Dynamic Probabilistic Indices - Probabilistic Composition of Preferences, Theory and Applications - page 72

best by every criterion given by the product of the probabilities of not being the best
according to each criterion. In this case, the value of the Malmquist index greater
than unity represents an increase of inef

ciency compared to the previous period.
Instead, values below 1 indicate increased ef ciency.

In Table 7.2 it can be seen that many companies present similar ef ciency

values, both in the static and the dynamic evaluations. In the 2009 analysis, only
twelve companies present a score above the threshold of 0.05 in the progressive
approach and only eighteen present a score lower than 0.95 in the conservative
approach. From 2008 to 2009, according to neither calculation of the Malmquist
index there were more than twelve companies outside the interval from 0.975 to
1.025.
The difference between the two approaches is enlightened by the scores of
CELTINS, which, serving a small market spread on a large region, derives from its
ample network the best score when the optimistic progressive algorithm is applied
and bad scores when the pessimistic conservative approach looks for good per-
formance with respect to all the criteria.
As an example of how the calculation is developed, Table 7.3 presents values of
COELBA evaluations. This distributor showed remarkable growth along the

rst
decade of this century without raising operational costs. While the operational cost
fell 3.6 % from 2003 to 2009, its network expanded 67 %, the number of customers
increased 38 % and the market third variable grew 42 %.
In the first lines of Table 7.3 , the entries 0.4818, 10.5197 and 11.9413 of
COELBA in Table 7.1 can be obtained dividing the absolute values of 201862,

Table 7.3 Computations in the determination of Malmquist indices for COELBA
Operational Cost (R$1,000.00) Network

(km)

Consumers Market

(MWh)

2008 absolute 418,981 201,862 4,407,561 5,003,158

2008 relative 0.4818 105.197 119.413

2009 absolute 436,436 215,001 4,622,046 5,342,574

2009 relative 0.4926 105.904 122.414

Probabilities relative to 2008 frontier
2008 max

0.1373 0.1629 0.0143

2008 min 0.0028 0.0037 0.0068

2009 max 0.1423 0.1635 0.0147

2009 min 0.0027 0.0037 0.0065

Probabilities relative to 2009 frontier
2009 max 0.1011 0.1617 0.0141

2009 min 0.0030 0.0035 0.0053

2008 max 0.0857 0.1610 0.0137

2008 min 0.0031 0.0036 0.0055