A capacitated network flow optimization approach for short notice evacuation planning

Abstract

We present a capacity constrained network flow optimization approach for finding evacuation paths, flows and schedules so as to maximize the total evacuees for short notice evacuation planning (SNEP). Due to dynamic nature of this optimization problem, we first construct a time-expanded network that expands the static network over the planning horizon for every time interval. Since the resulting evacuation networks become extremely large to solve, we have developed Evacuation Scheduling Algorithm (ESA) to expedite the solution process. ESA utilizes Dijkstra’s algorithm for finding the evacuation paths and a greedy algorithm for finding the maximum flow of each path and the schedule to execute the flow for each time interval. We show that the complexity of ESA is O(|Nc|·n2)+O(|Nc|·m·T). Numerical experiments show a tremendous advantage of ESA over an exact algorithm (CCEP) in computation time by running up to 41,682 faster than CCEP. In many test network instances, CCEP failed to find a solution within 12hours while ESA converged to a solution in less than 0.03seconds.