需求依赖库存且有时变短缺拖后率的非立即变质物品库存模型

研究了时变短缺部分拖后条件下非立即变质性物品的库存补给模型，其中物品的变质率随时间变化而变化。当库存水平为正值时，市场需求受销售价格影响；当库存为负值时，不能满足的需求被部分拖后，拖后率与在缺货期间已经发生的缺货量有关。通过考虑短缺拖后率和变质率同时随时间变化对库存补给策略的影响，建立具有短缺量部分拖后的非立即变质性物品的库存模型，并且给出模型最优解存在的必要条件,得到一类更加符合实际情形的库存模型。最后，用数值算例说明模型的实际应用。

Inventory model for deteriorating items with time-dependent partial backlogging rate and inventory-level-dependent demand rate

In this paper, a more general inventory model for deteriorating items with partial backlogging rate was developed, and the deterioration rate changed as the time was running on. When the inventory level was positive, the demand rate depended on the selling price; but when the inventory level was negative, some customers were more impatient to wait, therefore the sale opportunity was reduced and a bigger shortage led to a larger loss. With some analysis, the necessary condition for the existence of optimal solution to the general model was derived. The necessary conditions of the existence and uniqueness of the optimal solutions were introduced. At last, a case study was provided for the proposed model.