This work develops a mathematical programming model that characterizes the main variables present in the interaction dynamics of each agent in a collaborative vertical logistical system, such as a supply chain, and measures the synergy level of such system. The model is based on the interaction model developed by the IMP (Industrial Marketing and Purchasing) group and also on the DEA (Data Envelopment Analysis) framework. The basics of these two approaches allow modeling of the characteristics of an agent as well as the collaborative relationships with other agents within the chain. The model was validated using information of supply chain of leather and its products, classified by DANE (Departamento Nacional de Estadistica—Colombia) as the sector CIIU323.