Simulation and optimization in marketing: Optimal control of consumer goodwill, price and investment

Dynamic market optimization with respect to price, advertisement and investment is presented. The market model is nonlinear. Its main parameters are the elasticities with respect to price, advertisement and consumer income. Dynamic elements has been added to the static model based on the market elasticities. The parameters like seasonal index and consumer income are functions of time, and the whole market can grow due to the investment. The tools of the optimal control theory are applied to calculate optimal policy for product price, advertisement and investment, controlled simultaneously. The total revenue at the end of a fixed time interval is maximized.