Industrial processes in the food and chemical sectors often rely on equipment operating continuously, in which preventive maintenance is essential to ensure safety and avoid costly unplanned shutdowns. Optimization methods play a critical role in supporting maintenance decisions by enabling the design of scheduled maintenance downtime while preserving the desired service levels. This study addresses a real case in a food manufacturing facility that transforms agricultural raw materials into several manufactured products. The facility operates continuously throughout the year, with dozens of machines requiring periodic maintenance ranging from brief procedures to complex, multi-day operations. The key challenge lies in planning the maintenance operations efficiently, minimizing disruptions to production capacity. To tackle this problem, a mixed-integer programming (MIP) model was developed to generate optimized maintenance plans. The model was solved using Gurobi, achieving results in minutes for smaller problem instances and longer for large ones. The proposed approach delivers feasible and practical maintenance plans that align with the company's operational needs. Preliminary results demonstrate the potential of the model to support preventive maintenance planning in continuous-process industries. Future work will explore the application of MIP-based heuristics to handle larger instances more efficiently and improve computational scalability.