Practical experience and scientific research show that there is scope for improving the performance of inventory control systems by delaying a replenishment order that is otherwise triggered by generalised and all too often inappropriate assumptions. This paper presents the first analysis of the most commonly used continuous (s, S) policies with delayed ordering for inventory systems with compound demand. We analyse policies with a constant delay for all orders as well as more flexible policies where the delay depends on the order size. For both classes of policies and general demand processes, we derive optimality conditions for the corresponding delays. In a numerical study with Erlang distributed customer inter-arrival times, we compare the cost performance of the optimal policies with no delay, a constant delay and flexible delays. Sensitivity results provide insights into when the benefit of delaying orders is most pronounced, and when applying flexible delays is essential. 
On the benefits of delayed ordering