Forecast Evaluation and Risk Management Strategies in Base Stock Inventory Systems with Fill Rate Commitments

We consider forecasting in base stock inventory systems with commitments concerning the expected short-term fill rate. From the managerial perspective, the short-term fill rate is an important indicator to measure the customer service level as it can be monitored on a regular basis and is the actual/perceived fill rate in finite horizons. First, we present our forecasting task in the decision-theoretic framework and introduce the corresponding Murphy diagrams, which are graphical displays of elementary scoring functions having the property that every consistent loss function for the optimal forecast has a unique representation as a mixture of these functions. These diagrams constitute a significant addendum to the traditional inventory forecast evaluation with economic measures and efficiency curves. Second, we formalize a data-driven procedure to compute the forecasts of interest here assuming a stationary and strong mixing demand process and show that knowing the asymptotic distribution of either a parametric or a nonparametric estimator of the base stock level enables managing the risk of not meeting the fill rate requirement expressed in terms of the averagefill rate. Relying on asymptotic properties and using simulations we offer guidelines on risk management strategies, such as the actual confidence levels needed for making inventory decisions in practice