The weights are assigned by DBA to make each service unit look
as efficient as possible. In the above example, we did not know
the relative value of teller hours versus supplies. DBA calculated
a weight for these for B2 based on the linear program
formulation. The weights calculated for hours was vj = 1.429 and
V2 = 0.286 for supply dollars ($s). These weights when plugged
into the above model suggest that the BRS branches B3 and B4
have efficiency ratings of 1.0 or 100% and B2 has an efficiency
rating of 0.857 or 85.7%. Roughly, this means B2 is using about
15% excess resources based on the DBA analysis compared with
B3 and B4 and these savings would be achievable if B2 operated
more like B3 and B4.
When the manager of B 2 is informed that their unit is not
performing as well, the manager could question whether the
weights used for the inputs of hours and supplies are accurate
weights, particularly since these weights are not known in
practice. That manager can be challenged to find any other set of
weights that if applied to all the branches would make B2 look
more efficient while not allowing any other branch to be more
than 100% efficient. They would fail this challenge. The set of
weights calculated already make B2 appear as efficient as
possible compared with the other branches. Any other set of
weights applied to all the units would result in B2 having an even
lower efficiency rating than the current rating of 85.7%. This also
means that if we substitute another set of weights that are
believed to be more reflective of the market than the weights
assigned by DBA, the inefficiency will be greater and the
potential benefits of improving the inefficient units to approach
the best practices will be greater than estimated with the model
above. (Readers are encouraged to explore the impact of using a
different set of weights.)