Queuing approximations for capacity planning under common setup rules

We consider the problem of estimating the resulting utilization and cycle times in manufacturing settings that are subject to significant capacity losses due to setups when switching between different product or part types. In particular, we develop queuing approximations for a multi-item server with sequence-dependent setups operating under four distinct setup rules that we have determined to be common in such settings: first-in-first-out, setup avoidance, setup minimization and type priority. We first derive expressions for the setup utilization and overall utilization, and use Kingman’s well-known approximation to estimate the average cycle time at the station under each setup rule. We test the accuracy of the approximations using a simulation experiment, and provide insights on the use of different setup rules under various conditions.