A Single-Product Inventory Model for Multiple Demand Classes
针对服务多需求等级的单产品库存系统，提出一种基于临界水平控制策略和缺货清除机制的模型，并证明其与串行库存系统的等价性，进而开发高效启发式算法进行成本评估与优化。
We consider a single-product inventory system that serves multiple demand classes, which differ in their shortage costs or service-level requirements. We assume a critical-level control policy, and a backorder clearing mechanism in which we treat a backorder for a lower-priority class equivalent to a reserve-stock shortfall for the higher-priority class. We show the equivalence between this inventory system and a serial inventory system. Based on this equivalence, we develop a model for cost evaluation and optimization under the assumptions of Poisson demand, deterministic replenishment lead time, and a continuous-review (Q, R) policy with rationing. We propose a computationally efficient heuristic and develop a bound on its performance. We provide a numerical experiment to show the effectiveness of the heuristic and the value from a rationing policy. Finally, we describe how to extend the model to permit service times, and how to extend the model to a multi-echelon setting.