Clustering parts and machines into part families and machine cells is a major decision in the design of cellular\r\nmanufacturing systems which is defined as cell formation. This paper presents a non-linear mixed integer\r\nprogramming model to design cellular manufacturing systems which assumes that the arrival rate of parts into cells\r\nand machine service rate are stochastic parameters and described by exponential distribution. Uncertain situations\r\nmay create a queue behind each machine; therefore, we will consider the average waiting time of parts behind\r\neach machine in order to have an efficient system. The objective function will minimize summation of idleness cost\r\nof machines, sub-contracting cost for exceptional parts, non-utilizing machine cost, and holding cost of parts in the\r\ncells. Finally, the linearized model will be solved by the Cplex solver of GAMS, and sensitivity analysis will be\r\nperformed to illustrate the effectiveness of the parameters.
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