Stock-rationing policy for a make-to-stock production system with two priority classes and backordering

This article considers the problem of production control and stock rationing in a make-to-stock production system with two priority customer classes and backordering. The problem is formulated as a queueing control model. With Poisson arrivals and exponential production times, we show that the optimal production control and stock-rationing policies can be characterized by a single, monotone switching curve.