Optimal pulsing in an advertising diffusion model

Empirical evidence indicates that a given moderate number of advertisements per year may achieve higher effect when concentrated in flights than when spread equally. In the control-theoretic literature a few approaches have been developed for which the optimal policy is a pulsing schedule. The present communication analyses a two-state diffusion advertising model for repeat purchasing. Recognizing the interaction between customers and potential buyers, the optimal advertising policy turns out to be a persistent periodic oscillation. This provides a further interesting example in marketing for the existence of a stable limit cycle.