One of the most common problem in the area of the supply chain management is to take decisions concerning inventory and delivery questions in order to obtain the maximal possible profit. For that, the key source of information is a forecast of the demand, that is often based on sales historical data.
One of the first paradigm used to study this problem is the newsboy model, which requires a knowledge of the stochastic distribution of the demand. Several variants have been developed, using multi-period, multi-products, presence of extra costs : obsolescence, salvation, etc. This problem has a very simple and elegant analytical solution if one assumes an exact knowledge of the distribution of the demand.
The consequences of the limited knowledge we have upon the distribution of the future demand is usually addressed by a max-min search in the expected gain. Another possible approach, namely a min-max search in the expected ex post regret can also be used [3,5], but this will not be investigated here.
We will focus our attention onto the simplest newsboy model and consider
how the dispersion of the population can be summarized during the
max-min search. When the usual family 
is
considered, the Scarf's theorem follows [2,4,6].
In a previous paper [1], we have introduce another measure
of the dispersion, namely the inter-means parameter 
Eq. 6,
and it has been proved that assuming an exact knowledge of 
instead of 
leads to a different conclusion.