Designing Stochastic Cell Formation Problem Using Queuing Theory

This paper presents a new nonlinear mathematical model to solve a cell formation problem which assumes that processing time and inter-arrival time of parts are random variables. In this research, cells are defined as a queue system which will be optimized via queuing theory. In this queue system, each machine is assumed as a server and each part as a customer. The grouping of machines and parts are optimized based on the mean waiting time. For solving exactly, the proposed model is linearized. Since the cell formation problem is NP-Hard, two algorithms based on genetic and modified particle swarm optimization (MPSO) algorithms are developed to solve the problem. For generating of initial solutions in these algorithms, a new heuristic method is developed, which always creates feasible solutions. Also, full factorial and Taguchi methods are used to set the crucial parameters in the solutions procedures. Numerical experiments are used to evaluate the performance of the proposed algorithms. The results of the study show that the proposed algorithms are capable of generating better quality solutions in much less time. Finally, a statistical method is used which confirmed that the MPSO algorithm generates higher quality solutions in comparison with the genetic algorithm (GA).