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Single-machine scheduling with nonlinear deterioration

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Abstract

In this paper, we consider the single-machine scheduling problems with nonlinear deterioration. By the nonlinear deterioration effect, we mean that the processing times of jobs are nonlinear functions of their starting times. We show that even with the introduction of nonlinear deterioration to job processing times, single machine makespan minimization problem remains polynomially solvable. We also show that an optimal schedule of the total completion time minimization problem is V-shaped with respect to job normal processing times. A heuristic algorithm utilizing the V-shaped property is proposed, and computational experiments show that it performs effectively and efficiently in obtaining near-optimal solutions.

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Authors and Affiliations

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

    Ji-Bo Wang

  2. School of Management Science and Engineering, Dalian University of Technology, Dalian, 116024, China

    Ming-Zheng Wang

Authors
  1. Ji-Bo Wang
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  2. Ming-Zheng Wang
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Correspondence to Ming-Zheng Wang.

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Wang, JB., Wang, MZ. Single-machine scheduling with nonlinear deterioration. Optim Lett 6, 87–98 (2012). https://doi.org/10.1007/s11590-010-0253-3

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  • DOI: https://doi.org/10.1007/s11590-010-0253-3

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