In this thesis, a dynamic model of the vehicle routing problem is developed and analyzed. In this model, an vehicle with adequate volume travels at a constant velocity in a botmded Euclidean plane to provide services to demands, whose locations are independent and uniformly distributed over this region. The dynamic demands arrive according to a Poisson process in time and their on-site service times are generally distributed, independent of their locations. A median strategy for the dynamic model is proposed to reduce system time of the natural First Come First Served one, with the improvement of performance verified by simulation results