Parallel-machine group scheduling with inclusive processing set restrictions, outsourcing option and serial-batching under the effect of step-deterioration

  • Baoyu Liao
  • Qingru Song
  • Jun PeiEmail author
  • Shanlin Yang
  • Panos M. Pardalos


This paper investigates a parallel-machine group scheduling problem where non-identical jobs with arbitrary sizes and inclusive processing set restrictions can be either processed on in-house parallel machines in the form of serial batch or outsourced with cost. The objective of our study is aimed at minimizing the weighted sum of the in-house makespan and the total outsourcing cost for a platform manufacturing enterprise. Some structural properties are identified for the optimal solution in some special cases of the studied problem, which contribute to the optimal solution for the studied problem. Further, based on these properties, a novel hybrid algorithm VNS–NKEA is proposed to solve the studied problem, which integrates neighborhood knowledge-based evolutionary algorithm (NKEA) and variable neighborhood search (VNS). To demonstrate the better performance including solution quality and the convergence speed of the proposed algorithm, computational experiments are conducted to evaluate its performance by comparing with other proposed algorithms. The experiment results show that the hybrid algorithm performs quite better than other compared algorithms for each instance, which reflect that the hybrid algorithm can solve the studied problem effectively.


Serial-batching Group scheduling Step-deterioration Parallel machines Outsourcing Inclusive processing set restrictions Platform enterprise 



This work is supported by the National Natural Science Foundation of China (Nos. 71871080, 71601065, 71501058, 71690235, 71231004), and Innovative Research Groups of the National Natural Science Foundation of China (71521001), the Humanities and Social Sciences Foundation of the Chinese Ministry of Education (No. 15YJC630097), and Base of Introducing Talents of Discipline to Universities for Optimization and Decision-making in the Manufacturing Process of Complex Product (111 Project). Panos M. Pardalos is partially supported by the Project of “Distinguished International Professor by the Chinese Ministry of Education” (MS2014HFGY026).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Baoyu Liao
    • 1
    • 2
  • Qingru Song
    • 1
  • Jun Pei
    • 1
    • 2
    • 3
    Email author
  • Shanlin Yang
    • 1
    • 2
  • Panos M. Pardalos
    • 3
  1. 1.School of ManagementHefei University of TechnologyHefeiChina
  2. 2.Key Laboratory of Process Optimization and Intelligent Decision-Making of Ministry of EducationHefeiChina
  3. 3.Department of Industrial and Systems Engineering, Center for Applied OptimizationUniversity of FloridaGainesvilleUSA

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