Cost optimization and quality control of products from queues with preemptive priority

This paper describes a queueing theory application in quality control. Items to be processed arrive as a Poisson process at a production system and form a queue for processing and subsequent quality control inspection. If an item is found to be defective, it is fed back to the queue for further processing and the production cycle continues. We assume that there are two types of items competing for service, one with a higher priority than the other. The service discipline is preemptive and the processing times are exponentially distributed. A cost model involving waiting cost, processing and inspection costs is formulated, and is illustrated by numerical examples.