Service Measures in Inventory Models

Computing the fill rate is a little more involved. If demand is D and unfulfilled demand (i.e., units short) is given by S, then fill rate is given by 

For a newsvendor setting, both fill rate and units short are functions of the order quantity Q, and since expected demand in the newsvendor model is p, it follows that the expected fill rate is 

Computing S(Q) requires a loss function, which is typically available in look-up table form for the standard normal distribution. Thus, for normally distributed demand 

Using the data from Examples 3.1 and 3.2, we can compute p(Q ) = 0.9016, meaning that we would expect to fulfill about 90.2% of the demand for biker jackets in the 2012-2013 winter season if we order 10,558 of them. 

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