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Scheduling jobs with truncated exponential learning functions

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Abstract

In this paper we consider the single machine scheduling problem with truncated exponential learning functions. By the truncated exponential learning functions, we mean that the actual job processing time is a function which depends not only on the total normal processing times of the jobs already processed but also on a control parameter. The use of the truncated function is to model the phenomenon that the learning of a human activity is limited. We show that even with the introduction of the proposed model to job processing times, several single machine problems remain polynomially solvable. For the following three objective functions, the total weighted completion time, the discounted total weighted completion time, the maximum lateness, we present heuristic algorithms according to the corresponding problems without truncated exponential learning functions. We also analyse the worst-case bound of our heuristic algorithms.

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Authors and Affiliations

  1. School of Science, Shenyang Aerospace University, Shenyang, 110136, People’s Republic of China

    Ji-Bo Wang & Xiao-Yuan Wang

  2. School of Economics and Management, Xi’an University of Technology, Xi’an, 710054, People’s Republic of China

    Lin-Hui Sun

  3. School of Management, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Xiao-Yuan Wang & Lin-Yan Sun

  4. The State Key Laboratory for Manufacturing Systems Engineering, Xi’an, 710053, People’s Republic of China

    Ji-Bo Wang, Lin-Hui Sun & Lin-Yan Sun

  5. The Key Laboratory of the Ministry of Education for Process Control and Efficiency Engineering, Xi’an, 710049, People’s Republic of China

    Lin-Hui Sun & Lin-Yan Sun

  6. Knowledge Management & Innovation Research Centre of Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Ji-Bo Wang, Lin-Hui Sun & Lin-Yan Sun

Authors
  1. Ji-Bo Wang
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  2. Xiao-Yuan Wang
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  3. Lin-Hui Sun
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  4. Lin-Yan Sun
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Correspondence to Ji-Bo Wang.

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Wang, JB., Wang, XY., Sun, LH. et al. Scheduling jobs with truncated exponential learning functions. Optim Lett 7, 1857–1873 (2013). https://doi.org/10.1007/s11590-011-0433-9

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  • DOI: https://doi.org/10.1007/s11590-011-0433-9

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