Fill rate: from its definition to its calculation for the continuous (s, Q) inventory system with discrete demands and lost sales

Customer service measures are traditionally used to determine the performance or/and the control parameters of any inventory system. Among them, the fill rate is one of the most widely used in practice and is defined as the fraction of demand that is immediately met from shelf i.e. from the available on-hand stock. However, this definition itself set out several problems that lead to consider two different approaches to compute the fill rate: the traditional, which computes the fill rate in terms of units short; and the standard, which directly computes the expected satisfied demand. This paper suggest two expressions, the traditional and the standard, to compute the fill rate in the continuous reorder point, order quantity (s, Q) policy following these approaches. Experimental results shows that the traditional approach is biased since underestimate the real fill rate whereas the standard computes it accurately and therefore both approaches cannot be treated as equivalent. This paper focuses on the lost sales context and discrete distributed demands.