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 online markets, 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 refund price decisions to optimize the total profit of the chain. Furthermore, it is formulated as a mixed-integer non-linear programming (MINLP) model and solved by a Lagrangian relaxation algorithm. The numerical study and computational results indicate the efficiency and effectiveness of the proposed algorithm.

在设计具有随机价格敏感需求的三级不确定供应链网络时，本文解决了一个新的位置分配定价问题。利用市场细分问题，当价格较高的市场出现一些需求泄漏时，将开发一个具有两个分销渠道的供应链网络，该分销渠道包括实体市场和在线市场。由于缺乏在线市场上对产品的实际观察，因此使用了退货政策。因此，根据定价和退货政策来分析需求行为。该问题确定了位置，分配，订单数量，定价和退款价格决策，以优化链的总利润。此外，将其公式化为混合整数非线性规划（MINLP）模型，并通过拉格朗日松弛算法进行求解。