The total sales are not necessarily equal to total demand, since some demand may have been lost. For the case that lost demand is not recorded at all, Fisher et al. (2000) propose to estimate lost demand based on the moment at which the stock dropped to zero and the demand curve until that time. However, that method can not be applied in our case, since the moment at which the stock drops to zero is not recorded either. Fortunately, lost demand is partially recorded in our case, since the company does register lost demands that are received through the call center and the voice response system (but not through the website and regular mail). Moreover, we know the percentage distribution of total demand over the four sales channels. This information is used to scale up the registered lost demand for each SKU to get our estimate of total lost demand per SKU.
We refer interested readers to Bell (2000) for a discussion of estimating the distribution of demand based on sales data for multiple-period problems.