Optimal Evacuation Solutions for Large-Scale Scenarios

Evacuation, the process of moving people out of potentially dangerous areas, is a key response to many threats. Planning such an evacuation is therefore important, especially in large-scale emergencies, where routing becomes non-trivial. This paper deals with the optimization and simulation of the evacuation process. We draw our data from the study of the city of Padang in Indonesia, with its high threat of tsunami waves. Ford and Fulkerson (1962) introduced flows over time (dynamic flows), which have become integral to evacuation planning. In the standard flow over time model, each arc a has a constant transit time τ(a). Flow entering the tail of the arc at time θ leaves the head of the arc at time θ + τ(a). Capacity constraints limit the flow rate on each arc. Hamacher and Tjandra (2002) survey objectives in evacuation planning and discuss flow over time models in detail. Note that this model can be solved both deterministically (with every flow unit being deterministically allocated to a unique path with unique characteristics) and stochastically (with every flow unit selecting a path from a choice set with a certain probability, and the path characteristics being stochastic as well). While the former approach is more convenient from a mathe-