Queueing analysis of manufacturing systems with set ups

A manufacturing system with one server (machine), two classes of jobs, finite buffer sizes, and non-negligible set-up times is analysed. A cycling service discipline with a ’wait and see‘ set-up policy is invoked by the server. The state of the machine, whether in set up or in processing, is explicitly considered in the model. Utilization, mean queue length, and cycle time are derived using markovian analysis, first under a fixed lot size environment and then with random lot sizes. With lot sizes fixed, increasing arrival rates, set-up times, and service times generally increase the utilization, cycle time, and queue lengths. When lot sizes are random, there are negligible variations in the cycle time result, with somewhat smaller queue lengths compared to the fixed lot size case. An approximate mean value analysis is also developed and results are compared to those of the markovian analysis. Numerical studies show the robustness of the mean value analysis for most of the system parameters tested.