A probabilistic fuzzy goal programming model for managing the supply of emergency relief materials

The post-disaster humanitarian logistic operations deal with the supply of emergency relief materials to mitigate damages in the affected areas. Immediately after the disaster, it is challenging to estimate the demand for emergency relief materials. As a result, the demand for such materials at the point of demand and the corresponding transportation costs for the entire supply chain network becomes uncertain. This paper proposes a new probabilistic fuzzy goal programming model for making decisions to manage the post-disaster supply of emergency relief materials. A suggested procedure converts the proposed model to its deterministic equivalent when the demands for the relief materials follow uniform distributions. We implement the differential evolution, a metaheuristic technique, for analyzing demand satisfaction for relief materials under various scenarios. A case example based on the Nepal Earthquake in 2015 demonstrates the usefulness of the proposed approach. The solution of the model will help the Disaster Management Agency coordinate with the humanitarian organizations and foreign countries to provide the required emergency relief materials so that an adequate level of supply can be assured to the affected areas with the least possible transportation cost.