A multiobjective mathematical model for a humanitarian logistics multimodal transportation problem

Purpose The purpose of this paper is to introduce a three-echelon multimodal transportation problem applied to a humanitarian logistic case study that occurred in Mexico. Design/methodology/approach This study develops a methodology combining a transshipment problem and an adaptation of the multidepot heterogeneous fleet vehicle routing problem to construct a mathematical model that incorporates the use of land-based vehicles and drones. The model was applied to the case study of the Earthquake on September 19, 2017, in Mexico, using the Gurobi optimization solver. Findings 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 in a shorter CPU time with medium and small instances than with large instances. Research limitations/implications While the size of the instances limits the use of the model for big-scale problems, this approach manages to provide a good representation of a transportation network during a natural disaster using drones in the last-mile deliveries. Originality/value The present study contributes to a model that combines a vehicle routing problem with transshipment, multiple depots and a heterogeneous fleet including land-based vehicles and drones. There are multiple models present in the literature for these types of problems that incorporate the use of these transportation modes; however, to the best of the authors’ knowledge, there are still no proposals similar to this study.