Optimal advertising for a generalized Vidale-Wolfe response model

In this research, we formulate budget allocation decisions as an optimal control problem using a generalized Vidale-Wolfe model (GVW) as its advertising dynamics under a finite time horizon. One key element of our modeling work is that the proposed optimal budget allocation model (called GVW-OB) takes into account the roles of two useful indexes of the GVW model representing the advertising elasticity and the word-of-mouth (WoM) effect, respectively, in determining optimal budget. Moreover, we discuss desirable properties and provide a feasible solution to our GVW-OB model. We conduct computational experiments to assess our model's performance and its identified properties, based on real-world datasets obtained from advertising campaigns by three e-commerce companies on Google AdWords, Facebook Ads and Baidu Ads, respectively. Experimental results show that (1) our GVW-OB strategy outperforms four baselines in terms of both payoff and ROI in either concave or S-shaped settings; (2) linear budget allocation strategies favor concave advertising responses, while nonlinear strategies support S-shaped responses; (3) a larger ad elasticity empowers higher levels of optimal budget and corresponding market share and thus achieves higher payoff and ROI, so does a larger WoM effect; and (4) as the total budget increases, the resulting payoff by the GVW-OB strategy increases monotonically, but the ROI decreases, which is consistent with the law of diminishing marginal utility. From a methodological perspective, our GVW-OB strategy provides a feasible solution for advertisers to make optimal budget allocation over time, which can be easily applied to a variety of advertising media. The identified properties and experimental findings of this research illuminate critical managerial insights for advertisers and media providers.

Automated summary

The research formulates budget allocation decisions as an optimal control problem using a GVW model, considering advertising elasticity and word-of-mouth effect. Experimental results show the effectiveness of the GVW-OB strategy across different advertising scenarios, providing significant managerial insights for advertisers.