A multi-period shelter location-allocation model with evacuation orders for flood disasters

Floods are a significant threat for several countries, endangering the safety and the well-being of populations. Civil protection authorities are in charge of flood emergency evacuation, providing means to help the evacuation and ensuring that people have comfortable and safe places to stay. This work presents a multi-period location-allocation approach that identifies where and when to open a predefined number of shelters, when to send evacuation orders, and how to assign evacuees to shelters over time. The objective is to minimize the overall network distances that evacuees have to travel to reach the shelters. The multi-period optimization model takes into account that the travel times vary over time depending on the road conditions. People’s reaction to the flood evolution is also considered to be dynamic. We also assume that shelters become available in different time periods and have a limited capacity. We present a mathematical formulation for this model which can be solved using an off-the-shelf commercial optimization solver, but only for small instances. For real size problems, given the dynamic characteristics of the problem, obtaining an optimal solution can take several hours of computing time. Thus, a simulated annealing heuristic is proposed. The efficiency of the heuristic is demonstrated with a comparison between the heuristic and the solver solutions for a set of random problems. The applicability of the multi-period model and of the heuristic is illustrated using a case study which highlights the importance and the benefits of adopting a dynamic approach for optimizing emergency response operations.