Minimizing Makespan in Ordered Flow Shop Scheduling Using a Robust Genetic Algorithm

In this study, the ordered flow shop scheduling problem, which is in the class of NP-hard optimization problems, is considered. This problem is used especially to increase the efficiency and prevent delays in the production process. The problem was first identified in the literature during the 1970s. The main objective of this study is to develop an efficient and fast method to overcome the complexity of this problem. For this purpose, the ordered flow shop scheduling problem is explained in detail and a robust meta-heuristic method is proposed. First of all, a genetic algorithm is developed by considering Smith’s convexity criterion. While performing operations such as crossover and mutation in the genetic algorithm, the pyramid structure is integrated to ensure that the solution has certain symmetry. The developed method is compared with other methods, such as the Nawaz–Enscore–Ham (NEH), pair insert, and iterated local search (ILS) methods. In order to increase the reliability of the results, the Pyramid Structure Adapted Tabu Search (PSA-TS) algorithm is also developed. The results are validated by statistical analysis using the Wilcoxon signed-rank test and Friedman test. The proposed genetic algorithm outperforms the methods with which it is compared. To the best of the authors’ knowledge, there is no other method in the literature that preserves the pyramid structure in the ordered flow shop scheduling problem. Therefore, this study is expected to make a significant contribution to the literature in this respect.