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This paper addresses the problem of determining the optimal promotional policy for a diffusion model in a segment-specific market under the assumption that the additional demand of the new product also improves brand image in the form of goodwill of the firm. The model is framed with the assumption that the firm uses the mass and differentiated promotion effort for each segment. The differentiated promotional efforts target each market segment independently and the mass promotional effort reaches different segments with a fixed spectrum. We derive the optimal promotional effort policy for each segment using maximum-principle and also analyze the stability of the dynamical system by constructing a Lyapunov function through the graph theoretic approach. The analysis gives a deep insight into how the promotional effort should be planned by the decision makers keeping in mind the financial constrains without hindering the promotional effort at the end of the planning period.

Optimal promotional policy of an innovation diffusion model incorporating the brand image in a segment-specific market