Optimal advertising strategies

This paper considers advertising policies for a very general class of response functions. It is shown that if a pulsing policy is used, awareness (or sales) eventually settle down to a steady cycle and the average response over the cycle is a decreasing function of the length of the cycle. When response shows increasing returns to scale, it is possible (in theory) to use a device called chattering to replace the true response by a straight line which lies above the true response in the region in which chattering is used. A numerical example is given to show how the optimal policy can be computed when part of the response is linear and the results obtained are compared with those of the best practicable approximation to chattering. It is shown that the problem of maximising awareness or sales, subject to a budget constraint, is structurally identical with maximising profit after advertising, with or without a constraint. In either case it is possible that, for part of the time, the optimal policy involves chattering.