The isolated community evacuation problem with mixed integer programming

Abstract

As awareness of the vulnerability of isolated regions to natural disasters grows, the demand for efficient evacuation plans is increasing. However, isolated areas, such as islands, often have characteristics that make conventional methods, such as evacuation by private vehicle, impractical to infeasible. Mathematical models are conventional tools for evacuation planning. Most previous models have focused on densely populated areas, and are inapplicable to isolated communities that are dependent on marine vessels or aircraft to evacuate. This paper introduces the Isolated Community Evacuation Problem (ICEP) and a corresponding mixed integer programming formulation that aims to minimize the evacuation time of an isolated community through optimally routing a coordinated fleet of heterogeneous recovery resources. ICEP differs from previous models on resource-based evacuation in that it is highly asymmetric and incorporates compatibility issues between resources and access points. The formulation is expanded to a two-stage stochastic problem that allows scenario-based optimal resource planning while also ensuring minimal evacuation time. In addition, objective functions with a varying degree of risk are provided, and the sensitivity of the model to different objective functions and problem sizes is presented through numerical experiments. To increase efficiency, structure-based heuristics to solve the deterministic and stochastic problems are introduced and evaluated through computational experiments. The results give researchers and emergency planners in remote areas a tool to build optimal evacuation plans given the heterogeneous resource fleets available, which is something they have not been previously able to do and to take actions to improve the resilience of their communities accordingly.