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The multi Vehicle Routing Problem with Pickup and Delivery with Time Windowsis a challenging version of the Vehicle Routing Problem. In this paper, byembedding many complex assignment routing constraints through constructing amulti dimensional network, we intend to reach optimality for local clustersderived from a reasonably large set of passengers on real world transportationnetworks. More specifically, we introduce a multi vehicle state space timenetwork representation in which only the non dominated assignment based hyperpaths are examined. In addition, by the aid of passengers cumulative servicepatterns defined in this paper, our solution approach is able to take controlof symmetry issue, a common issue in the combinatorial problems. At the end,extensive computational results over the instances proposed by Ropke andCordeau 2009 and a randomly generated data sets from the Phoenix subarea, Cityof Tempe, show the computational efficiency and solution optimality of ourdeveloped algorithm.

Embedding Assignment Routing Constraints through Multi Dimensional  Network Construction for Solving the Multi Vehicle Routing Problem with  Pickup and Delivery with Time Windows