The research presented in this paper was carried out under the European Community ESPRIT Project HChLOUSO: Hydrocarbon and Chemical Logistics under Uncertainty via Stochastic Optimization. The formulation of deterministic optimization problems to model logistic operations for a consortium of operators (including AGIP and CLH) were outlined in the CORO model developed by the UITESA and CLH research groups and the DROP (Depot and Refinery Optimization Problem) model treated in our companion paper for strategic or tactical level planning of a company's activities. In this paper we discuss the technical requirements of implementing a stochastic programming formulation. To project random demands for oil products at different locations into the future, and to consider fluctuations in their prices/costs, a stochastic data simulator has been developed and implemented as a part of our overall modelling system. The research reported here is currently in progress, but in our opinion the complexities of the stochastic problem require at this time a detailed report on progress to date. From the viewpoint of the implementation of large stochastic programming models, this work constitutes a case study at the challenging leading edge of the field in that it involves decisions in both space and time in the face of uncertain product demands and prices. This paper treats the specification, generation and solution of the stochastic DROP model in detail, including the analysis of alternative stochastic modelling of the uncertainties on a small -- but realistic -- test problem supplied by CLH. A number of novel related research questions and implications are also discussed.