A bi-level bi-objective mathematical model for cellular manufacturing system applying evolutionary algorithms

The present study aimed to design a bi-objective bi-level mathematical model for multi-dimensional cellular manufacturing system. Minimizing the total number of voids and balancing the assigned workloads to cells are regarded as two objectives of the upper level of the model. However, the lower level attempts to maximize the workers' interest to work together in a special cell. To this aim, two nested bi-level metaheuristics including particle swarm optimization (NBL-PSO) and a population-based simulated annealing algorithm (NBL-PBSA) were implemented to solve the model. In addition, the goal programming approach was utilized in the upper level procedure of these algorithms. Further, nine numerical examples were applied to verify the suggested framework and the TOPSIS method was used to find the better algorithm. Furthermore, the best weights for upper level objectives were tuned by using a weight sensitivity analysis. Based on computational results, all three objectives were different from their ideal goals when decisions about inter and intra-cell layouts, and cell formation to balance the assigned workloads by considering voids and workers' interest were simultaneously madeby considering a wide assumption-made problem closer to the real world. Finally, NBL-PBSA could perform better than NBL-PSO, which confirmed the efficiency of the proposed framework.