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A Unified Approach to Single-Machine Scheduling with Position-Based Processing Times, Machine Availability, and Job Rejection

Author

Listed:
  • Min Ji

    (School of Management and E-Business, Contemporary Business and Trade Research Center, Zhejiang Gongshang University, Hangzhou, 310018, P. R. China)

  • Kaili Qi

    (School of Management and E-Business, Contemporary Business and Trade Research Center, Zhejiang Gongshang University, Hangzhou, 310018, P. R. China)

  • T. C. E. Cheng

    (Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Kowloon, Hong Kong)

  • Yiwei Jiang

    (School of Management and E-Business, Contemporary Business and Trade Research Center, Zhejiang Gongshang University, Hangzhou, 310018, P. R. China)

Abstract

We present a unified approach to single-machine scheduling with position-based processing times, an availability constraint, and job rejection. The approach uses two general position-based processing time functions to model both the learning and aging effects in scheduling. In addition, taking machine availability and job rejection into consideration, the models are more realistic, which seek to minimize the sum of the makespan of the accepted jobs and the total penalty of the rejected jobs. We present fully polynomial-time approximation schemes to address the two NP-hard problems.

Suggested Citation

  • Min Ji & Kaili Qi & T. C. E. Cheng & Yiwei Jiang, 2023. "A Unified Approach to Single-Machine Scheduling with Position-Based Processing Times, Machine Availability, and Job Rejection," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 40(06), pages 1-17, December.
    • Handle: RePEc:wsi:apjorx:v:40:y:2023:i:06:n:s0217595922500403
    DOI: 10.1142/S0217595922500403
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