In this paper we consider periodic review systems under stochastic demands. First, we study the single product periodic review problem and propose a simple solution procedure which is near optimal. Then, given the existence of this simple procedure, we study the joint replenishment problem for multiple items under stochastic demands and suggest simple heuristics which provide very good results. We find the simple procedures combined with the robustness of the cost function to be very attractive in other applications which require coordination of cycle times under stochastic demands.