A Mathematical Model for Integrated Disaster Relief Operations in Early-Stage Flood Scenarios

When a flood strikes, the two most critical tasks are evacuation and relief distribution. It is essential to integrate these tasks, particularly before the floodwater reaches the vulnerable area, to minimize loss and damage. This paper presents a mathematical model of vehicle routing problems to optimize an integrated disaster relief operation. The model addresses routing for both the evacuation and relief distribution tasks in the early stages of a flood, aiming to identify a minimal number of vehicles required with their corresponding routes to transport vulnerable individuals and simultaneously distribute emergency relief. The new model incorporates several features, including vehicle reuse, multi-trip and split delivery scenarios for evacuees and emergency relief items, uncertainty in evacuation demands, and closing time windows at evacuation points. Due to the complexity of vehicle routing problems, particularly in large-scale scenarios, the exact approach for obtaining optimal solutions is time-consuming. Therefore, we propose the use of a metaheuristic algorithm, specifically a modified genetic algorithm, to find an approximate solution for the proposed model. We apply the developed model and modified algorithm to various simulated flood scenarios and a real-life case study from Indonesia. The experimental results demonstrate that our approach requires fewer vehicles compared to standard models for similar scenarios. Moreover, while the exact approach fails to find optimal solutions within a reasonable timeframe for large-scale scenarios, our new approach provides near-optimal solutions in a much shorter time. In smaller simulated scenarios, the modified genetic algorithm obtains optimal or near-optimal solutions approximately 92.5% faster than the exact approach.