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.
- Nonlinear differential equation
- Cross-border e-commerce
- Return rate
As market competition continues to intensify, allowing customers to return goods has become a means of competition widely adopted by retailers. For example, JD.com and Tmall allow customers to return unsatisfied products. Returning goods will incur logistics, inspection, and repackaging costs . It is estimated that the US electronics industry spent 13.8 billion US dollars in processing returns in 2007. The main reason for returns is that the products cannot match the needs of customers. Therefore, how to reduce the product return rate is an important issue that retailers face to solve. Current methods to reduce product returns include improving the product design quality, charging replacement fees, and shortening product delivery time. In addition, providing store assistance services can also effectively reduce the product return rate.
Research on customer returns is relatively rich. Some scholars have studied the supply chain decision-making problems affected by returns under different channel structures and gave the chain members' preference for channel structure selection. Some scholars assume that the amount of refunds affects demand and solves the problem of inventory decision-making and return policy formulation in the supply chain. These documents focus on analyzing the impact of customer returns without considering the issue of reduction in return rates. Some scholars believe that store ancillary services can reduce the unreasonable return rate of products and improve the impact of the return rate on market demand. He gave the product pricing and dual-channel strategy of competing companies. Some scholars have further studied the issue of how companies choose to store auxiliary service strategies. The results show that the strength of the difference in the return rate affects the company's strategic choices . Some scholars have constructed a shop assistant decision-making model in the context of asymmetric customer return information. Some scholars have extended the store-assisted decision-making problem to the VMI scenario.
In recent years, certain results have been achieved in studying supply chain optimization and coordination issues affected by returns from a dynamic perspective . By establishing a differential game model and solving the problem, the supply chain's optimal pricing and store-assisted strategy under the background of consignment sales are given. Design a dynamic consignment price contract to achieve supply chain coordination. However, the study did not fully consider the return processing costs caused by product returns and the impact of returns on demand, which is not completely consistent with the actual situation.
This article comprehensively considers the impact of product return rate on market demand. Research on the pricing of supply chain and auxiliary decision-making of stores in a dynamic context. The article uses differential game theory to give pricing and store assistance strategies under decentralized and centralized decision-making. At the same time, a contract is designed to realize supply chain coordination under this background.
This article considers a supply chain consisting of a manufacturer and a retailer. The manufacturer produces the product and sells the product to the end consumer through the retailer. Retailers allow consumers to return unsatisfactory products after purchasing products . The returned products can be sold again but will incur disposal costs for the retailer. In addition, retailers can reduce the return rate of products by improving store assistance to increase product sales and profits.
In the context of the research of this article, the level of store assistance is related to the store assistance efforts invested by retailers. The following differential equation describes it:
The product return rate
Store assistance cost is the quadratic function of store assistance effort, that is,
Under centralized decision-making, all members of the supply chain decide the price of the product and the auxiliary strategy of the store, namely decision
The optimal path for the store assistance level is
To solve the optimal control problem, we introduce the common state variable
Because of the application of the principle of maximum value, the optimal decision should meet the following conditions:
From equation (10) and equation (11), we can get
Two characteristic roots of matrix B
The eigenvector corresponding to the eigenroot of matrix B
Then the solution of the system of differential equations can be expressed as
Determine the constants
So you can get
The optimal strategy under centralized decision-making has a formula
This shows that the higher the efficiency of store assistance level in reducing the product return rate, the more store assistance efforts are invested . The level of store assistance will be correspondingly higher, but the price will be lower. Shop assistance efforts to improve the level of shop assistance efficiency will also produce similar results.
The form of the wholesale price in this contract is
Then the retailer accepts the contract and maximizes its profits to determine the product's retail price and the store's extra service efforts.
The fee-based contract can achieve supply chain coordination. The objective function of the retailer under this contract is
Introduce the common state variable
We can get the optimal decision under the contract
The optimal decision under the contract is the same as that under the centralized decision so that the supply chain can be coordinated by a two-part fee contract . The optimal profit of the retailer and the manufacturer under the contract is
To ensure that the two members accept the contract, the parameters in the contract need to meet the condition
It is assumed that the influence of store assistance level on product return rate and product retail price and return rate on market demand is linear. This linear characterization can reflect the relationship between these quantities and is widely used in existing studies . Of course, it is more accurate to describe the nonlinear structure, but it is more difficult to solve the model and excavate the meaning of management.
This section mainly discusses the impact of system parameter changes on the stable values of product pricing, store assistance efforts and store assistance level, and coordination contracts through numerical examples. Assume parameter
Figure 1 and Figure 2 show that the optimal store assistance level and store assistance effort under centralized decision-making are higher than the corresponding values under decentralized decision-making. This shows that centralized decision-making is more conducive to improving the level of store assistance . In addition, whether it is centralized or decentralized decision-making, the level of store assistance and store assistance efforts increases with store assistance efficiency or store assistance effort efficiency. On the contrary, the retail price of the product becomes smaller. From Figure 3 and Figure 4, it can be seen that when falls between, and the supply chain can be coordinated, and the income of each member is better than in the case of decentralized decision-making. In addition, as the parameters continue to increase, the win-win area will continue to grow larger.
This paper uses differential game theory to study supply chain pricing and store auxiliary strategy issues and designs contracts in a dynamic environment to coordinate the supply chain. Studies have shown that centralized decision-making is conducive to promoting the supply chain to improve store assistance efforts. Still, centralized decision-making does not always mean that the supply chain should lower retail prices. The two-part fee contract designed in this paper can realize supply chain coordination.