Direct marketing of an event under hazards of customer saturation and forgetting

We address the problem of optimising the intensity of online advertising. In contrast to the classical literature, we tackle the advertising interaction between the firm and the potential customer, for the sale of a onetime event, in a very limited time horizon. The problem is intrinsically dynamic due to two conflicting situations: the first arises when the customer is subjected to intense advertising pressure, which may lead to customer saturation and even irritation, while the second is the tendency for customers to forget if they are not reminded systematically through advertising. In order to determine an optimal event-advertising policy and develop an efficient enumerative shooting algorithm to solve the problem, we suggest a hazard rate-based approach to modelling the conflicting factors. Our analysis shows that the initial level of customer interest in the event has a non-trivial effect on the dynamics of the optimal advertising policy. In particular, this advertising policy consists of a monotonic increase over time prior to the event in the case of high initial interest and a concave, peak-wise form in the case of low initial interest.