Location-Routing Problem for Relief Distribution in the Early Post-Earthquake Stage from the Perspective of Fairness

To address the shortage of relief in disaster areas during the early stages after an earthquake, a location-routing problem (LRP) was studied from the perspective of fairness. A multi-objective model for the fair LRP was developed by lexicographic order object optimal method in consideration of the urgent window constraints, partial road damage, multimodal relief delivery, disaster severity, and vulnerability of each demand node when its demand is not satisfied. The goals of this model are to minimize (1) the maximum loss of demand node, (2) the total loss of demand node, and (3) the maximum time required for the demand node to receive relief. A hybrid heuristic algorithm was proposed to solve the model. Finally, the utility and fairness of the model and algorithm were demonstrated by a case study during the first day after the great Wenchuan earthquake in China.