The pick-up and dispatch routing problem in the railway logistics center is considered as the vehicle routing problem with simultaneous pickup-delivery and stochastic travel and service time. A stochastic programming model with recourse is formulated. An improved iterated local search algorithm is designed, in which the split delivery is considered for the construction algorithm, local operators and perturbation mechanism. Three classes of instances, which are named small scale instances, medium scale instances and large scale instances, are tested. Better solutions are obtained because of the split delivery in most of the medium scale instances and large scale instances, where there are reductions for both the cost and the vehicles used in the optimum solution. The ratio of the delivery customers to the customers decreases as the scale of the instances grows, even through there are more split customers in the larger scale problem. With the level of stochastic factors getting high, the value of the objective grows, but the number of split customers are not affected.