Optimizing evacuation via budget constrained maximum dynamic flow with speed variation and intermediate storage

During any type of disaster, managing the evacuation of people at risk and planning humanitarian support constitute a critical challenge due to the presence of heavy traffic congestion in urban areas. Among them, flow maximization and time minimization models in bi-directional contraflow network have been emerging in addressing these issues. Resource limitation is one of the critical issues in such scenarios. The main objective of this work is to maximize the number of evacuees by best utilizing budget allocation and improving speed adjustment, which minimize congestion during evacuation. Since a limited budget is available, a set of bottleneck arcs is first identified, and then the budget is optimally allocated to some of these arcs to increase their capacities within given space bounds. The remaining arcs are then updated with new speed adjustment, where the travel time should be reduced. In this model, the flow is increased by settling evacuees in intermediate shelters, intended for those who may not reach the final destination due to network capacity or permissible time window constraints. The presented algorithms are polynomial, and their validity is proved. This novel approach could be a milestone in saving lives and reducing traffic congestion, as it offers both theoretical and practical value and contributes to more effective traffic management during emergencies, special events, and rush hour periods. To demonstrate their efficacy, the proposed models are applied to a real-world network case study of the Kathmandu Valley.