In this paper the authors propose a bi-level mathematical programming model for humanitarian logistics to optimize decisions related to the distribution of international aid after a catastrophic disaster. In this situation, non-profit international organizations and foreign countries will offer to help by shipping certain necessary products, such as bottled water, food and medicine, but will want to minimize the shipping costs. At the same time, the affected country seeks to distribute the received aid to the affected areas as efficiently and quickly as possible. To deal with the considered problem, we reformulate the bi-level model and reduce it into a nonlinear single-level mathematical model; then we linearize it to obtain a mixed integer programming problem. To validate the proposed mathematical model, we consider as a case study the earthquake in Chile in 2010. We solve the reformulated model by using real data simulating the aid distribution scenario, and we interpret the obtained numerical results, giving some recommendations for aid distribution following future disasters.
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