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Multi-objective inverse scheduling optimization of single-machine shop system with uncertain due-dates and processing times

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Abstract

Generally, ideal manufacturing system environments are assumed before determining effective scheduling. However, the original schedule is no longer optimal or even to be infeasible due to many uncertain events. This paper investigates a multi-objective inverse scheduling problem in single-machine shop system with due-dates and uncertain processing parameters. Moreover, in order to more close the addressed problem into the situations encountered in real world, the processing parameters are considered to be uncertain stochastic parameters. First, a comprehensive mathematical model for multi-objective single-machine inverse scheduling problem (MSMISP) is addressed. Second, an effective hybrid multi-objective evolutionary algorithm (HMNL) is proposed to handle uncertain processing parameters (uncertainties) and multiple objectives at the same time. In HMNL, using an effective decimal system encoding scheme and genetic operators, the non-dominated sorting based on NSGA-II is adapted for the MSMISP. In addition, hybrid HMNL are proposed by incorporating an adaptive local search scheme into the well-known NSGA-II, where applies a separate local search process, total six strategies, to improve quality of solutions. Furthermore, an on-demand layered strategy is embedded into the elitism strategy to keep the population diversity. Afterwards, an external archive set is dynamically updated, where a non-dominated solution is selected to participate in the creation of the new population. Finally, 36 public problem instances with different scales and statistical performance comparisons are provided for the HMNL algorithm. This paper is the first to propose a mathematical model and develop a hybrid MOEA algorithm to solve MSMISP in inverse scheduling domain.

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Abbreviations

n :

Number of jobs

\(J_{j}\) :

Job j(j= 1, 2,..., n)

\(\sigma \) :

A processing sequence of jobs

\(P_{j}\) :

Normal processing time of job j

\(\bar{p}_j\) :

Adjusted processing time of job j

\(d_{j}\) :

Due date of job j

\(\bar{d}_j\) :

Adjusted due date of job j

\(C_{j}\) :

Completion time of job j

\(\bar{c}_j\) :

Adjusted completion time of job j

\(\bar{T}_j\) :

Tardiness of job j, \(T_{j}\) = max(0, \(\bar{c}_j -d_{j})\)

\(\bar{E}_j\) :

Earliness of job j, \(E_{j}\) = max(0, \(d_{j}-\bar{c}_j )\)

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Acknowledgements

The authors would like to thank the editor and anonymous referees whose comments helped a lot in improving this paper. This research work was supported by the National Science Foundation of China (NSFC) under Grant No. 51605267; the Natural Science Foundation of Shandong Province, China, under Grant No. ZR2016EEQ07; and Colleges and universities of Shandong province science and technology plan projects under Grant No. J16LB04.

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Authors and Affiliations

  1. School of Mechanical Engineering, Shandong University of Technology, Zibo, 255000, People’s Republic of China

    Jianhui Mou

  2. The State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, 430074, People’s Republic of China

    Liang Gao, Xinyu Li & Quanke Pan

  3. Huali Science and Technology College, Guangzhou, 510000, People’s Republic of China

    Jiancai Mu

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Correspondence to Jianhui Mou.

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Mou, J., Gao, L., Li, X. et al. Multi-objective inverse scheduling optimization of single-machine shop system with uncertain due-dates and processing times. Cluster Comput 20, 371–390 (2017). https://doi.org/10.1007/s10586-016-0717-z

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