A model for multi-segment marketing

We consider a linear optimal control model for the marketing of seasonal products which are produced by the same firm and sold by retailers in different market segments. The horizon is divided in two consecutive non-intersecting intervals. production and selling periods, respectively. The production period state variables are the inventory levels and two kinds of goodwills (for consumers and for retailers) while the selling period state variables are the sales levels and the two kinds of goodwills. In the production interval there are three kinds of controls: on production, quality and advertising, while in the selling one the controls are on communication via advertising, promotion for consumers and incentives for retailers. We consider the case of several kinds of communications. The oplimal control problem is transformed into an equivalent nonlinear programming problem.