Abstract: In order to solve the inventory problem in current apparel industry, this article discussed the inventory problem of a two echelon supply chain which is consisting of a single-buyer and a single-vendor with service level constraint. For the purpose of meeting the actual, the demand during lead time is consumed to be normally distributed and the lead time can be shortened with continuous function. We also considered the impact of transport costs on the total cost of the inventory. First, we set up the basic model of the supply. Second, we proposed the solution algorithm of the model according to the basic of minimized inventory cost. Finally, through numerical examples we can identify the feasibility as well as the efficiency of the model and the impact of the initial service level on the optimal results.

Key words: service level constraint, controllable lead-time, crashing cost, two echelon supply chain, inventory