Semi-permutation-based genetic algorithm for order acceptance and scheduling in two-stage assembly problem

  • Mohammad YavariEmail author
  • Mozhgan Marvi
  • Amir Hosein Akbari
Original Article


The joint decision-making of order acceptance and scheduling has recently gained increasing attention. Besides, the two-stage assembly scheduling problem has various real-life applications. The current paper considers an integrated model for order acceptance and scheduling decisions in two-stage assembly problem. The objective is maximizing profit which is the sum of revenues minus total weighted tardiness of the accepted orders. A mixed-integer linear programming model is developed based on time-index variables. Also, a new concept of semi-permutation scheduling is introduced assuming that positions of each job on all of the machines have no significant difference in the optimal solution. This problem is NP-hard, and therefore, a genetic algorithm (GA)-based heuristic is proposed to apply semi-permutation concept, named semi-permutation GA (SPGA), to solve the problem efficiently. The solutions of SPGA are compared with those of CPLEX and non-semi permutation GA (N-SPGA). Computational experiments are conducted in a diverse range of problem instances indicating that the SPGA performs much better than CPLEX regarding the average percentage of improvement, ranging from 1.4 to 168.84%, and run time. The results revealed that an increasing number of machines and orders could lead to a dramatic decrease in the performance of CPLEX and N-SPGA than SPGA. Also, the effect of semi-permutation scheduling is investigated. According to the result, semi-permutation scheduling had a strong effect on the performance of the algorithm. As a result, the SPGA algorithm outperformed the non-semi permutation version of GA completely. Moreover, SPGA could represent the better performance of 36.27% in average in comparison with N-SPGA.


Two-stage assembly Order acceptance and scheduling Mixed-integer linear program Genetic algorithm 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  • Mohammad Yavari
    • 1
    Email author
  • Mozhgan Marvi
    • 1
  • Amir Hosein Akbari
    • 2
  1. 1.Department of Industrial Engineering, Faculty of Technology and EngineeringUniversity of QomQomIran
  2. 2.Department of Industrial EngineeringUniversity of TehranTehranIran

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