Shelter Location and Evacuation Route Assignment Under Uncertainty: A Benders Decomposition Approach

Abstract

Shelters are safe facilities that protect a population from possible damaging effects of a disaster. For that reason, shelter location and traffic assignment decisions should be considered simultaneously for an efficient evacuation plan. In addition, as it is very difficult to anticipate the exact place, time, and scale of a disaster, one needs to take into account the uncertainty in evacuation demand, the disruption/degradation of evacuation road network structure, and the disruption in shelters. In this study, we propose an exact algorithm based on Benders decomposition to solve a scenario-based two-stage stochastic evacuation planning model that optimally locates shelters and that assigns evacuees to shelters and routes in an efficient and fair way to minimize the expected total evacuation time. The second stage of the model is a second-order cone programming problem, and we use duality results for second-order cone programming in a Benders decomposition setting. We solve practical-size problems with up to 1,000 scenarios in moderate CPU times. We investigate methods such as employing a multicut strategy, deriving Pareto-optimal cuts, and using a preemptive priority multiobjective program to enhance the proposed algorithm. We also use a cutting plane algorithm to solve the dual subproblem since it contains a constraint for each possible path. Computational results confirm the efficiency of our algorithms.

Political Storms: Tracking Hurricane Evacuation Behavior Using Smartphone Data

“…Topics include supply pre-positioning, evacuation planning, search and rescue, and infrastructure repair and recovery. Bayram and Yaman (2017) extend an early paper by Sherali et al (1991) to optimize emergency shelter locations and assign residents to specific shelters, to minimize total evacuation time. Guikema et al (2014) develop a random forest model to predict hurricane-related power outages by spatial region, taking into account wind speeds and other topographic factors.…”

A stochastic programming approach for Shelter location and evacuation planning

“…In this study, we were able to solve the stochastic programs in small CPU times as the number of scenarios was small. In a follow up study (Bayram and Yaman [9]), we work on decomposition approaches to solve the problem with large number of scenarios.…”

Evacuation Trees with Contraflow and Divergence Considerations

“…Also, arc (20,19) is used when we have a lower budget, but as budget increases, this arc becomes unimportant for all the costs. Similarly, for cost −1 the arc (5,9) and for cost t − T arc (12,11) have been used when we allow lower budget for contraflows. It is interesting to note that from figure 4.10 how the rate of evacuation changes as the budget for contraflows is increased.…”

“…Evacuation rates shows the lanes used for the contraflows by the model for all three types of costs. According to 1), (1,3) and lane (5,9) are very important for the cost −1 as these lanes keep appearing frequently in all the combinations. Similarly, lanes (1,3), and (2,1) are important for the costs −t and t − T .…”

“…(a) 5 contraflows allowed (b) 10 contraflows allowed x (5,9) x (6,5) x (7,18) x (13,24) x (16,10) x (16,17) x (18,16) x (20,19) x (20,22) x x Table 4.7. Arcs used in contraflow scheme for cost: −t Arcs Contraflows 5 10 (2,1)…”