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This problem concerns the inventory stocking policies for type O negative blood at a particular hospital. Although some blood types are compatible...

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13.
This problem concerns the inventory stocking policies
for type O negative blood at a particular hospital. Although
some blood types are compatible with others, a person having
type O negative cannot receive any other type. Thus we can
isolate this type and treat it separately from others. The supply
of this type occurs essentially at random from public donations
at a mean rate of, say, four pints per day. The demands are also
essentially random in nature, at a rate of three pints per day. On
the average, more is received than is used, and some will be
discarded. It is expensive to keep (on the order of $5 per pint per
day) because special procedures needed to protect the medical
quality. Therefore, it has been decided to establish a maximum
inventory level, N, such that whenever the available supply is N
additional donations will be refused or used to replace "old"
blood whose shelf life has made it less desirable than new blood.
Because of the random nature of both supply and demand, there
will be occasions when there is a need for blood and none is on
hand. Whenever this happens, blood can be obtained on very
short notice from another hospital at a cost of $30 per pint. There
is no medical problem associated with doing this; it is purely a
matter of cost. Using a continuous time Markov model, show
how to determine the optimal N.

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