The real-time time-dependent vehicle routing problem

In this article, the real-time time-dependent vehicle routing problem with time windows is formulated as a series of mixed integer programming models that account for real-time and time-dependent travel times, as well as for real-time demands in a unified framework. In addition to vehicles routes, departure times are treated as decision variables, with delayed departure permitted at each node serviced. A heuristic comprising route construction and route improvement is proposed within which critical nodes are defined to delineate the scope of the remaining problem along the time rolling horizon and an efficient technique for choosing optimal departure times is developed. Fifty-six numerical problems and a real application are provided for demonstration.