On the δ-service level for demand substitution in inventory control ^⁎

In retail, it is usual to measure the performance of inventory control by a so-called service level which measures the number of days (probability) that demand is fulfilled for a certain product, i.e. the product is not out of stock. Part of the customers that do not encounter the product in stock will look for a substitute. To measure the performance, we introduce a so-called δ-service level which measures the availability of the substitute. We investigate the effect of safety levels and substitution probability on the δ-service level and illustrate them based on the case of poisson demand.