New Optimal Control Decisions for Channel System With Lagged Effect: Dynamic Advertising and Pricing Cases

In this paper, optimal control decision problems are discussed for a class of dynamic advertising models with lagged effect. Here, the dynamic model with input delay is introduced to depict the impact of the lagged effect on the development of goodwill. The purpose of the addressed problem is to utilize optimal control theory such that the performance of the channel system is maximized while achieving optimal strategy level. Specifically, by utilizing the maximum principle, optimal control decisions of channel members are obtained in the integrated and decentralized systems. Our results demonstrate whether two members benefit from the integrated system is closely related to the delay time of the advertising effect. Also, the contribution of these results is to offer a reference for making optimal control decision and the choice of decision mechanism in the channel system. Finally, an illustrative example is performed to illustrate the effectiveness of the proposed results.