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This paper describes anticipatory algorithms for the dynamic vehicle dispatching problem with pickups and deliveries, a problem faced by local area courier companies. These algorithms evaluate alternative solutions through a short-term demand sampling and a fully sequential procedure for indifference zone selection. They also exploit an unified and integrated approach in order to address all the issues involved in real-time fleet management, namely assigning requests to vehicles, routing the vehicles, scheduling the routes and relocating idle vehicles. Computational results show that the anticipatory algorithms provide consistently better solutions than their reactive counterparts.