توسعه مدل ریاضی زمان بندی کارگاهی منعطف با در نظر گرفتن محدودیت‌های دوگانه منابع انسانی و ماشین آلات، تاثیر یادگیری و وقفه‌های تولید

احمد صفری; محمدرضا  فیلی زاده; اسماعیل  مهدی زاده; مجید  وزيري سرشک; رویا  محمد علی اهری

Authors

Ahmad Safari Department of Industrial Engineering, Na.C., Islamic Azad University, Najafabad, Iran Author https://orcid.org/0009-0001-3729-1994
Mohammad Reza Feylizadeh Department of Industrial Engineering, Shi.C., Islamic Azad University, Shiraz, Iran Corresponding author https://orcid.org/0000-0002-1382-7328
Esmaeil Mehdizadeh Department of Industrial Engineering, Faculty of Industrial Engineering and Mechanical Engineering, Qa.C., Islamic Azad University, Qazvin, Iran Author https://orcid.org/0000-0002-1149-905X
Majid Vaziri Sarshak Department of Industrial Engineering, Na.C., Islamic Azad University, Najafabad, Iran Author https://orcid.org/0000-0003-4178-4959
Roya Mohammad Ali Ahari Department of Industrial Engineering, Na.C., Islamic Azad University, Najafabad, Iran Author https://orcid.org/0000-0002-8952-8682

Keywords:

Flexible Job Shop Scheduling, Dual Resource Constraints, Learning Effect, Production Interruptions, Metaheuristic Algorithm, Manufacturing Resilience

Abstract

This study aims to develop a comprehensive mathematical model for the Flexible Job Shop Scheduling Problem (FJSP) by simultaneously considering dual resource constraints, learning effects, and production interruptions. In the proposed model, each operation requires not only assignment to an eligible machine but also allocation to a qualified human operator. Furthermore, operation processing times are modeled as a function of the operator’s learning level to capture workforce experience and productivity improvements over time. To enhance the practical applicability of the model, production interruptions are explicitly incorporated as disruptive events affecting the scheduling process. A mixed-integer mathematical programming model is first formulated to represent the problem. Given the NP-hard nature of the FJSP, a metaheuristic solution approach is subsequently employed to efficiently obtain high-quality solutions for problem instances of varying sizes. To evaluate the effectiveness of the proposed model and solution methodology, a comprehensive set of small-, medium-, and large-scale benchmark instances is generated and solved. The computational results demonstrate that the proposed approach consistently produces feasible and high-quality solutions across all problem scales and significantly improves the objective function value compared with the baseline approach. In addition, sensitivity analysis reveals that increasing the frequency and severity of production interruptions negatively affects system performance, whereas workforce learning can partially mitigate these adverse effects by reducing processing times and improving operational efficiency. These findings highlight the critical role of operator skill development and experience in enhancing not only production efficiency but also the resilience of manufacturing systems against operational disruptions. Overall, by integrating dual resource constraints, operator learning effects, and production interruptions into a unified optimization framework, this research provides a more realistic and practical formulation of the Flexible Job Shop Scheduling Problem. The proposed model offers valuable decision support for scheduling and resource allocation in complex and dynamic manufacturing environments.

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