An optimum budget allocation model for dynamic,interacting market segments

This paper formulates a model for determining the optimal allocation of a given advertising budget over M interacting market segments and a time domain of T periods. Guidance for budget size optimization is provided via a shadow price. The basic input parameters are in terms of sales saturation levels and advertising elasticities, concepts experienced advertising executives understand and are willing to estimate. Economic and political developments in Western Europe are increasing the interactions among geographically defined segments, and recent development in discrimination techniques may soon make market segmentation a practical strategy for the United States market. In relation to the time domain, the simplistic and often unrealistic constraint of a constant carryover effect is relaxed in that current advertising is hypothesized to generate sales both by creating new customers and by interacting with the residual effects of past advertising (goodwill) thus reinforcing preferences of past customers. This interactive formulation relating past and future expenditures allows a model user greater flexibility in specifying the relationship between advertising and sales. The mathematical programming technique used is a form of convex programming.