In order to illustrate a practical application of DEA we consider
an example from the empirical study of Scheel (1999). This
concrete data analysis is about the efficiency of 63 agencies of a
German insurance company, see Table 12.1. The input
and output
variables
were as follows:
Clients of an insurance company are those who are currently served
by the agencies of the company. They are classified into several
types which reflect, for example, the insurance coverage. Agencies
should sell to the clients as many contracts with as many premiums
as possible. Hence the number of clients (,
,
) are
included as input variables, and the number of new contracts
(
) and the sum of new premiums (
) are included as output
variables. The potential new premiums (
) is included as input
variables, since it depends on the clients' current coverage.
Summary statistics for this data are given in Table 12.2.
The DEA efficiency scores and the DEA efficient levels of inputs
for the agencies are given in Tables 12.3 and
12.4, respectively. The input efficient score for each
agency provides a gauge for evaluating its activity, and the
efficient level of inputs can be interpreted as a 'goal' input.
For example, agency 1 should have been able to yield its activity
outputs (,
) with only 38% of its inputs, i.e.,
,
,
, and
. By contrast, agency
63, whose efficiency score is equal to 1, turned out to have used
its resources 100% efficiently.