A maximin procedure for the optimal insertion timing of ad executions

It has been recommended that dominant brands should not suffer from long periods with little or no advertising. For such brands in a product category which is not subject to seasonality, it is important not to let the minimum effectiveness level fall too low. Toward this end, we present an analytical model for determining the optimal insertion timing pattern of a long run ad campaign which consists of a number of varying executions. We develop a computational procedure to calculate the time between the insertions within a pulse in order to maximize the minimum effectiveness level at any point in time. The focus of the procedure is to provide conceptual insights and on benchmark solutions, which can reduce the computational burden of simulations, rather than on providing an exact solution. We also provide a theoretical justification for the two common economic axioms of nonsatiation and diminishing marginal returns, in the context of an advertising model with exponential forgetting.