Study On Optimal Inventory With Controllable Lead Time

The competition between the supply chains is becoming more and more complicate under the development of the global economics and financial crisis. Inventory is an important link in the supply chain, whose function can not be ignored and can improve the competition for the supply chain and the companies cooperating in the same chain. At present, papers on multi-echelon inventory systems have solve some problems, but they still have many limitations. Firstly, those papers assumed the lead time is constant. There are many uncertain incidents in the practice which lead to the lead time uncertain. Secondly, the existing inventory models assumed the demand follows normal distribution without testing the historical date, whose result has some distance compared with reality. Thirdly, many papers only concentrate on single inventory system, but a supply chain is a two-echelon or over two-echelon system. We first consider the single-echelon inventory after introducing the theory about inventory, and the buyer' lead time is controllable and demand is assumed to be normal distributed. We use the service level to replace the shortage cost, which avoid the deviation caused by rough calculation, and then we build an optimal model with constraint. In addition, this paper extends the single-echelon inventory model to the two-echelon inventory model. A total cost per unit time for the vendor and buyers with stochastic demand and controllable lead time is developed. The objective is to minimize the total cost of the two-echelon inventory. At last, an example was used to prove the model'feasibility.