The objective of this paper is to develop a dynamic mixed integer linear programming model (MILP) of analysis of robustness to supply chain disruptions. The proposed approach allows analysing different causes of disruptions for supply chains, and how these interruptions prevent the bottom-of-the-pyramid (BoP) organisations from fulfilling their purpose of eradicating poverty. Critical operational performance indicators were used to evaluate the impacts of interruptions at the beginning of the supply chain and their implications for the BoP organisations. We consider different types of disruptions that mainly affect the first links of the chain of the BoP. In addition, the proposed approach measured the impact of the demand satisfaction of final products for the same population. The efficiency of the proposed approach has been tested using real data obtained from a dairy supply chain management in Cundinamarca (Colombia). The obtained results show the benefits of the proposed model.