gray wolf algorithm

This study aims to develop a mathematical model for flexible job shop scheduling. The main focus is on optimizing three

the makespan, the maximum machine workload, and the total workload. The ultimate goal is to enhance productivity and flexibility in manufacturing systems.

Two metaheuristic algorithms, NSGA-II and MOGWO, were used to solve the model. The model was first validated on a small scale, and then sensitivity analysis was conducted on larger instances. The performance of the algorithms was compared based on accuracy and solution quality metrics.

Results indicated that MOGWO performs better in medium-sized problems, while in large-scale cases, the difference between the two algorithms is not significant. The highest sensitivity among the objectives was observed with respect to production and maintenance costs. Additionally, a resource allocation pattern and optimal sequence of operations were derived.

 The originality of this research lies in developing and applying a multi-objective mathematical model for flexible job shop scheduling, considering real-world constraints such as costs and resource limitations. The simultaneous use and detailed comparison of NSGA-II and MOGWO across different problem sizes is another contribution. Furthermore, the proposed operational pattern improves the applicability of the results in industrial environments.

In this research, the open shop scheduling problem has been discussed. In this environment, scheduling for jobs and planning for assembly operations are usually considered independently. However, it may not lead to the best results for the entire production system. On the other hand, the problem of assembly planning has many applications in industries and has recently attracted the attention of researchers. Since in the models that were used before, the assembly operation is not integrated in the open shop scheduling, in this research, inspired by the real production units and to bring the model closer to the real world, the assembly operation is included, which is a step after the completion of the production process. To solve this problem, after modeling it, the Lagrangian relaxation method is used to solve problems in medium dimensions and the gray wolf algorithm is used in large dimensions. Next, to check the quality of the results obtained from the gray wolf algorithm, the Lagrangian relaxation method and GAMS outputs in small-size instances and simulated annealing algorithm in large-size instances have been compared. The obtained results show that the solutions obtained from the proposed algorithm are of good quality.