Characterizing order processes of continuous review (s,S) and (r,nQ) policies

We provide a novel approach to characterize the order process of continuous review (s,S) and (r,nQ) inventory policies, and study the impact of the batching parameter (the value of Q or S-s) on the variability in the order process. First, we characterize the distribution of the time between orders, as well as the distribution of order sizes. We find that the coefficient of variation (cv) of the time between orders is smaller than the cv of the time between demands. The size of the orders can exhibit either variance amplification or dampening, compared to the demand sizes, depending on the demand size distribution and the value of the batching parameter. This may motivate a supplier to adjust his imposed fixed order cost to influence the batching size. Second, we look at the compound order process, defined by the number of units ordered during an arbitrary interval. The compound order process always exhibits variance amplification compared to the compound demand, which increases linearly in the batching parameter for large values of Q or S-s; for small values, the variance amplification is fluctuating. We point out that the time interval, during which the number of units ordered/demanded is observed, also impacts the level of variance amplification, and we show to what extent larger time intervals (resulting in more aggregation of the data) lead to lower values of variance amplification. Both perspectives (looking at time between orders and order quantities, or observing the compound order process) provide useful information for the upstream supplier.