Adil ve etkin büyük ölçekli tahliye planlaması için doğrusal olmayan karışık tamsayılı modeller ve algoritmalar

Traffic management during an evacuation and the decision of where to locate the shelters are of critical importance to the performance of an evacuation plan. We develop a model that optimally locates shelters and assigns evacuees to the nearest shelter sites by assigning them to shortest paths, shortest and nearest with a given degree of tolerance, so that the total evacuation time is minimized. The resulting model is a nonlinear mixed integer programming model. We develop a solution method that can handle practical size problems using second order cone programming techniques. Using our model, we investigate the trade-off between efficiency and fairness. The second model we propose is a scenario-based two-stage stochastic evacuation planning model that optimally locates shelter sites and that assigns evacuees to shelters and paths to minimize the expected total evacuation time. The model considers the uncertainty in the evacuation demand and the disruption in the road network and shelter sites. We present a case study for an impending earthquake in Istanbul, Turkey. We compare the performance of the stochastic programming solutions to solutions based on single scenarios and mean values. We also propose an exact algorithm based on Benders decomposition to solve the stochastic problem. To the best of our knowledge, ours is the first algorithm that uses duality results for second order cone programming in a Benders decomposition setting. We solve practical size problems with up to 1000 scenarios in moderate CPU times. We investigate methods to enhance the proposed algorithm.