Modelling flow and jobbing shops as a queueing network for workload control

Abstract

Workload control is an approach for production planning and control that attempts to manage manufacturing lead times rather than treat them as a forecasting problem. It is particularly appropriate for jobbing and flow shops in the make-to-order sector of industry. It is based on Little's well known formula in queueing theory that the time an arrival spends in the system is the average number in the system divided by the arrival rate. However, the workload control approach treats the jobbing shop as a single entity and thus ignores the complexities caused by competing jobs arriving at a work station at the same time thus forming queues. This paper describes how the job shop environment may be formulated as an open queueing network. It is computationally impossible to solve the model exactly if there are more than three or four work stations. Results for an exact Markov process model for a triangular configuration of work stations are described. Initial results suggest that treating each work station as an independent queueing system leads to significant under-estimation of the manufacturing lead times, even for such a simple manufacturing system. Some initial ideas on deriving an approximation of the exact model to cover larger systems are also discussed.