Page 35 - Azerbaijan State University of Economics

THE JOURNAL OF ECONOMIC SCIENCES: THEORY AND PRACTICE, V.77, # 1, 2020, pp. 31-50

In this case, the input-oriented BCC model is calculated by solving the efficiency of
(= 1,…, n) of DMU0 by solving the following linear programming model,

(BCC0) min θB (6)

Constraints are θBx0 – X λ ≥ 0; yλ ≥ y0; eλ = 1; λ ≥ 0 where θB is a numeric value.
The dual multiplier form of this linear program (BCC0) is as follows;

max z = y0 – u0 (7)

Constraints are vx0=1; -vX + uY - u0e ≤ 0; v ≥ 0, u ≥ 0; where; u0 is a free signal
variable (positive, negative or zero), and z and u0 are numerical values.

In DEA, panel data is collected and used in Window Analysis to overcome problems
experienced when the number of the decision-making units (DMU)s is limited to the
number of input and output variables. The mean efficiency of DMU can be monitored by
Window Analysis (Charnes et al. 1984). Thus, performance comparisons of the DMUs
within a fixed time can be made with the same DMU and another DMU within the same
period of time. This analysis evaluates the performance of DMU in time by supposing that
there is a different unit in each period (Kutlar, Kabasakal and Babacan, 2015: 78).

DEA is a nonparametric measurement approach for Window Analysis. Let the
number of DMUs is represented by N (n = 1,2, ..., N) supposing that m is used to
produce output in the period T (t = 1,2, ..., T) s. In this case, there are as many
t
observations as NxT, in the period t, r dimensional input vector of n DMUn is
n
n
n
n
n
n
n
n
xt =(x1t ,x2t ,...xrt ) and s-dimensional output vector yt =(y1t ,y2t ,...yst ). At the width
of w (1 ≤ w ≤ T), , k is indicated by kw in the window starting at time t and observed
up to NxW (Asmild et al., 2004: 70).

The matrix for the inputs and outputs of this Window Analysis can be formed as
follows:

1 2 … 1 2 …

1

1
2
2

= +1 +1 … +1 ; = +1 +1 … +1 (8)
⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮
2
1

2
( 1 + … + ) ( + + … + )
+

ı
The input-oriented DEA window analysis formula can be written for DMUt under
the assumption of constant returns to scale as follows (Charnes et al. 1984):

θkwt = minθ,λθ (9)
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