Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate

Abstract This article constructs a nonlinear differential equation model that incorporates non-defective return factors and minimizes the expected cost of the inventory control problem under the cross-border e-commerce overseas warehouse model. Under the dynamic background, the problem of pricing and shop assistant decision-making in the supply chain is studied, and the differential game model is constructed. We use differential game theory to give pricing and store assistance strategies under decentralized and centralized decision-making. At the same time, we designed a contract to achieve supply chain coordination in this context. Numerical examples calculate the optimal return price and optimal order quantity under supply chain coordination.