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<p>This study investigates a two-stage, three-machine assembly flowshop scheduling problem with job- and machine-specific step-learning effects, where the objective is to minimize total completion time. In the considered environment, each operation has a learning date, and its processing time changes from a normal value to an improved value when the operation starts after this threshold. This structure creates a sequencing trade-off because assigning a job earlier may reduce its immediate completion time, whereas assigning another job first may allow the former job to benefit from the improved processing time. To solve the problem, this study develops both exact and approximate methods. A Branch-and-Bound algorithm with dominance properties and a lower bound is proposed to obtain optimal solutions for small-sized instances. For larger instances, a State- and Learning-Adaptive heuristic with Insertion-Based Local Search is developed to account for current machine states and potential learning-driven processing-time reductions. Cloud Simulated Annealing and a Genetic Algorithm are implemented as metaheuristic benchmarks. Computational experiments show that the proposed exact method solves instances with up to 16 jobs, while the proposed heuristic achieves average error below 6% for small-sized instances and provides a practical balance between solution quality and computational time for larger instances.</p>

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Learning-adaptive scheduling for three-machine assembly flowshops with step-learning effects

  • 期刊论文

  • 发表日期：

    2026年7月8日

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  • Yu-Hsiang Chung

摘要

This study investigates a two-stage, three-machine assembly flowshop scheduling problem with job- and machine-specific step-learning effects, where the objective is to minimize total completion time. In the considered environment, each operation has a learning date, and its processing time changes from a normal value to an improved value when the operation starts after this threshold. This structure creates a sequencing trade-off because assigning a job earlier may reduce its immediate completion time, whereas assigning another job first may allow the former job to benefit from the improved processing time. To solve the problem, this study develops both exact and approximate methods. A Branch-and-Bound algorithm with dominance properties and a lower bound is proposed to obtain optimal solutions for small-sized instances. For larger instances, a State- and Learning-Adaptive heuristic with Insertion-Based Local Search is developed to account for current machine states and potential learning-driven processing-time reductions. Cloud Simulated Annealing and a Genetic Algorithm are implemented as metaheuristic benchmarks. Computational experiments show that the proposed exact method solves instances with up to 16 jobs, while the proposed heuristic achieves average error below 6% for small-sized instances and provides a practical balance between solution quality and computational time for larger instances.