Advertising strategies and coordination for supply chain based on consignment platform with delayed effect

In this paper, the optimal control method is used to discuss the advertising investment decisions for the consignment platform, where the delayed effect of the advertising is introduced to reflect the dynamics of platform goodwill. Firstly, the optimal advertising investment policies are obtained in the integrated and decentralized decision strictures by applying the optimal control theory. Besides, the comparisons of the optimal profits are provided in two decision strictures. Our results suggest that the centralization leads to higher channel performance only when time delay is below a certain threshold. Secondly, a consignment contract with the bilateral participation and the constant platform use fees is proposed to coordinate the decentralized system. Finally, some simulations are employed to obtain more management insights and to illustrate the coordination capability of the proposed contract.