We have derived a newsvendor model with two buyers
having different priorities in case of shortages, and a price
setting supplier offering a pre-order opportunity. Though the
pre-order opportunity should favor the supplier, enabling him
to allocate some risk to his buyers, it turns out that when he is
a price setter, he will set the price for pre-ordering high enough
that this option will not be used by the buyers. Of course, as the
data set presented to support this claim is very limited (though
some more data are available than presented in this paper), it
is obvious that more comprehensive numerical studies should
be undertaken. It also seems to be the case that the supplier
can make his pre-order price decision using a more aggregate
model. This is of course of great help as the detailed model is
very complex and involves finding Nash-equilibria.