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Parallel-Machine Scheduling with Step-Deteriorating Jobs to Minimize the Total (Weighted) Completion Time

Author

Listed:
  • Cuixia Miao

    (School of Mathematical Sciences, Qufu Normal University, Qufu 273165, P. R. China)

  • Fanyu Kong

    (School of Mathematical Sciences, Qufu Normal University, Qufu 273165, P. R. China)

  • Juan Zou

    (School of Mathematical Sciences, Qufu Normal University, Qufu 273165, P. R. China)

  • Ran Ma

    (School of Management Engineering, Qingdao University of Technology, Qingdao 266525, P. R. China3University Research Center for Smart City, Construction and Management of Shandong Province, Qingdao 266525, P. R. China)

  • Yujia Huo

    (School of Mathematical Sciences, Qufu Normal University, Qufu 273165, P. R. China)

Abstract

In this paper, we consider the parallel-machine scheduling with step-deteriorating jobs. The actual processing time of each job deteriorates as a step function if its starting time is beyond a given deteriorating date. We focus on the case of the common job deteriorating date. For the minimization problem of total completion time, we first show that the problem is NP-hard in the strong sense. Then we propose one property of any optimal schedule. Furthermore, we prove that two special cases of common normal processing time or common penalty are polynomially solvable. For the minimization problem of total weighted completion time, we analyze the NP-hardness and present a polynomial time optimal algorithm for the case of common normal processing time and common penalty.

Suggested Citation

  • Cuixia Miao & Fanyu Kong & Juan Zou & Ran Ma & Yujia Huo, 2023. "Parallel-Machine Scheduling with Step-Deteriorating Jobs to Minimize the Total (Weighted) Completion Time," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 40(01), pages 1-13, February.
    • Handle: RePEc:wsi:apjorx:v:40:y:2023:i:01:n:s0217595922400115
    DOI: 10.1142/S0217595922400115
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