Optimal control problems for a new product with word-of-mouth

In this paper, we consider a firm to maximize its profit by choosing a production capacity and determining the production and sales policies for a new product during the lifetime of the product. We extend Bass demand process into more general case including the negative effectiveness of word-of-mouth. Under some mild conditions, we show that the optimal sales policy is myopic, then we obtain the closed forms of the optimal production and sales policies in three cases. Furthermore, we can determine the optimal production capacity by solving several equations.