A queuing theory-based approach to designing cellular manufacturing systems

This paper presents a new cell formation and cell layout problem considering multiple process routings and subcontracting using the principles of queuing theory. It is assumed that each machine operates as an M/M/1 queuing system and a queuing network is used to obtain in-process inventories and machine utilization. The problem is formulated as a mixed-integer nonlinear program with the objective of minimizing the total costs, including the production, subcontracting, material handling, machine idleness, and holding costs. Due to the computational complexity of the problem, a heuristic method is suggested to effectively solve the problem. A numerical example is given to clarify the proposed approach, and finally, further instances are solved to verify the performance of the solution method and to accomplish comparisons. The computational results show that the proposed heuristic is both effective and efficient.