Assuming a low value of uncertainty 
obviously leads to
an order quantity near the identified mean demand. On the contrary,
the preceding section has shown that the optimal order quantity may
vary to a great extent for different demand models even when assuming
the same characteristics 
, especially
for high value of 
. Let us now discuss the
meaning and the potential validity of the hypotheses that were assumed
to obtain these results.
The first point to be mentioned concerns what is modeled. A probability
function like 
can model our lack of actual
knowledge concerning the future demand. We may for example think that
a better knowledge (at ordering time) can be reached but that its
cost would stay beyond the additional benefits resulting from this
additional knowledge. A discussion of such cost balancing is undertaken
in (Eeckhoudt and Godfroid, 2000). Another point of view is that markets
are intrinsically wild and turbulent so that the probability function
models the very nature of market, and not only a lack of knowledge.
The second point concerns what experimental procedure can be used
to determine . A ''gedachte Experiment''
is as follows: starting with a great number of exact copies of the
actual world, put different order quantities in these worlds, inducing
them to evolve (independently) in different manners and observe what
happens at selling time. This experiment is obviously impossible to
carry out. One cannot escape this point of view by considering approximations
obtained from times series, since only ergodicity can justify such
approximations, without mentioning the fact that actual times series
are quite ever too short to conclude, even assuming ergodicity.
A third point is that the actual demand cannot be measured, even afterwards
when the demand overflows the inventory. In such a case, the only
actual knowledge is the observation of the stock-out 
,
not the exact value of 
1. Therefore, a slight shift towards over-sizing the inventory could
be a good policy since it results into a better knowledge for a slight
cost (Tang and Grubbstrom, 2002).
From these considerations, a more realistic point of view is to consider the optimization of the purchase decision against a family of demand models with common practically identifiable characteristics. Examining this situation with the max-min method when assuming that the usual dispersion parameters are identifiable is the aim of the following Section.