Optimizing the Number of Cells and Makespan in Cellular Manufacturing System

In the competitive shoe manufacturing industry, efficient production scheduling often struggles to balance minimizing makespan (MS) and reducing the number of cells, leading to increased complexity. This study introduces a biobjective optimization model to minimize the MS and the number of cells in a cellular manufacturing (CM) system. The model includes three phases: (1) a capacity phase calculates the required number of cells to meet the production demand within a suitable production rate; (2) a scheduling phase calculates the start and finish times for each product within a machine; (3) an optimization phase uses genetic algorithm (GA) for generating a set of optimal solutions considering the workforce distribution and product sequencing. The performance of the developed model was evaluated using a case study discussed in the literature to demonstrate its capabilities and highlight its superiority over similar models. These results showed a significant reduction of 0.4% in MS while maintaining the same number of cells compared to other models. A sensitivity analysis is conducted by varying the crossover and mutation probabilities. The findings indicate that the model achieves the most stable and consistent performance for paired crossover–mutation settings with crossover probabilities between 70% and 90% (corresponding to mutation probabilities between 30% and 10%), resulting in the lowest average MS and the most balanced cell utilization. The capabilities of the developed model provide production managers with reliable insights for identifying the production requirements of the shoe manufacturing company. The algorithm was also benchmarked on 12 published instances using 30 independent runs per instance to assess solution quality and stability.