A stochastic model for the cell formation problem considering machine reliability

This paper presents a new mathematical model to solve cell formation problem in cellular manufacturing systems, where inter-arrival time, processing time, and machine breakdown time are probabilistic. The objective function maximizes the number of operations of each part with more arrival rate within one cell. Because a queue behind each machine; queuing theory is used to formulate the model. To solve the model, two metaheurstic algorithms such as modified particle swarm optimization and genetic algorithm are proposed. For the generation of initial solutions in these algorithms, a new heuristic method is developed, which always creates feasible solutions. Both metaheurstic algorithms are compared against global solutions obtained from Lingo software's branch and bound (B&B). Also, a statistical method will be used for comparison of solutions of two metaheurstic algorithms. The results of numerical examples indicate that considering the machine breakdown has significant effect on block structures of machine-part matrixes.