Challenges in the Era of Globalization - iaabd

Challenges in the Era of Globalization
Edited by Emmanuel Obuah
was to determine the mathematical methods used to measure efficiency, data used, models specified,
sensitivity analysis employed, validity and robustness of techniques, results obtained and policy
implications. In terms of methods used to measure efficiency, Hollingsworth found that the main
technique used is the non-parametric Data Envelopment Analysis (DEA). In fact up to 1997, he found that
two thirds of the studies used DEA models alone and about one fifth used DEA along with regressions
analysis. His findings were similar in 2003 where about 50% used DEA alone and about a quarter used a
two stage analysis with DEA and regression analysis. Although more complex analysis, such as the
application of the Malmquist Index are being used, the non parametric DEA technique has been by far the
most frequently used mathematical technique to measure efficiency in healthcare. He also found that the
studies focus on technical rather than allocative efficiency. Moreover, according to Coelli et al. (2005),
DEA is greatly preferred in efficiency analysis in non-profit sector such as health institutions because
random noise is less of a problem, multiple inputs are used and multiple outputs are produced. Also price
data are difficult to find and setting up a production function is difficult. Data Envelopment Analysis
defines efficiency as the measure of how much output is achieved in relation to how much input is used.
More output for the same input achieves greater efficiency as does producing the same output for less
input. Since its development by Charnes et al. (1978), the DEA has been widely applied to non-profit
organizations. DEA uses Linear Programming to establish the efficiency frontier from a sample data. The
efficiency of a DMU is then measured relative to the efficiency of all others in the sample, subject to the
restriction that all DMUs lie on or below the frontier (Bjurek et al. 1990). The original DEA mathematical
model was proposed by Charnes et al. (1978).The proposed fractional programming model is replaced
with an equivalent linear programming formulation through a series of transformations (Charnes et al.,
1978). Efficiency can either be characterized with an input orientation or an output orientation. In this
study we will consider the input orientation (Djerdjouri et al., 2007). For the input oriented model a
decision-making unit (DMU) is not efficient in utilizing its inputs to produce given amounts of output if it
can be shown that some other DMU or a combination of DMUs can produce the same amount of output
with less of some resource (input) and no more of any other resource. Conversely, a DMU is efficient if
this is not possible. The linear programming model is formulated as:
[VRS]: Minimize E (1)
Subject to: WX ≤ EX0 (2)
WY ≥ Y0 (3)
WI = 1 (4)
W ≥ 0 (5)
where X and Y are the input and output matrices, respectively; X0 and Y0 are the input and output vectors,
respectively for the DMU being assessed; W is a vector representing the weights (%) of inputs and
outputs of DMUs used in constructing a composite DMU; and E is the efficiency index. If the optimal
solution of the model gives E=1, then the test DMU is relatively efficient and if E