Sensitivity calculation of the throughput of a flexible manufacturing system with respect to the routing mix using perturbation analysis

The effect of the change of the routing mix on the throughput is an important question to be answered by operations management both at the planning and control phases of a Flexible Manufacturing System. This paper presents a method for the calculation of the gradient of the throughput with respect to the routing mix. The algorithm is based on perturbation analysis and on the product form properties of certain types of queuing networks. The provided gradient estimate is exact when conditions on the product form equilibrium distribution of the network are met and the interchangeability of differentiation and expectation holds, but it can also give good approximate results in other cases. Numerical examples are presented to illustrate the proposed calculation.