Vehicle Routing Problems (VRPs) are prevalent in all large pick up and delivery logistics systems and are critical to city logistics operations. Of notable significance are three key extensions to classical VRPs: (1) multi-depot scenario; (2) probabilistic demand; and (3) time-window constraints, which are considered simultaneously with VRPs in this paper. The issue then becomes a Multi Depot Probabilistic Vehicle Routing Problem with a Time Window (MDPVRPTW). The underlying complexities of MDPVRPTW are analyzed and a heuristic approach is presented to solve the problem. Genetic algorithms (GAs) are found to be capable of providing an efficient solution to the so-called MDPVRPTW. Within the GAs, two modification operators namely, crossover and mutation, are designed specially to solve the MDPVRPTW. Three numerical examples with 14, 25, and 51 nodes are presented to test the efficiency of the algorithm as the problem size grows. The proposed algorithms perform satisfactorily and the limiting case solutions are in agreement with the constraints. Additional work is needed to test the robustness and efficiency of the algorithms as the problem size grows.
