Optimizing emergency relief logistics: a multi-scenario vehicle routing model with heterogeneous fleet deployment

This research develops a mathematical model for optimizing transportation routing in relief supply distribution during flood disasters to address a critical challenge within emergency logistics. The primary objective is to minimize the expected total delivery time through efficient route planning, accounting for vehicle capacity, split deliveries, and scenario-dependent mode-route accessibility with heterogeneous fleet deployment. Building upon the vehicle routing problem framework, the proposed model is formulated as a scenario-based stochastic mixed-integer linear program, where accessibility is strictly modeled through scenario-dependent binary mode–route constraints. The structure is generic and can be adapted to other disaster contexts by redefining scenario probabilities and accessibility matrices. The model leverages the Gurobi optimizer to handle complex instances and serves as a vital decision support system. The results indicate optimized vehicle routes across five distinct scenarios, achieving a minimum expected total delivery time of 116.54 minutes. Sensitivity analyses assessing extreme flood severity, relief kit weights, and demand variations on relief item delivery times highlight the robustness and adaptability of the model. In conclusion, the primary contribution of this research yields actionable managerial insights and practical implications across strategic, tactical, and operational supply chain levels, transforming reactive crisis management into proactive, time-effective relief distribution.