Solving the “Marketing Mix” Problem using Geometric Programming

This paper investigates the optimal allocation of the marketing budget within the marketing-mix decision variables so that sales (or profit) is maximized in a planning horizon. Since the influence of marketing mix variables upon sales are, in reality, nonlinear and interactive, a geometric programming algorithm is used that solves this problem. A procedure to estimate a functional of sales on the marketing mix and environmental variables utilizing the experienced judgments of the firm's executives and the raw data is provided. The derived functional is later optimized by the Geometric Programming algorithm under a constraint set consisting of budget and strategy restrictions imposed by a firm's marketing environment, and conditions under which the optimal solution is either local or global are identified. An empirical application for a large midwestern brewery is provided which utilizes and illustrates both the estimation an optimization procedures.