Abstract
An optimal control model that brings together the marketing function and the operations function in a firm is considered. The Model Predictive Technique (MPC) yields a closed form solution for the optimal production rate and the optimal advertising rate. The importance of the choice of the goal variables for a model of the tracking type is shown. Also, the importance of the gap between the initial values of the state variables and the initial values of the corresponding goal variables, as well as the choice of the solution technique used, are investigated. We find that, to minimize its cost, the firm should start with an initial value as close as possible to the goal value at the beginning of the prediction interval. We also find that Pontryagin's maximum principle (MP) should be used for small values of the horizon T and MPC should be used for large values of T.