This paper considers vehicle routing problems (VRP) where customer locations and service times are random variables that are realized dynamically during plan execution. It proposes a multiple scenario approach (MSA) that continuously generates plans consistent with past decisions and anticipating future requests. The approach, which combines Al and OR techniques in novel ways, is compared with the best available heuristics that model longdistance courier mail services [Larsen et al, 2002]. Experimental results shows that MSA may significantly decrease travel times and is robust wrt reasonably noisy distributions.