Dynamic optimization for coordinated replenishment system considering seasonal demand and price quantity discount

Steel structure (SS), as an essential part of heavy equipment (HE), generally has the characteristics of being heavy, oversized, and with unique shapes, making fabrication, storage, and transportation very costly. Therefore, SS supplier has a strong motivation to coordinate with their customers on all trading activities to obtain an optimal linkage between them to reduce the total relevant cost over the planning horizon. A two-echelon single product replenishment model using mixed integer programming (MIP) was proposed in the past for the SS replenishment problem. However, it cannot easily be used to solve large-size replenishment problems because the computational burden has involved the MIP's branch-and-bound solution process. In this study, the echelon stock concept is adopted to separate the stock holding costs between the supplier and the buyer. Therefore, it can be used to decompose the two-echelon single-item replenishment problem into a series of single-echelon single-item lot-sizing problems. Then, a dynamic programming method is used to solve each single-echelon single-item lot-sizing problem to obtain an optimal solution for the SS replenishment problem in a reasonable time. A numerical example demonstrates that the proposed dynamic programming method is more efficient than the traditional MIP method for the large-size replenishment problem. Finally, sensitivity analysis proves that the proposed method allows the supplier to flexibly and quickly adjust delivery policies in response to changes in demand.