Modelling the impact of advertising and quality on goodwill under dynamic conditions

The process of forming goodwill is intricate, and various factors such as advertising and product quality influence the formation of goodwill of a firm. In this paper, we formulate an optimal control model to derive the optimal control policies of advertisement, price and quality level for a product. The model is framed with the assumption that the firm employs one marketing strategy, namely, advertising effort as well as one operational strategy, namely, quality improvement through product innovation. The stock of goodwill increases in proportion to advertising effort and quality effort because of the positive effects of both advertising and product quality on goodwill. Using maximum-principle, we derive the optimal control effort policies, and the effectiveness of the proposed model is validated through numerical examples. The control theoretic analysis provides a deep insight of how the decision makers should plan the advertising and quality during the planning period.