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5. Fuad Selamzade: Measurement of the Efficiency of Azerbaijan Region Hotel
6. Organization: Window Analysis and Malmquist Index
By using a priori knowledge about the relative values of inputs and outputs for DEA
window model, the model including multiplier constraints to obtain definitive and
more realistic productivity estimates is suggested by Asmild et al. (2004). Here, the
i
dimensions sxL and rxL are included in the model, being used through the C input
o
and C output constraint matrices respectively. In this case, the formula (9) takes the
following form:
Θkwt = minθ,λ,Zθ (10)
The effect of adding these multiplier constraints to the DEA model is to eliminate
them by the constraints, although there are some old (or unconstrained) reference
points. This is done by adding flexibility to z`s. As a result, while the calculation of
the greater efficiency and Malmquist index for observations within the bounds, the
results of the small input activity scores, lower super-efficiency scores are obtained
for the observations out of bounds.
"Malmquist Index Total Factor Productivity" (TFP) was developed by Malmquist
(1953) to determine how the efficiency changes over time in the evaluation process
of efficiencies. This index measures the change in TFP between two data points by
calculating the differences ratios of each data point by using common technology.
This measurement is performed with the distance function which is used to define
production technologies having multiple inputs and outputs without specifying
targets such as cost minimization or profit maximization (Griffel-Tatje & Lovell:
1995: 171).
When a technology is discussed as the reference technology for the period t, the
output-oriented Malmquist TFP change index can be written for the s (base period)
and t periods as follows (Coelli, et al., 1998: 291);
( , )
( , , , ) = ( , ) (11)
0
0
0
Alternatively, when discussing the period s as reference, the calculation changes as
follows:
( , )
0
( , , , ) = ( , ) (12)
0
0
s
As it can be seen from the equations above, d0 (yt,xt) notation shows the production
element from period t to period s. Malmquist TFP Index can be shown as the geometric
mean of different functions as follows (Kutlar, Yuksel and Bakirci, 2011: 139);
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