Customer behavior modeling is important for businesses in order to understand, attract and retain customers. It is critical that the models are able to track the dynamics of customer behavior over time. We propose FC-CSM, a Customer Segmentation Model based on a Fragmentation-Coagulation process, which can track the evolution of customer segmentation, including the splitting and merging of customer groups. We conduct a case study using transaction data from a major Australian supermarket chain, where we: 1) show that our model achieves high fitness of purchase rate, outperforming models using mixture of Poisson processes; 2) compare the impact of promotions on customers for different products; and 3) track how customer groups evolve over time and how individual customers shift across groups. Our model provides valuable information to stakeholders about the different types of customers, how they change purchase behavior, and which customers are more receptive to promotion campaigns.