考虑可变库存费和销售机会损失的库存模型

Inventory model with variable holding cost and lost sales

经典的EOQ模型所解决的问题都视库存费为常数,文章首先考虑可变库存费和销售机会损失,研究了当库存费的变化率为存储时间的函数h(t)时,发展了部分短缺量延期供给和可变库存费的变质性物品的库存模型;其次,对建立的模型进行分析,从理论上证明了该模型具有唯一的整体最优解;最后,针对存储时间的函数为h(t)=τeδt时,通过数值计算分别对延交系数β和参数δ进行数值分析,揭示了库存费的变化及销售机会损失对库存系统最优订货策略的影响。

The holding cost is regarded as constant in the classical economic order quantity（EOQ） models concerning inventory problems.In this paper,firstly,the variable holding cost and the lost sales during the shortage period are studied,and an inventory model is developed for deteriorating items with the partial backlogging and the variable holding cost as the variable holding cost is a function of the length of the holding time,that is h（t）.Secondly,through the theoretical analysis,it is proved that the model has a unique optimal integral solution.Finally,for the holding cost function h（t）=τeδt,a numerical analysis of the coefficient of back-orders β and the parameter δ is given by the numerical calculation,and the effect of the change in holding costs and lost sales on the optimal order policy for the inventory system is revealed.