The problem for a class of advertising strategies in a supply chain is studied based on the impacts of the lagged and memory effects. The functional differential equation is developed to depict the impacts of lagged and memory effects on the evolution of product's brand goodwill. By applying the differential game theory, the optimal advertising investment levels of manufacturers and retailers, advertising scheduling and the brand goodwill of products are obtained in the decentralized and centralized decisions. Also, the paper comparatively analyzes the optimal equilibrium strategies in the two decision systems. The results show that the centralized decision can simulate the advertising investment of supply chain members; meanwhile, the lagged effect and memory effect not only influence the determination of advertising timing schemes and advertising schedule policies, respectively, but also affect the choice of decision mechanism.