Understanding the Relationship between Fill Rate, Demand Distribution, and Modelling Uncertainty

Inventory systems represent an important part of firms' investments, with a direct impact on competitiveness. Inventory management intends to achieve a compromise between customer satisfaction and inventory costs. To this end, service level metrics such as the Cycle Service Level and Fill Rate are typically used to optimise the inventory parameters that define the inventory system performance. The Cycle Service Level is common in research, due to its mathematical simplicity. However, in practice the Fill Rate is more widely used, as it is more closely connected to firms' requirements. Yet, this often involves complex approximations and estimation procedures. First, we investigate the connection between fill rate and the demand distribution, and second, we develop a new formulation for calibrating inventory systems using the fill rate. The advantage of our proposed approach is that it recognises the difference between demand and modelling uncertainty, offering additional flexibility in tuning the inventory parameters. We demonstrate the efficacy of the procedure using simulated demand processes, to investigate the formulations under different conditions, and real data from a fast moving consumer goods company