Modeling and solving for bi-objective cutting parallel machine scheduling problem

  • Ronghua Meng
  • Yunqing RaoEmail author
  • Qiang Luo
S.I.: Project Management and Scheduling 2018


This paper addresses a bi-objective cutting parallel machine scheduling problem aiming to minimize the total makespan and total tardiness. This problem is inspired from a structural metal-cutting plant that combines identical and unrelated parallel machine scheduling problems. To formulate this complicated problem, a new mixed-integer programming (MIP) model is presented in consideration of total makespan and total tardiness. The machine-job-dependent processing times are considered along with the setup times, pickup times, different delivery times, and machine eligibility constraints. Owing to the complex characteristics of the problem, an appropriate non-dominated sorting Genetic Algorithm III (NSGAIII) with an embedded variable neighborhood structure strategy (VNSGAIII) is developed. A number of randomly generated datasets are used to test the performance of VNSGAIII in comparison with NSGAII, and NSGAIII on solving the engineering problem addressed herein. The experimental results demonstrate that the suggested VNSGAIII statistically outperforms the compared algorithms, especially in the distribution of Pareto solutions. The ε-constrained method is implemented in the direct MIP model by CPLEX for comparison with the proposed evolutionary algorithms. The proposed algorithm performs efficiently when obtaining the Pareto solutions.


Parallel machine scheduling problem NSGA III Bi-objective problem Makespan Tardiness 



This work is supported by the National Natural Science Foundation of China (Grant No. 51675206); the open fund project of the Hubei Key Laboratory of Hydroelectric Machinery Design & Maintenance (Grant No. 2017KJX10) and the new intelligent manufacturing models for rail transit shield machine funded by Ministry of Industry and Information Technology of China. All supports are gratefully acknowledged.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.The State Key Laboratory of Digital Manufacturing Equipment and TechnologyHuazhong University of Science and TechnologyWuhanPeople’s Republic of China
  2. 2.Hubei Key Laboratory of Hydroelectric Machinery Design and MaintenanceChina Three Gorges UniversityYichangChina

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