| Abstract: | The primary goal of this article is to extend the results of a previous article to the case where the effect of advertisement on sales lasts more than one period. Monotonicity of the optimal advertising and inventory policies in the various factors is investigated. Also, attention will be focused on the relationship between the fluctuations over time of the optimal policies and the variations over time of the factors involved, such as demand distributions and holding costs. For example, if over a finite interval the demand decreases from one period to the next, reaches a minimum, and then increases, then the optimal advertising policy will produce the opposite effect. The period of minimum demand never precedes that of maximum goodwill; moreover, the optimal inventory level decreases while the demand decreases. Finally, when demand distributions are just translates of one another, the results of this article can be extended to nonperishable goods. |
