With the development of international economy and the aggravation of market competition, people have found great importance in logistics industry. The main goal of logistics industry is to reduce the total cost of the logistics. The cost of inventory, which may exist in all the links of logistics, occupies large-scale percentages among the total cost of the logistics. Therefore, to effectively control the inventory cost is very important for the reduction of the total logistics cost. In this paper, compared to the traditional inventory models for items with a linear trend in demand, we propose new non-linear trend in demand inventory models based on the allowance of product shortage and not allowance of product shortage.