A generalized Vidale–Wolfe model on existing and new customers advertising strategy in a segmented market

Business firms and companies are constantly adopting the concept of market segmentation, which plays an important role in the promotion of a product. Additionally, advertising is another component that strengthens the company’s communication with customers. To have effective marketing strategies, the implementation of independent advertising strategies for each segmented market is important. This paper deals with an optimal control problem that aims to obtain a dynamic advertising policy for new customers as well as minimize the decay rate for existing customers in a segment-specific market. We will an derive explicit optimal dynamic advertising efforts policy using Pontryagin’s maximum principle. The analysis gives a deep insight into how the advertising effort should be planned by the decision-makers, designing strategies that maximize long-term profitability while effectively controlling advertising costs. The effectiveness of the suggested strategy is supported by numerical examples, along with parameter estimation to estimate the value of certain parameters.