库存管理模型

仅介绍业界最简单的economic order quantity（EOQ）model，其他的模型请参考书目：Principles of Inventory Management。

实际上，此类工业界长期使用的模型，大概率已封装在相关的软件系统中，更好的解决方案是购买商业产品。之前朋友咨询如何爬取facebook的用户邮箱，给其的建议是直接购买相关数据库，亦是同理。

1、the purpose of the model

To determine how much to purchase （order quantity）and when to place the order（the reorder point）.

2、the assumptions underlying the model

 The demand is stable over time, known rate of   units per year.

 Whenever an order is placed, a fixed cost K is incurred.  Each unit of inventory costs $I to stock per yaer per dollar and a unit's purchasing cost is C.

 The order arrives  years after the placement of the order.

 All the model parameters are unchanging over time.

3、model development

The order quantity denoted by Q,  also remains stationary.

We get the following objective function by adding three types of costs together（purchasing cost、placing cost、holding cost）, which we want to minimize over Q：

To compute the optimal order quantity, we take the first derivative of Z(Q) with respect to Q and set it equal to zero. 

4、more insights

let us explore additional properties the optimal solution posesses.