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

Abstract

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.

Advertising strategy and contract coordination for a supply chain system: immediate and delayed effects

“…For example, aimed at a supply chain with one manufacturer and one retailer, a seminal model has been presented by Chen et al (2017), where the change of goodwill is generated by the previous advertising and goodwill decay. Guo et al (2019) and Yu et al (2020) have spread the work of Chen et al (2017) to an extent and simultaneously taken the manufacturer's and retailer's delayed effects into consideration. The main difference between Guo et al (2019) and Yu et al (2020) lies in the dynamic characterization of brand goodwill.…”

“…Guo et al (2019) and Yu et al (2020) have spread the work of Chen et al (2017) to an extent and simultaneously taken the manufacturer's and retailer's delayed effects into consideration. The main difference between Guo et al (2019) and Yu et al (2020) lies in the dynamic characterization of brand goodwill. Cao et al (2020) and Li et al (2021) have utilized differential game theory to obtain the optimal advertising strategy for the dual-channel and O2O supply chain systems.…”

“…As mentioned above, it is a remarkable fact that delayed advertising should be given adequate consideration. Some theoretical results on delayed effect have recently posted several emerging challenges, which have received ever-increasing research attention within the development and implementation of the advertising strategy, as well as the choice of decision mechanism for a supply chain (Chen et al , 2017; Yu et al , 2018; 2020; Yu and Chen, 2019; Guo et al , 2019; Cao et al , 2020). Besides, by observing the effect of advertising in the franchise industries, it is confirmed that advertising has both immediate and delayed effects (Eisend and Langner, 2010; Küster and Eisend, 2016; Park and Jang, 2016; Machowska, 2019).…”

Optimal Control of the Logistics Automation Transmission System Based on Partial Differential Equation

“…With the development of society and economy, automatic transmission has become more and more complex, and the amount of automatic transmission is sometimes very large. Scientific organization of automatic transmission can effectively reduce the cost of logistics activities and realize the change of the space position of the required items in time to effectively improve its space [5,6].…”

Application of optimal control theory on optimal advertising expenditure in monopoly

“…If we use notation as a system, control variables or state variables we may imagine a machine. A lot of authors ( [4], [5], [6], [7]) are using economic applications of optimal control theory. E.g.…”