Spatiotemporal Allocation of Advertising Budgets

53 Pages Posted: 28 Jun 2011

See all articles by Ashwin Aravindakshan

Ashwin Aravindakshan

University of California, Davis

Kay Peters

University of Hamburg - Institute for Marketing and Media; Hamburg Center for Health Economics; UC Davis, GSM

Prasad A. Naik

University of California, Davis

Date Written: April 15, 2011

Abstract

How should brand managers determine the optimal advertising budget to generate sales and maximize profit from multiple regions and over time? How much of it should be set aside for national advertising? How should they allocate the rest across multiple regions? This paper addresses these questions by developing a method for optimal allocation of resources based on an empirically validated model of how national and regional advertising generate sales over time. We derive the profit-maximizing total budget, its optimal split between national and regional spends, and its optimal allocation across multiple regions. To this end, we formulate a spatiotemporal model that accounts for spatial and serial dependence, spatial heterogeneity, neighborhood effects and sales dynamics. Because of spatial and serial dependence, correlated multivariate Brownian motion drives the sales dynamics, resulting in a second-order differential equation for the Hamilton-Jacobi-Bellman (HJB) equation with multiple states (i.e., regional sales) and multiple controls (i.e., regional and national advertising expenditures). By solving the HJB equation analytically, we furnish closed-form expressions for the optimal total budget and its regional allocations. In addition, we develop a method to estimate the proposed model and apply it to market data from a leading German cosmetics company. Using the estimated parameters, we evaluate the optimal budget and allocations. Comparing them with actual company policy, the proposed approach enhances profit by 5.07%. Finally, the proposed method not only identifies which regions under- or over-spend, but also reveals how much budget to shift from national to regional advertising (or vice versa).

Keywords: Advertising, Budget Allocation, Spatiotemporal Model, Optimal Allocation, Neighborhood Effects, Spatial Dependence, Spatial Heterogeneity

JEL Classification: M3

Suggested Citation

Aravindakshan, Ashwin and Peters, Kay and Naik, Prasad A., Spatiotemporal Allocation of Advertising Budgets (April 15, 2011). Available at SSRN: https://ssrn.com/abstract=1873570 or http://dx.doi.org/10.2139/ssrn.1873570

Ashwin Aravindakshan (Contact Author)

University of California, Davis ( email )

One Shields Avenue
Davis, CA 95616
United States

HOME PAGE: http://ashwin.faculty.ucdavis.edu

Kay Peters

University of Hamburg - Institute for Marketing and Media ( email )

Welckerstrasse 8
Hamburg, 20354
Germany

Hamburg Center for Health Economics ( email )

Von-Melle-Park 5
Hamburg, 20146
Germany

UC Davis, GSM ( email )

One Shields Avenue
Davis, CA 95616
United States

Prasad A. Naik

University of California, Davis ( email )

One Shields Avenue
Davis, CA 95616
United States

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