic is proposed to solve the problem. Lower bounds are developed to evaluate the heuristic algorithm. Extensive numerical computations are performed and the results show that the heuristic generates solutions with makespan within 2% above the lower bounds in average, and outperforms CPLEX 12.6 for large scale and complex problems.

Suggested Citation

  • Caixia Jing & Wanzhen Huang & Lei Zhang & Heng Zhang, 2022. "Scheduling High Multiplicity Jobs on Parallel Multi-Purpose Machines with Setup Times and Machine Available Times," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 39(06), pages 1-25, December.
    • Handle: RePEc:wsi:apjorx:v:39:y:2022:i:06:n:s0217595922500129
    DOI: 10.1142/S0217595922500129
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