In this paper, we study a service parts inventory management system for a single product at a parts distribution center serving two priority-demand classes: critical and non-critical. Distribution center keeps a common inventory pool to serve the two demand classes, and provides differentiated levels of service by means of inventory rationing. We assume a continuous review one-for-one ordering policy with backorders and Poisson demand arrivals. Only one demand class provides advance demand information whose orders are due after a deterministic demand lead time, whereas the orders of the other demand class need to be satisfied immediately. The problem has been studied before, but remained a challenging problem. The quality of the existing heuristic for estimating the critical class service levels can diminish significantly in some settings and the search routine for the service level optimization model relies on a brute force approach. Our contribution to the literature is twofold. For the given class of inventory replenishment and allocation policies, first we determine the form of the optimal solution to the service level optimization model, and then we derive an exact optimization routine to determine the optimal policy parameters provided the steady-state distribution is available. The computation of steady-state probabilities is needed only once. Second, we propose an alternative approach to estimate steady-state probabilities. By analyzing the limiting behavior of transition probabilities during infinitesimal time intervals, we are able to characterize the relationships between the steady-state probabilities, which satisfy nicely formed balance equations under the so-called Independence Assumption. In the numerical study section, we show that our approach provides superior performance in estimating service levels than the existing heuristic for all the examples considered. We also compare the performance of using the critical class service levels computed according to our method against the service levels computed by the existing heuristic, and show that our method can provide inventory savings up to 16.67%.

在本文中，我们研究了在零件配送中心针对单一产品的服务零件库存管理系统，该系统具有两种优先级需求：关键和非关键。配送中心保留一个公共的库存池来满足这两种需求类别，并通过库存配给的方式提供不同级别的服务。我们假设有延期交货和Poisson需求到达的连续审查一对一订购政策。只有一个需求类别提供预先确定的需求提前期后到期的提前需求信息，而另一需求类别的订单需要立即得到满足。该问题之前已经研究过，但仍然是一个具有挑战性的问题。现有启发式算法的质量危急类服务级别在某些设置中可能会大大减少，并且服务级别优化模型的搜索例程依赖于蛮力方法。我们对文学的贡献是双重的。对于给定的库存补充和分配策略类别，首先我们确定服务水平优化模型的最优解决方案的形式，然后在可获得稳态分布的情况下，导出精确的优化例程以确定最优策略参数。稳态概率的计算仅需要一次。其次，我们提出了另一种方法来估计稳态概率。通过分析无限时间间隔内转移概率的极限行为，我们可以表征稳态概率之间的关系，独立假设。在数值研究部分中，我们表明，对于所有考虑的示例，我们的方法在估计服务水平方面均比现有的启发式方法具有更好的性能。我们还将使用根据我们的方法计算的关键类服务水平与现有启发式方法计算的服务水平的性能进行了比较，并表明我们的方法可以节省多达16.67％的库存。