Stock Rationing in an M/Ek/1 Make-to-Stock Queue
研究多需求等级、缺货损失的单品按库存生产系统的库存配给问题，发现工作存储水平这一单状态变量可完全刻画库存与生产状态，并给出最优配给与生产策略的临界值特征。
This paper considers the stock rationing problem of a single-item, make-to-stock production system with several demand classes and lost sales. When demand is Poisson and processing time has an Erlang distribution, we show that a single-state variable called work storage level can be employed to completely capture the information regarding inventory level and the status of current production. The optimal rationing policy can be characterized by a sequence of monotone critical work storage levels. For each demand class, there exists a work storage 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. The optimal production policy can also be characterized by a critical work storage level. Our numerical examples indicate that a critical stock level policy, which ignores information on the status of current production, performs very well.