Flexible Job Shop Scheduling Problem Considering Upper Bounds for the Amount of Interruptions Between Operations and Machines Maintenance Activities

In modern production environments where perishable products are manufactured in a job shop system, machine reliability is of utmost importance, and delays during job processing are not acceptable. Therefore, it becomes crucial to consider machines maintenance activities and set upper bounds for interruptions between job operations. This paper tackels the Flexible Job Shop Scheduling Problem taking into account these factors. The study is conducted in two phases. Initially, a novel Mixed-Integer Linear Programming (MILP) model is elaborated for the problem and juxtaposed with the Benders decomposition method to assess computational efficiency. Nevertheless, owing to the elevated complexity of the problem, attaining an optimal solution for instances of realistic size poses an exceptionally challenging task using exact methods. Thus, in the second stage, a Discrete Grey Wolf Optimizer (D-GWO) as an alternative approach to solve the problem is proposed. The performance of the extended algorithms is evaluated through numerical tests. The findings indicate that for small instances, the Benders decomposition method outperforms other approaches. Nevertheless, as the instances grow in size, the efficiency of exact methods diminishes, and the Discrete Grey Wolf Optimizer (D-GWO) performs better under such conditions. Overall, this study highlights the importance of considering machines maintenance activities and interruptions in scheduling of job shop for the production of perishable products. The proposed model and Benders decomposition method in small instances, and the metaheuristic algorithm in large instances provide viable solutions.