Differential model of customer loyalty evolution as loyalty forecasting tool

The paper introduces a differential model of customer loyalty evolution which enables one to construct solutions, based on hypotheses and incorporated sub-models of factors affecting the loyalty. We consider first heuristically a differential equation holding the balance between selected factors affecting one another (functionality, quality, and price) and are related to the notion customer loyalty. Such an equation classified as the first integral ('the first way to solution') in the theory of differential equations enables one to rigorously analyse it and construct hypothesis-driven solutions. A special (simplified) case is considered to demonstrate how the approach works. The model allows to construct solutions depending on particular representations of functionality, quality and price impacts. Serving as a prototype of a corporate tool, the model is shown with simple examples to generate the loyalty evolution forecasts. It is especially useful with further adaptation for practitioners and those who have commitment to integrated corporate management solutions.