A communication mix for an event planning: a linear quadratic approach

The communication mix is a relevant decision issue for an organization that plans the advertising campaign for a fixed future event. It is assumed that the objectives of the organization are to minimize the cost of the advertising campaign and to drive the final demand as close as possible to a target value. Two different advertising channels are available: the first affects deterministically the consumers' demand, whereas the second presents some stochastic aspects which are out of decision-maker's control. Some recent mathematical developments on the stochastic linear quadratic control problem allow to formulate and solve some interesting instances of the problem. A comparative analysis of the efficiency of deterministic and stochastic controls is done and the optimal feedback policies are discussed. The trade-off between efficiency and risk of an advertising channel is essential to understand the features of the optimal solutions.