This paper addresses a new location-allocation-pricing problem in designing a three-level uncertain supply chain network with stochastic price-sensitive demands. Using the market segmentation problems, a supply-chain network is developed with two distribution channels that consist of Brick & Mortar and onlinemarkets, when some demand leakages occur from the market with a higher price. Due to the lack of physical observation of products in online markets, a return policy is used. So, demand behavior is analyzed in terms of the pricing and return policy. The problem established location, allocation, order quantities, pricing and refundprice decisions to optimize the total profit of the chain. Furthermore, it is formulated as a mixed-integer nonlinearprogramming (MINLP) model and solved by a Lagrangian relaxation algorithm. The numerical study andcomputational results indicate the efficiency and effectiveness of the proposed algorithm