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

Min Ji (), Kaili Qi (), T. C. E. Cheng () and Yiwei Jiang
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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

Asia-Pacific Journal of Operational Research (APJOR), 2023, vol. 40, issue 06, 1-17

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.

Keywords: Single machine; position-based processing times; machine availability; job rejection; FPTAS (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0217595922500403

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