Application of optimal control to the dynamic advertising decisions for supply chain with multiple delays

Systems Science & Control Engineering

Dongyan Chen¹  Chaoqun Dong²  Xinyuan Feng³  Hui Yu⁴  Shizhen Bai⁴ 

[1] Department of Applied Mathematics, Harbin University of Science and Technology;School of Economics and Management, Harbin University of Science and Technology;School of Electrical and Electronic Engineering, Harbin University of Science and Technology;School of Management, Harbin University of Commerce;

关键词: optimal control;    delayed effect;    memory effect;    stochastic disturbance;   

DOI  :  10.1080/21642583.2020.1733129

来源: DOAJ

【 摘 要 】

This paper is concerned with application problem of optimal control to a class of dynamic advertising models with multiple delays. Here, a dynamic model with state and control delays is introduced to describe the impacts of advertising delayed and memory effects on the evolution of brand goodwill. In the decentralized and centralized systems, the optimal advertising strategies of supply chain members are presented by utilizing the nonzero-sum differential game governed by differential equation with multiple delays in state and control variables. Special effort is made to analyse the geometrical shapes of advertising strategy and provide the optimal decision structure of supply chain system. Furthermore, nonzero-sum stochastic differential game is applied to explore the dynamic advertising decision problems of supply chain system with the multiple delays and stochastic cases. Finally, numerical examples are exploited to illustrate the effectiveness of the proposed results.

【 授权许可】

Unknown