Supply Chain Joint Scheduling and Algorithm Using Continuity of Nonlinear Differential Equation Function

Abstract

To improve the integrity of the supply chain and get the optimal joint scheduling of the complete supply chain, in this exploration, first, the supply chain related theory is elaborated. Then, the dynamic model of product recovery in enterprise joint scheduling is established. Finally, based on the differential game theory (based on the continuity of nonlinear differential equation function) and Hamilton function, the optimal scheduling strategies with manufacturer and retailer as the main recycling body in the complete supply chain are calculated respectively. The results show that the product recovery rate with manufacturer as the main recycling body is higher than that with retailer as the main recycling body. There is no transfer price in the recovery based on the manufacturer. However, in the recovery based on the retailer, if the transfer price increases, the product recovery rate of the system will also increase; if the transfer price increases, the manufacturer’s instant profit will appropriately increase; if the transfer price value is high [Formula: see text], the manufacturer’s instant profit is higher. If the transfer payment is low [Formula: see text], the instant profit of manufacturer with manufacturer as the main recycling body will be first lower and then higher than that with retailer as the main recycling body. When the system is stable, the instant profit with the manufacturer as the main recycling body is higher than that with retailer as the main recycling body; the total profit of the manufacturer with the retailer as the recycling body is first lower and then higher than that with the manufacturer as the main recycling body. Whether the transfer payment is high or low, the retailer’s profit level is higher when the manufacturer is the main recycling body. When the retailer is the main recycling body, the retailer’s profit level is inversely proportional to the transfer payment. Finally, in the centralized supply chain environment, enterprises can maximize their total profits and promote the good development.