A universal challenge in solving a variety of vehicle routing problems (VRPs) is the exponential increase of computation time when the number of entities such as roads, vehicles, and destinations increases. This article studies a class of VRPs in which multiple vehicles located at different locations are dispatched to multiple destinations. Real time VRP in large road networks with time dependent travel time remains a challenge because computation time for the optimal vehicle routes and assignment increases significantly as the size of road networks increases. This article (a) applies a shortest path algorithm with arc labelling to reduce required computer storage space; (b) develops a revised Hungarian method to minimize the latest arrival time and total travel time; and (c) uses appropriate computer programs and tools to reduce computation time for optimal vehicle routing. The algorithm developed in this article identifies the optimal vehicle routes and assignment in six minutes for large and dense road networks.