Inventory rationing in a make-to-stock production system with several demand classes and lost sales

This paper considers the stock rationing problem of a single-item, make-to-stock production system with several demand classes and lost sales. For the case of Poisson demands and exponential production times, we show that the optimal policy can be characterized by a sequence of monotone stock rationing levels. For each demand class, there exists a stock rationing level at or below which it is optimal to start rejecting the demand of this class in anticipation of future arrival of higher priority demands. A simple queueing model is analyzed to compute the operating cost of a rationing policy. In a numerical study, we compare the optimal rationing policy with a first-come first-served policy to investigate the benefit of stock rationing under different operating conditions of the system.