In the practice of enterprises management

inventory is a double-edged sword. Adequate inventories can gain more profit and reputation for enterprises. But overstock will add inventory expenses

increase cost

reduce profit and go against management level for enterprises. On the contrary

low inventories can cause the decline of service level and affect the sales profit and reputation. This paper mainly studies the inventory decision problems of the retailers under the condition of variable lead time and partial admission for delay in delivery

and analyzes it when service level is bounded and the demand follows free distribution. The dissertation adopts the accurate solution method and the Minmax method to find the optimal order quantity respectively. In the end

it analyzes the differences of the optimal solution under different inventory models

and takes sensitivity analysis in service level and safety factor into consideration

through which the enterprises can know the lost cost for the 1% increasing of the service level when the service level and lost cost are taken into account at the same time. If the retailer only consider the service level

not stock-out

the retailer will not know how much is their loss of the cost for service level declining. It must be considered not the lost cost but also service level to find the best combination of the two points

so that the enterprise can adjust the strategy in the competition

to gain competitive advantage.