Fourth party logistics network design considering quantity discount

Under the complex and changeable business environment, demand uncertainty brings great challenges to the operation of supply chain and how to design effective supply chain is an important issue in supply chain management. The fourth party logistics (4PL) is a fast developing and efficient supply chain operation mode, and in the 4PL system, 3PLs often launch discount promotion to attract more customers, in order to explore how to better design 4PL network, a novel 4PL network design problem considering quantity discount is proposed. Considering the constraint of service level, a chance constraint programming model is established, the service level constraint and quantity discount lead to the nonlinear characteristic of model, therefore a MIP reformulation is given to ensure the model can be sovled straightly. The model is solved using CPLEX and numerical experiment with different scales are conducted, results show the effectiveness of proposed model. Furthermore, the impact of demand level, quantity discount and discount coefficient on 4PL network designing are revealed.