Abstract: An order and selling inventory model is concerned based on the inventory theory. Considering that lot-size discount phenomenon usually exists in the actuality, so suppose to have lot-size discount in the model. And also suppose that the need speed is continuous and uniform, and shortage is allowed, which brings shortage cost. The mean total inventory cost includes order cost, inventory cost and shortage cost. An order and selling inventory model with shortage allowed under the condition of limited-space warehouse and lot-size discount is developed approaching to actuality as possible. And make use of mathematics method to solve the model, then the optimal order quantity, the optimal order cycle and the minimum mean total inventory cost are confirmed. Finally, the application of the model is illustrated by an example.

Key words: inventory model, discount, order quantity, order cycle

摘要： 利用存贮论知识，研究了一类订货销售存贮模型。考虑到在现实中往往存在订货批量折扣现象，因此在模型中假设有批量折扣，同时假设需求速度是连续的、均匀的；允许发生缺货，并产生缺货费用。库存系统的平均总费用包括订货费用、存贮费用和缺货费用。据此建立有批量折扣且允许缺货的订货销售存贮模型，使模型更接近于实际，并利用数学方法对该模型进行了求解，确定了最优订货批量和最优订货周期，以及平均每天的最小总费用。 最后，通过实例说明了模型的应用。

关键词: 存贮模型, 折扣, 订货批量, 订货周期