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 (multi-period, multi-product, 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 [4,1]. Nevertheless, when applying this solution, the Gaussian distribution is often used, sometimes without justification, or outside its natural range of validity.
In this paper, our aim is to analyze the consequences of a limited
knowledge concerning the distribution of the demand. For that, we
will use the simplest newsboy model and consider how the dispersion
of the population can be summarized. The usual choice 
is considered, but also another one, the inter-means parameter, that
seems to be efficient.
In the next sec:The-newsboy-problem, we will recall the
optimal solution of the classical newsboy problem, together with the
formula of the cost of uncertainty. This cost appears to be the sum
of two terms, the cost of excessive inventory and the loss of opportunity.
In 3, we will assume that the average
demand is precisely known and analyze the impact of the choice of
the shape of the distribution of the demand together with the value
of the standard deviation 
.
The 4 analyzes how to optimally describe
the dispersion of the demand and introduces a new parameter that appears
to be a more efficient one. By the way, we will give a closed form
of a bound for the cost of uncertainty. This appears to be surprisingly
linear in and in the unit selling price.