Abstract: In order to determine the locations of distribution centers and the quantity of stocks to be prepared ahead of time in each distribution center under uncertain demands of customers, the location-distribution problem with stochastic demand based on the “self-operating + outsourcing” distribution mode is proposed. A two-stage continuous stochastic programming model is established, the goal is to minimize the total costs including the fixed operating cost of distribution centers, the self-operating distribution cost from supply to the distribution centers, the inventory holding cost in the distribution centers, the expected self-operating distribution cost from distribution center to the customs, the outsourcing distribution cost and the shortage cost of customers. In the first stage, the locations of the self-operating distribution centers and the quantity of stocks to be prepared ahead of time in each distribution center are determined; In the second stage, the quantity of self-operating transportation and outsourcing transportation under the given scenario are respectively determined so as to minimize the sum of distribution cost and the shortage cost. Because it is difficult to solve the continuous stochastic programming model directly, the samples average approximation method based on Monte Carlo sampling simulation is proposed. The L-shaped algorithm for solving large-scale stochastic programming model is designed. The superiority of the two-stage stochastic programming model and the effectiveness of the samples average approximation algorithm are verified by simulation examples; Finally, the sensitivity analysis are done on the fixed operation cost of distribution center, the unit cost of self-operating distribution and the unit cost of outsourcing distribution. The optimal distribution strategies corresponding to various range of parameters value are obtained. The results show that, the “self-operating + outsourcing” distribution mode is the best strategy under most cases. The main contribution of this paper is that both the decision variables of the distribution centers location and the quantity of stock to be prepared ahead of time in each distribution center are included in the first stage of the stochastic programming model, which can help the enterprises to make more reasonable decisions, so as to reduce the total costs, shorten the delivery time and improve the customer’s satisfaction. d algorithm of this paper is efficifent for solving large-scale two-stage stochastic programming model, and can be extended to solving more complexity stochastic programming model. The model and algorithm of this paper can not only be used to solve the location-distribution problem of distribution center under the “self-operating + outsourcing” distribution mode, but also can help the E-commerce enterprises to detemine the quantity of goods to be transportated to the pre-warehouse near by the customers with uncertainty demands，so as to reduce response time for customers demand.

Key words: uncertain demand; location-distribution; stochastic programming; sample average approximation；L-shaped algorithm