This study is dedicated to a complex Vehicle Routing Problem (VRP) applied to the response phase after a natural disaster. Raised by the last mile distribution of relief goods after earthquakes, it is modelled as a rich VRP involving a heterogeneous fleet of vehicles, multiple trips, multiple depots, and vehicle-site dependencies. The proposed method is a generic hybrid heuristic that uses a Set Partitioning formulation to add memory to a Multi-Start Iterated Local Search framework. To better fit the requirements of last mile distribution, the algorithm has been developed in partnership with members of the International Charter on Space and Major Disasters and has been evaluated on real scenarios from Port-au-Prince earthquake. The heuristic quickly computes efficient routes while determining the number of required vehicles and the subset of depots to be used. Moreover, the computational results show that the proposed method is also competitive compared to the state of the art heuristics on closely related problems found in industrial distribution.