Stochastic Cell Formation Problem within Queuing Theory and Considering Reliability

In this study, the stochastic cell formation problem with developing model within queuing theory with stochastic demand, processing time and reliability has been presented. Machine as server and part as customer are assumed where servers should service to customers. Since, the cell formation problem is NP-Hard, therefore, deterministic methods need a long time to solve this model. In this study, genetic algorithm and modified particle swarm optimization algorithm are presented to solve problems. Because the metaheurstic algorithms quality depends strongly on selected operators and parameters, design of experiment is done for set parameters. The deterministic method of branch and bound algorithm is used to evaluate the results of modified particle swarm optimization algorithm and the genetic algorithm.Evaluates indicate better performance of the proposed algorithms in quality the metaheurstic algorithms final solution and solving time in comparing with the method of Lingo software’s branch and bound. Ultimately, the results of numerical examples indicate that considering reliability has significant effect on block structures of machine-part matrixes.