In this paper, we consider the Inventory-Routing Problem with Transshipment (IRPT) under stochastic demand. Traditional methods that optimize the decisions of stochastic problems often approximate the probability distribution by a set of scenarios. Although for small instances this approach often results in good quality solutions, the computational requirements make it unsuited for the optimization of large-scale problems. We investigate how such a sample average approximation method can be adjusted so that large instances of the stochastic IRPT can be solved within reasonable time. For this purpose we intersperse the optimization steps with a simulation phase that eliminates uninteresting solutions. We also develop a sequential simulation procedure to effectively select the optimal solution in the final stage of the algorithm. The experimental results show that the adjusted sample average approximation algorithm is able to solve instances with up to 35 retailers within reasonable time. © 2018 EUROSIS. All rights reserved.