Effective scheduling is challenging in Component Maintenance, Repair, and Overhaul (CMRO) operations due to the complexity of dynamically allocating resources across multiple jobs with varying priorities and technical constraints. Current industry practices typically rely on static, manual scheduling, resulting in suboptimal resource allocation and insufficient adaptability to operational disruptions. Most existing studies approach specific job shop problems by incorporating individual features, such as job prioritization or resource constraints, without considering the combined operational complexities of CMRO shops. Therefore, this research presents a scheduling model using the Flexible Job Shop Scheduling Problem (FJSSP), tailored to dynamic CMRO environments. The model uses Mixed Integer Linear Programming (MILP) to simultaneously schedule technicians and machines while accounting for skill requirements, resource constraints, and job prioritization. The approach balances multiple objectives, including tardiness and earliness, to enhance shop performance metrics such as Turnaround Time (TAT) and On Time Delivery (OTD) rates. Outcomes from a case study applied to real-world data from CMRO shops demonstrate significant operational improvements, achieving a reduction in TAT of up to 34% and an improvement in OTD by approximately 23% relative to historical shop performance. Furthermore, the model incorporates schedule robustness measures, minimizing deviations from planned schedules, despite operational uncertainties. Additionally, comparative analysis with a traditional heuristic dispatching rule model confirms the superior performance of the proposed optimization framework. This framework can be broadly applied to improve scheduling efficiency and stability in CMRO shops and similar workshop environments.