Two-stage three-machine assembly scheduling problem with sum-of-processing-times-based learning effect

  • Yunqing Zou
  • Dujuan WangEmail author
  • Win-Chin Lin
  • Jia-Yang Chen
  • Pay-Wen Yu
  • Wen-Hsiang Wu
  • Yuan-Po Chao
  • Chin-Chia Wu
Methodologies and Application


Researchers claim that the processing of most products can be formulated as a two-stage assembly scheduling model. The literature states that cumulative learning experience is neglected in solving two-stage assembly scheduling problems. The sum-of-processing-times-based learning effect means that the actual processing time of a job becomes shorter when it is scheduled later, which depends on the sum of processing time of the jobs already processed. Motivated by this observation, we investigate a novel two-stage assembly scheduling with three machines and sum-of-processing-times-based learning effect to minimize the makespan criterion, where two machines operate at the first stage and an assembly machine operates at the second stage. To solve this NP-hard problem, a branch-and-bound method incorporating with ten dominance properties and a lower bound procedure is first derived to obtain an optimal solution. Three heuristics based on Johnson’s rule with and without improvement are then applied separately to a genetic algorithm and a cloud theory-based simulated annealing algorithm, which are further modified with an interchange pairwise method for finding near-optimal solutions. Finally, the numerical results obtained using all proposed algorithms are reported and evaluated.


Two-stage assembly scheduling Learning effect Genetic algorithm Makespan 



This article is supported in part by the National Natural Science Foundation of China (Nos. 71501024, 71871148), by China Postdoctoral Science Foundation (Nos. 2018T110631, 2017M612099), by Sichuan Science and Technology Planning Project (No. 2019JDR0161), by the Fundamental Research Funds (Nos. YJ201842, 2018hhs-47), and in part by Ministry of Science and Technology of Taiwan (No. MOST 108-2410-H-035-046).

Compliance with ethical standards

Conflict of interest

The authors certify that there is no conflict of interest with any individual/organization for the paper.

Human and animals rights

The paper does not involve human participants and animals. All authors have checked the paper and have agreed to the submission.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Yunqing Zou
    • 1
  • Dujuan Wang
    • 1
    • 2
    Email author
  • Win-Chin Lin
    • 3
  • Jia-Yang Chen
    • 3
  • Pay-Wen Yu
    • 4
  • Wen-Hsiang Wu
    • 5
  • Yuan-Po Chao
    • 6
  • Chin-Chia Wu
    • 3
  1. 1.School of Maritime Economics and ManagementDalian Maritime UniversityDalianChina
  2. 2.Business SchoolSichuan UniversityChengduChina
  3. 3.Department of StatisticsFeng Chia UniversityTaichungTaiwan
  4. 4.Department of Physical EducationFu Jen Catholic UniversityNew Taipei CityTaiwan
  5. 5.Department of Healthcare ManagementYuanpei University of Medical TechnologyHsinchuTaiwan
  6. 6.Department of Business ManagementCheng Shiu UniversityKaohsiungTaiwan

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