A Model of Adaptive Control of Promotional Spending

Companies try to conduct their marketing operations so as to respond to changing market conditions. A model of such a process is studied for the case of setting promotion rate. Company sales are functions of promotional spending, but the relation changes with time. An adaptive system is devised that works as follows: Information about sales response is collected by performing an experiment. The experimental results are used to update a sales response model. Promotion rate is chosen to maximize expected profit in the next time period. The cycle is repeated. In designing the experiment, sample size is chosen to minimize the cost of imperfect information plus the cost of experimentation. The model employs a quadratic sales response function with a parameter that, changes according to a first order, autoregressive process. The optimal adaptive system turns out to involve exponential smoothing of the experimental results. A numerical example is studied analytically and by simulation. The adaptive system is found to work better than various other policies. In a sensitivity analysis, an adaptive system derived for one underlying model of the market is found to perform well even when certain other models actually apply.