The Effect of Worker Learning on Scheduling Jobs in a Hybrid Flow Shop: A Bi-Objective Approach

  • Farzad PargarEmail author
  • Mostafa Zandieh
  • Osmo Kauppila
  • Jaakko Kujala


This paper studies learning effect as a resource utilization technique that can model improvement in worker’s ability as a result of repeating similar tasks. By considering learning of workers while performing setup times, a schedule can be determined to place jobs that share similar tools and fixtures next to each other. The purpose of this paper is to schedule a set of jobs in a hybrid flow shop (HFS) environment with learning effect while minimizing two objectives that are in conflict: namely maximum completion time (makespan) and total tardiness. Minimizing makespan is desirable from an internal efficiency viewpoint, but may result in individual jobs being scheduled past their due date, causing customer dissatisfaction and penalty costs. A bi-objective mixed integer programming model is developed, and the complexity of the developed bi-objective model is compared against the bi-criteria one through numerical examples. The effect of worker learning on the structure of assigned jobs to machines and their sequences is analyzed. Two solution methods based on the hybrid water flow like algorithm and non-dominated sorting and ranking concepts are proposed to solve the problem. The quality of the approximated sets of Pareto solutions is evaluated using several performance criteria. The results show that the proposed algorithms with learning effect perform well in reducing setup times and eliminate the need for setups itself through proper scheduling.


Bi-objective scheduling hybrid flow shop learning effect meta-heuristic 


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The authors thank the editor and reviewers fortheir comments, which helped in improving the quality of the paper.


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Copyright information

© Systems Engineering Society of China and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Farzad Pargar
    • 1
    Email author
  • Mostafa Zandieh
    • 2
  • Osmo Kauppila
    • 1
  • Jaakko Kujala
    • 1
  1. 1.Industrial Engineering and Management, Faculty of TechnologyUniversity of OuluOuluFinland
  2. 2.Department of Industrial Management, Management and Accounting FacultyShahid Beheshti University, G.C.TehranIran

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