The Mathematical Model for Location-Routing Problem of Relief Logistics Considering the Types of People Under Conditions of Uncertainty

Crisis management holds significant importance during the occurrence of disasters to ensure  maximum reduction in damages and casualties. From a crisis management perspective, emergency logistics occupy a special position because swift transportation of relief personnel and necessary supplies to the affected area, as well as the evacuation of the injured and others during and after a disaster, are amongst the critical needs. This research addresses the locating, routing, and        distribution of emergency supplies in the context of earthquakes. Objectives of this research include maximizing the probability of successfully navigating routes, minimizing emergency response costs, and reducing discrepancies in the allocation of relief personnel to affected regions. The proposed mathematical model, enhanced with an augmented epsilon constraint approach, has been solved using the GAMS software for a case study of Tehran's 11th district. The consideration of various types of injured individuals, including those with minor injuries and those in critical condition, as well as the homeless and relief workers in a concurrent manner, and the development of a three-objective, multi-commodity, multi-vehicle mathematical model with scenarios incorporating uncertainty, are among the innovations of this study.