A multiobjective mathematical model for a multimodal transportation problem in Humanitarian Logistics

Abstract

From 2001 to 2013, 4 out of 32 major public health emergencies worldwide were caused by earthquakes. The destruction caused by earthquakes generates problems like lack of shelters to accommodate people, food, and water shortage, but above all, the need to distribute emergency supplies for the most affected people when the roads are damaged (Lurie et al., 2013). The research papers Drone Delivery Models for Healthcare (Scott & Scott, 2017) and A metaheuristic algorithm to solve the selection of transportation channels in supply chain design (Olivares-Benitez et al., 2013) were of great influence in the development of this project. The purpose of this research is to formulate a mathematical model that minimizes the delivery time and the transportation costs of emergency medical supplies in the most critical stage of an earthquake, to save as many lives as possible. Moreover, this study pretends to encourage other researchers to expand the area of knowledge in Humanitarian Logistics. To fulfill the aforementioned, a mathematical model that incorporates the combination of land and air transportation was developed and solved with the optimization software Gurobi. Subsequently, the model was applied to a case study and to analyze the results, a Pareto Front was constructed. To taste the efficiency of the model, instances of different sizes were used. The results ratified the relevance of the study, showing an inverse relationship between transportation costs and delivery time, on the flip side, the model performed a in shorter CPU time with medium and small instances than with large instances.