Estimating job waiting times in production systems with cross-trained setup crews

We model a production system with multiple machines, each serving a variety of jobs. The machines require setups to switch from one job to another. Setup operations are performed by a limited number of setup crews who are cross-trained to perform all setup operations. We develop an approximation model that takes into account the effect of delays caused by unavailability of the setup crews, and obtain average job waiting times in the system. A numerical study demonstrates that our approximation performs very well. Our study also provides insights into the importance of explicitly modeling the effects of cross-trained setup crews on performance measures, and whether and when the cross-training of setup crews improves system performance.