Demand forecasting under lost sales stock policies

Demand forecasting is a crucial task within supply chain management. Stock control policies are directly affected by the precision of probabilistic demand forecasts. For instance, safety stocks and reorder points are based on those forecasts. However, forecasting and replenishment policies have typically been studied separately. In this work, we explore the influence of inventory assumptions on the selection of the forecasting model. In particular, we consider when the stock policy follows a lost sales context and the demand is estimated by means of sales data. In that case, forecasting models should use censored demand estimations. Unfortunately, the literature about censored demand forecasting remains very limited, without an accepted general solution for this problem. In this work, we bridge that gap by proposing the Tobit Kalman filter (TKF). To the best of our knowledge, this is the first time that the TKF has been applied to supply chain demand forecasting, and this approach may represent a general solution for lost sales contexts. The TKF is compared with a previous ad hoc censored demand forecasting solution that is based on single exponential smoothing. In addition, we show the performance of the TKF when dealing with trends where ad hoc approaches are not available for use as benchmarks. To express the potential benefits of the proposed approach in terms of costs and the service level, a newsvendor stock policy is employed. Simulated demand data and a case study are used to illustrate the significant advantages of the proposed tool.