Modeling and Solving the Flow‐Shop Scheduling Problem with Sequence‐Dependent Setup Times by Firefly Algorithm (Case Study: Automotive Industry)

Abstract

Progress in today’s modern industry requires a lot of knowledge, one of which is scheduling. Flow-shop scheduling is one of the most widely used optimization problems. In this research, considering the importance of simultaneously order in different stages of production in the automotive industry, and also in order to make the problem more practical, we have investigated the problem of scheduling the flow-shop, taking into account the lead time and the costs of each order. Due to the fact that in most research studies, the lead time and costs of an order have been ignored because they made it difficult to find the initial solution to the problem. In this research, using the firefly meta-heuristic method, a suitable solution is provided to overcome this problem. Therefore, considered objective function is to minimize the total completion time. Absolute relative error (ARE) has been used to validate the model in a deterministic and meta-heuristic mode. According to the ARE result, the difference in the results between the two algorithms is negligible. Then, the sequence results are determined according to the desired algorithm for 5 tasks considered for automobile parts. The results show that the completion time of job 1 is 1397.85; job 2 is 771.44; job 3 is 608.65; job 4 is 1163.87; and job 5 is 479.45.