In this paper, we have shown that the best decision for the newsboy
problem depends heavily on the choice of the dispersion measure. The
"Scarf's rule" follows when assuming an exact knowledge
of the variance, while another strategy follows when assuming an exact
knowledge of the intermeans parameter 
.
Thereafter, we have studied the relations between and 
and have shown that 
for all the
distributions of relevance when modeling the supply chain. Moreover,
we have studied how this new measure of the dispersion can be extracted
from historical data and have shown that the estimator 
doesn't behave worse than the estimator 
.
Further work must be done in order to obtain more exact results concerning
the sampling distribution of . In particular, obtaining distribution
free bounds for the bias and the dispersion of would be
useful.
In any case, the exact identification of reduced parameters concerning
the demand models seems to be questionable, and a description using
larger families of pdf with confidence intervals such as 
or 
seems to
be the way of a robust description of the problems to solve concerning
the supply chain.