A model for the marketing of a seasonal product with different goodwills for consumer and retailer*

We consider a firm which produces and sells a seasonal product in two consecutive time intervals and propose an optimal control model for its marketing. The production period state variables are the inventory level and two goodwills (for consumer and for retailer) while the selling period state variables are the sales level and the two goodwills. In the production period there are three controls : on production, quality and advertising, while in the selling period the only control allowed is on communication. The linear case is considered in detail and transformed into an equivalent non-linear programming problem.