BOOKS OF RtfiDIfGS - PAHO/WHO

First, the policy that minimizes the total expected one-period cost was derived
[5]. It was shown that this policy involves the following operaiions:
(I) first allocate all available retention units so as to equalize the utilization
rates at all HBB's;
(2) then allocate all available rotation units (which are not subject to spoilage)
so as to equalize the availability rates at ai1 HBB's.
It was shown thait this pucicy is independent of the unit penalty. costs, and that is
maximizes both the availability and the utilization of blood in the region, simultaneously.
That is, any deviation froni the policy that would reduce utilization would also
result in reduced availability for the next period, and vicc versa. It was next shown
[6] that this policy was not only myopically optimal but also approximately optimal
in the long run. Further, in a large number of cases that were tested by computer, the
utilization and availability rates computed froni the myopic results also corresponded
to the absoluite optimal values comnputed.
This result established the principle that a distribution policy should seek to
equalizc utilization rates and availability rates. This is also a policy that has thc
essential elerents of "fairness' in equally spr!ading the nonavailability and
nonutilization risks among hospitais regardless of their relative size and is consequently
a highly defensible policy.
Finally, it was shown that the highest possiblc regionil availability and utilization
rates are achieved whcin the desired inventory level for each blood type in each
HBB is at the value that minimizes the total number of rotational units that are
required to achieve these availability and utilization rates.
It is a straightforward effort by computer to calculate the combination of inventory
level and schcduling factor that requires the minimum number of rotational
units. The minimum number of rotational units required to achieve a fixed utilization
rate of 98% and an availability rate of 95% are indicated by the points connected by
the straight line segments in Figure 2. Thc irregular behavior of this solution is due to
the fact that inventory levels must be integer values and rounding occurs on very
small absolute values. As an example, the minimum rotational shipments required to
an HBB of mean usage of 1.5 units daily to obtain the target goals above occur when
the desired inventory is 5 units, and the scheduling factor is set to 0.67. The trend
line which is drawn in the heavy line in Figure 2 is meant to indicate simultaneously
the optimal values in inventory level and scheduling factor for given values of mean
usage.
Adding operational constrainis
The above distribution model of equalizing availability rates and utilization
rates among the HBB's is illustrated by the two curved lines in Figure 3. The upper
curved line shows the minimum total shipments required to achieve a fixed
availability rate at a HBB of a given mean usage. The lower curved line shows the
maximum retention shipments to achieve a fixed utilization rate. The area between
the curves would have to be met by rotational shipments. As can be seen from the
right end of the curves where the tails meet, this results in a situation where the larger
usage HBB's receive almost all of their shipments in older retention units, while the
smaller usage HBB's receive almost all of their shipments in fresh rotation units.
UITERFACES November 1979
- 314 -