A BRKGA-DE algorithm for parallel-batching scheduling with deterioration and learning effects on parallel machines under preventive maintenance consideration

  • Min Kong
  • Xinbao Liu
  • Jun PeiEmail author
  • Hao Cheng
  • Panos M. Pardalos


This paper introduces a parallel-batching scheduling problem with deterioration and learning effects on parallel machines, where the actual processing time of a job is subject to the phenomena of deterioration and learning. All jobs are first divided into different parallel batches, and the processing time of the batches is equal to the largest processing time of their belonged jobs. Then, the generated batches are assigned to parallel machines to be processed. Motivated by the characteristics of machine maintenance activities in a semiconductor manufacturing process, we take the machine preventive maintenance into account, i.e., the machine should be maintained after a fixed number of batches have been completed. In order to solve the problem, we analyze several structural properties with respect to the batch formation and sequencing. Based on these properties, a hybrid BRKGA-DE algorithm combining biased random-key genetic algorithm (BRKGA) and Differential Evolution (DE) is proposed to solve the parallel-batching scheduling problem. A series of computational experiments is conducted to demonstrate the effectiveness and efficiency of the proposed algorithm.


Scheduling Deterioration Learning Parallel-batching BRKGA-DE 

Mathematics Subject Classification (2010)



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This work is supported by the National Natural Science Foundation of China (Nos. 71231004, 71871080, 71601065, 71690235, 71501058, 71601060), 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), Anhui Province Natural Science Foundation (No. 1608085QG167), Base of Introducing Talents of Discipline to Universities for Optimization and Decision-making in the Manufacturing Process of Complex Product (111 project), the Project of Key Research Institute of Humanities and Social Science in University of Anhui Province, Open Research Fund Program of Key Laboratory of Process Optimization and Intelligent Decision-making(Hefei University of Technology), Ministry of Education. 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 Nature Switzerland AG 2018

Authors and Affiliations

  • Min Kong
    • 1
    • 2
  • Xinbao Liu
    • 1
    • 2
  • Jun Pei
    • 1
    • 2
    • 3
    Email author
  • Hao Cheng
    • 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.Center for Applied Optimization, Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA

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