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Optimal advertising for a generalized Vidale–Wolfe response model

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Abstract

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.

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Acknowledgements

We are thankful to the associate editor and anonymous reviewers who provided valuable suggestions that led to a considerable improvement in the organization and presentation of this manuscript. This work is partially supported by the NSFC (National Natural Science Foundation of China) grants (71672067).

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Authors and Affiliations

  1. School of Management, Huazhong University of Science and Technology, Wuhan, 430074, China

    Yanwu Yang & Baozhu Feng

  2. Qatar Computing Research Institute, HBKU, Doha, Qatar

    Joni Salminen & Bernard J. Jansen

  3. Turku School of Economics, Turku, Finland

    Joni Salminen

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  1. Yanwu Yang
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Yang, Y., Feng, B., Salminen, J. et al. Optimal advertising for a generalized Vidale–Wolfe response model. Electron Commer Res 22, 1275–1305 (2022). https://doi.org/10.1007/s10660-021-09468-x

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