Spatiotemporal Allocation of Advertising Budgets

This article develops a method for optimal allocation of resources based on an empirically validated model of how national and regional advertising generate sales over time. The authors derive the profit-maximizing total budget, its optimal split between national and regional spends, and its optimal allocation across multiple regions. They 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, the authors furnish closed-form expressions for the optimal total budget and its regional allocations. In addition, they develop a method to estimate the proposed model and apply it to market data from a leading German cosmetics company. Using the estimated parameters, they evaluate the optimal budget and allocations. Comparing them with actual company policy, the proposed approach enhances profit by 5.07%, and it not only identifies which regions under-or overspend but also reveals how much budget to shift from national to regional advertising (or vice versa).

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