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Single machine scheduling with general time-dependent deterioration, position-dependent learning and past-sequence-dependent setup times

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Abstract

The paper deals with single machine scheduling problems with setup time considerations where the actual processing time of a job is not only a non-decreasing function of the total normal processing times of the jobs already processed, but also a non-increasing function of the job’s position in the sequence. The setup times are proportional to the length of the already processed jobs, i.e., the setup times are past-sequence-dependent (p-s-d). We consider the following objective functions: the makespan, the total completion time, the sum of the δth (δ ≥ 0) power of job completion times, the total weighted completion time and the maximum lateness. We show that the makespan minimization problem, the total completion time minimization problem and the sum of the δ th (δ ≥ 0) power of job completion times minimization problem can be solved by the smallest (normal) processing time first (SPT) rule, respectively. We also show that the total weighted completion time minimization problem and the maximum lateness minimization problem can be solved in polynomial time under certain conditions.

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Authors and Affiliations

  1. School of Science, Shenyang Aerospace University, Shenyang, 110136, Liaoning, China

    Xue Huang

  2. School of Management, Xi’an Jiaotong University, The State Key Lab for Manufacturing Systems Engineering, The Key Lab of the Ministry of Education for Process Control & Efficiency Engineering, Xi’an, 710049, China

    Gang Li

  3. Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    Yunzhang Huo & Ping Ji

Authors
  1. Xue Huang
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  2. Gang Li
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  3. Yunzhang Huo
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  4. Ping Ji
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Correspondence to Xue Huang.

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Huang, X., Li, G., Huo, Y. et al. Single machine scheduling with general time-dependent deterioration, position-dependent learning and past-sequence-dependent setup times. Optim Lett 7, 1793–1804 (2013). https://doi.org/10.1007/s11590-012-0522-4

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  • DOI: https://doi.org/10.1007/s11590-012-0522-4

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