Best part-machine incidence matrix.

Cell formation (CF) and machine cell layout are two critical issues in the design of a cellular manufacturing system (CMS). The complexity of the problem has an exponential impact on the time required to compute a solution, making it an NP-hard (complex and non-deterministic polynomial-time hard) problem. Therefore, it has been widely solved using effective meta-heuristics. The paper introduces a novel meta-heuristic strategy that utilizes the Genetic Algorithm (GA) and the Technique of Order Preference Similarity to the Ideal Solution (TOPSIS) to identify the most favorable solution for both flexible CF and machine layout within each cell. GA is employed to identify machine cells and part families based on Grouping Efficiency (GE) as a fitness function. In contrast to previous research, which considered grouping efficiency with a weight factor (q = 0.5), this study utilizes various weight factor values (0.1, 0.3, 0.7, 0.5, and 0.9). The proposed solution suggests using the TOPSIS technique to determine the most suitable value for the weighting factor. This factor is critical in enabling CMS to design the necessary flexibility to control the cell size. The proposed approach aims to arrange machines to enhance GE, System Utilization (SU), and System Flexibility (SF) while minimizing the cost of material handling between machines as well as inter- and intracellular movements (TC). The results of the proposed approach presented here show either better or comparable performance to the benchmark instances collected from existing literature.