Analysis of a production system in a general configuration

We consider a production system comprising multiple stations (or workshops) such as an entry station, a set of work stations, a central station, and an exit station, which are arranged in a general configuration. A worker (or a vehicle tool) is assigned to each station, who sends a part from the station to the destination station according to the required process path of the part. Any part is allowed to visit a work station more than once if its process path requires. We propose a new control strategy with the push policy for instructing each worker to send a part and the kanban mechanism for controlling the work-in-process (WIP) in each work station. As all work stations have limited local buffers, the central station is used for storing blocked parts temporarily. Such a production system is modeled as an open queueing network in a general configuration with a Markovian part sending policy and a machine no blocking mechanism. The queueing network is analytically characterized. Some important performance measures are compared with other control strategies. A semi-open decomposition approach is applied to the queueing network for computing the blocking probabilities when parts arrive at the work stations. An algorithm is developed based on the semi-open decomposition approach. Numerical experiments show the quality of the solutions obtained by the algorithm as well as a property of a performance measure.