Application of optimal impulsive control method to advertising

Advertising departments in companies face hard choices when have to decide how much and when to spend on advertising over the year in order to maximize the customer goodwill and minimize the advertising expenditure. To address these issues, this paper proposes an optimal impulsive control method, in which the control is discrete and only applied when the goodwill is below some pre-specified level. Optimality conditions for impulse driven systems are derived first. Simulation results based on optimal impulsive control method and an existing technique are presented. Analysis of the results shows that integrated goodwill is greater with the optimal impulsive control method. Furthermore, this paper describes how to find a feasible suboptimal solution when an optimal solution does not exist.