Optimal Control Approach to Advertising Strategies of a Supply Chain Under Consignment Contract

The retailer's platform goodwill and the manufacturer's brand goodwill are important factors that influence the consumer's purchasing behavior under a consignment contract. In order to examine these effects on firm's decisions under different channel structures, a supply chain, including a single manufacturer and a single retailer, is considered, where the retailer provides the sales platform and the manufacturer sells the product through the retailer's sales platform under the consignment contract. By constructing a price-dependent and goodwill-dependent demand and using the differential game theory, the optimal equilibrium strategies are obtained under the decentralized and centralized structures. Our results demonstrate that the relationship of retail prices under two channel structures depends on the share of the revenue, and the centralized scenario could not always lead to a higher advertising effort. Subsequently, the decentralized supply chain is coordinated by designing the linear goodwill-dependent contract. Finally, the effects of the share of revenue and the effectiveness of advertising efforts on the equilibrium strategies as well as profits are illustrated by some simulations.