Large-Scale Evacuation Network Model for Transporting Evacuees with Multiple Priorities

Abstract

There are increasing numbers of natural disasters occurring worldwide, particularly in populated areas. Such events affect a large number of people causing injuries and fatalities. With ever increasing damage being caused by large-scale natural disasters, the need for appropriate evacuation strategies has grown dramatically. Providing rapid medical treatment is of utmost importance in such circumstances. The problem of transporting patients to medical facilities is a subject of research that has been studied to some extent. One of the challenges is to find a strategy that can maximize the number of survivors and minimize the total cost simultaneously under a given set of resources and geographic constraints. However, some existing mathematical programming methodologies cannot be applied effectively to such large-scale problems.

In this thesis, two mathematical optimization models are proposed for abating the extensive damage and tragic impact by large-scale natural disasters. First of all, a mathematical optimization model called Triage-Assignment-Transportation (TAT) model is suggested in order to decide on the tactical routing assignment of several classes of evacuation vehicles between staging areas and shelters in the nearby area. The model takes into account the severity level of the evacuees, the evacuation vehicles’ capacities, and available resources of each shelter. TAT is a mixed-integer linear programming (MILP) and minimum-cost flow problem. Comprehensive computational experiments are performed to examine the applicability and extensibility of the TAT model.

Secondly, a MILP model is addressed to solve the large-scale evacuation network problem with multi-priorities evacuees, multiple vehicle types, and multiple candidate shelters. An exact solution approach based on modified Benders’ decomposition is proposed for seeking relevant evacuation routes. A geographical methodology for a more realistic initial parameter setting is developed by employing spatial analysis techniques of a GIS. The objective is to minimize the total evacuation cost and to maximize the number of survivors simultaneously. In the first stage, the proposed model identifies the number and location of shelters and strategy to allocate evacuation vehicles. The subproblem in the second stage determines initial stock and distribution of medical resources. To validate the proposed model, the solutions are compared with solutions derived from two solution approaches, linear programming relaxation and branch-and-cut algorithm. Finally, results from comprehensive computational experiments are examined to determine applicability and extensibility of the proposed model.

The two evacuation models for large-scale natural disasters can offer insight to decision makers about the number of staging areas, evacuation vehicles, and medical resources that are required to complete a large-scale evacuation based on the estimated number of evacuees. In addition, we believe that our proposed model can serve as the centerpiece for a disaster evacuation assignment decision support system. This would involve comprehensive collaboration with LSNDs evacuation management experts to develop a system to satisfy their needs.