Formation of Manufacturing Cell Using Theory and Considering Reliability

In this paper, a stochastic cell formation problem is studied considering the queuing theory and the reliability concept. A novel probabilistic mathematical model is presented considering interarrival times, processing times, and machines breakdown. Since the cell formation problem is NP-Hard, two algorithms are developed based on genetic and modified particle swarm optimization (MPSO) algorithms. Since the structure of the problem contains multiple irregularities, a new heuristic method is developed, which produces effective feasible solutions on demand. A deterministic branch and bound (B B) algorithm is used to evaluate the results of modified particle swarm optimization algorithm and the genetic algorithm. The results indicate that proposed algorithms have better performance than the B B algorithm of Lingo software according to the mixed effect of solution quality and computational times. The solution of two metaheurstic algorithms is compared by the t-test method. Ultimately, the results of numerical examples indicate that considering reliability has significant effect on the block structures of machine-part.