  We consider the vehicle routing problem with stochastic demands (VRPSD) on
tree structured networks with a single depot. The problem we are concerned with
in this paper is to find a set of tours for the vehicle with minimum expected
length. Every tour begins at the depot, visits a subset of customers and
returns to the depot without violating the capacity constraint. Randomized
approximation algorithm achieving approximation guarantees of 2 for
split-delivery VRPSD, and 3 for un-split delivery VRPSD are obtained.
