A simple procedure for determining order quantities under a fill rate constraint and normally distributed lead-time demand

One of the most common practical inventory control problems is considered. A single-echelon inventory system is controlled by a continuous review (R, Q) policy. The lead-time demand is normally distributed. We wish to minimize holding and ordering costs under a fill rate constraint. Although, it is not especially complicated to derive the optimal solution, it is much more common in practice to use a simple approximate two-step procedure where the order quantity is determined from a deterministic model in the first step. We provide an alternative, equally simple technique, which is based on the observation that the considered problem for each considered fill rate has a single parameter only. The optimal solution for a grid of parameter values is stored in a file. When solving the problem for an item we use interpolation, or for parameter values outside the grid special approximations. The approximation errors turn out to be negligible. As an alternative to the interpolation we also provide polynomial approximations.