We consider a capacitated supply system that produces a single item that is demanded by several classes of customers. Each customer class may have a different backorder cost, so stock allocation arises as a key decision problem. We model the supply system as a multicustomer make-to-stock queue. Using dynamic programming, we show that the optimal allocation policy has a simple and intuitive structure. In addition, we present an efficient algorithm to compute the parameters of this optimal allocation policy. Finally, for. a typical supply chain design problem, we illustrate that ignoring the stock allocation dimension-a frequently encountered simplifying assumption-can lead to incorrect managerial decisions.