Data-driven inventory forecasting in periodic-review inventory systems adjusted with a fill rate requirement

We propose an integrated forecasting and optimization framework for base stock decisions in periodic-review inventory systems subject to requirements for these systems' infinite-horizon fill rates as agreed service levels. We provide a detailed discussion of the conditions necessary for the uniqueness of the required optimal solutions, examine some properties of our data-driven computational procedure, and address the task of directly modeling base stock levels with the help of chosen semiparametric nonlinear dynamic models. To demonstrate the effectiveness of our strategy, we evaluate it on real data sets, finding that it achieves fill rates close to the target values and low implicit inventory costs. Our empirical assessment also highlights the usefulness of generalized autoregressive score (GAS) models for inventory planning based on medium-sized historical demand samples. These models can be recommended for applications with nominal fill rates of 90-95%, but also for careful so-called "focus forecasting" when required service levels are as high as 99-99.9%.