Performance evaluation of cellular flexible manufacturing systems: A decomposition approach

In a cellular flexible manufacturing system, a majority of the part types manufactured by the system require machining in a single cell only. However, a few part types (called rare parts) need processing in two or more cells. It is precisely the intercell movement of these rare parts that leads to weak interaction among the otherwise independent cells. We show how this structure can be exploited to achieve significant computational savings in the performance evaluatiion of the cellular flexible manufacturing systems by using product form closed queueing network models and generalised stochastic Petri net models. In product form closed queueing network models, the performance measures of individual cells are computed first, and then the system performance measures are obtained from the performance measures of the cells, suitably accounting for cell interactions. In generalised stochastic Petri net models, the structure of the system enables us to apply the techniques of near-complete decomposability to the the underlying continuous-time Markov chain. The state aggregation in the Markov chain is based on identifying the fast and slow transitions corresponding to intra-cell and inter-cell workpiece movements, respectively. This decomposition leads to a significant reduction in the state space of the Markov chain to be analysed. We also present a comparison of the computational requirements of the analysis using decomposition approach and the exact analysis.