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Shortest Path Problem (SPP) has many Civil Engineering particularly Transportation Engineering applications. This study considers a variant of SPP; the Elementary Shortest Path Problem with Resource Constraints and Late Arrival Penalties (ESPPRCLAP). Time and capacity are considered as the resources and any delay violation of time window causes a late arrival penalty. An application of ESPPRCLAP is given in relation with Vehicle Routing and scheduling Problem with Time Windows (VRPTW), which is used as a principal tool to evaluate many city logistics measures such as route optimization, to mitigate typical problems caused by urban goods movement. Finally benefits of incorporating late arrival penalties has been shown by using ESPPRCLAP as subproblem in column generation solution of VRPTW based on data derived from practical road network.

ELEMENTARY SHORTEST PATH PROBLEM WITH RESOURCE CONSTRAINTS AND TIME DEPENDENT LATE ARRIVAL PENALTIES