We consider the distribution of goods from manufacturers to customers by a logistics provider, where manufacturers' supplies and customers' demands are given and cannot be controlled. The goods may temporarily be stored in warehouses to compensate for the stochastic behavior of the supplies and demands. Manufacturers, warehouses and customers are geographically connected by transportation links, e.g. roads, railways, waterways. The problem of a logistics provider is to determine which of these links to use and how much to ship through them, such that total costs are minimized and demands are met. This paper presents a method for designing close to optimal network topologies for this type of problem. We introduce a two-layer optimization procedure, which finds a cost-effective topology with a very limited number of links for a set of stochastic supplies and demands. In addition, we show that the obtained topology is only sensitive to changes in the first moments of supply and demand distributions. Hence, with only information about the individual means, a close to optimal topology can be determined based on a constructed set of stochastic time series of supplies and demands.