Optimal Control Strategies for a Supply Chain System With Delay and Reference Price Effects

This paper mainly discusses the impacts from the time delay of advertising and the reference price of consumer onto the cooperative advertising decisions. In our model, both the retailer’s platform goodwill (RPG) and the manufacturer’s brand goodwill (MBG) involved with their own advertising efforts are modeled by the delay differential equations. In addition, the RPG and the MBG have positive effects on the consumer’s reference price. The equilibrium advertising strategies of two channel members are firstly derived within the centralized and decentralized scenarios by resorting to the optimal control theory. Besides, the corresponding equilibrium advertising strategies and optimal channel profits are compared, which shows that the centralization brings higher profit to whole channel only when the time delays locate within a specified geometric region and the existence of time delay caused by manufacturer’s advertising also implies smaller advertising participation rate provided by the retailer. Subsequently, a new mechanism is designed to coordinate the supply chain system in the decentralized case under the consignment mode. Finally, a numerical example is employed to illustrate the impacts from key system parameters onto the coordination results when the supply chain is coordinated.