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Journal of Industrial and Management Optimization

2026, Volume 22, Issue 9: 4151-4175. doi: 10.3934/jimo.2026146
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Research on the single-machine group scheduling problem with general deteriorating setup times and learning effects

  • School of Economics and Management, Shenyang Aerospace University, Shenyang 110136, P. R. China
  • Published: 06 August 2026

  • 90B35

  • This paper considers a single-machine group scheduling problem with general deteriorating setup times and learning effects characterized by truncated exponential functions. The goal is makespan minimization. We establish that the optimal ordering of jobs inside any group adheres to the shortest processing time (SPT) rule, and further identify a sufficient condition that determines the optimal sequence of groups. We solve the problem using four approaches: a branch-and-bound algorithm, a heuristic, a mixed-integer linear programming (MILP) model, and a mixed-integer nonlinear programming (MINLP) model. The effectiveness and efficiency of the proposed methods are examined via numerical experimentation.

    Citation: Heng Yin, Jia-Ming Gu, Ji-Bo Wang. Research on the single-machine group scheduling problem with general deteriorating setup times and learning effects[J]. Journal of Industrial and Management Optimization, 2026, 22(9): 4151-4175. doi: 10.3934/jimo.2026146

    Related Papers:

  • This paper considers a single-machine group scheduling problem with general deteriorating setup times and learning effects characterized by truncated exponential functions. The goal is makespan minimization. We establish that the optimal ordering of jobs inside any group adheres to the shortest processing time (SPT) rule, and further identify a sufficient condition that determines the optimal sequence of groups. We solve the problem using four approaches: a branch-and-bound algorithm, a heuristic, a mixed-integer linear programming (MILP) model, and a mixed-integer nonlinear programming (MINLP) model. The effectiveness and efficiency of the proposed methods are examined via numerical experimentation.



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