1. The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1463-5771.htm
Indian business
Performance modeling of Indian schools
business schools: a DEA-neural
network approach
221
S. Sreekumar
Rourkela Institute of Management Studies, Rourkela, India, and
S.S. Mahapatra
Department of Mechanical Engineering, National Institute of Technology,
Rourkela, India
Abstract
Purpose – The main purpose of the present study is to develop an integrated approach combining
data envelopment analysis (DEA) and neural network (NN) for assessment and prediction of
performance of Indian B-schools for effective decision making as error and biasness due to human
intervention in decision making is appreciably reduced.
Design/methodology/approach – DEA, being a robust mathematical tool, has been employed to
evaluate the efficiency of B-schools. DEA, basically, takes into account the input and output
components of a decision-making unit (DMU) to calculate technical efficiency (TE). TE is treated as an
indicator for performance of DMUs and comparison has been made among them. A sensitivity
analysis has been carried out to study robustness of the ranking of schools obtained through DEA.
Finally, NN is used to predict the efficiency when changes in inputs are caused due to market
dynamism so that effective strategies can be evolved by the managers with limited available data.
Findings – A total of 49 Indian B-schools are chosen for benchmarking purpose. The average score of
efficiency is 0.625 with a standard deviation of 0.175 when Charnes, Cooper and Rhodes (CCR) model is
used. Similarly, when the Banker, Charnes and Cooper (BCC) model is used the average score is 0.888 with a
standard deviation of 0.063. The rank order correlation coefficient between the efficiency ranking obtained
through CCR and BCC model is 0.736 ( p ¼ 0.000) which is significant. The peer group and peer weights for
the inefficient B-schools have been identified. This is useful for benchmarking for the inefficient DMUs.
They can identify the parameters in which they lack and take necessary steps for improvement. The peer
group for the inefficient B-schools indicates the efficient B-schools to which the inefficient B-schools are
closer in its combination of inputs and outputs. The TE obtained through DEA is used as output variable
along with input variables considered in DEA as input and output parameters in a generalized regression
NN during training phase. It can be observed that root mean square error is 0.009344 and 0.02323 for CCR-
and BCC-efficiency prediction, respectively, during training. Similarly, root mean square error is 0.08585
and 0.03279 for CCR- and BCC-efficiency prediction, respectively, during testing. Now, individual schools
can generate scenario with the data within their control and test their own performance through NN model.
Originality/value – This work proposes integration of DEA and NN to assist the managers to
predict the performance of an individual DMU based on input consumed and generate various
“what-if” scenarios. The study provides a simple but comprehensive methodology for improving
performance of B-schools in India.
Keywords Benchmarking, Data analysis, Decision making units, Neural nets
Paper type Research paper
Benchmarking: An International
Journal
Vol. 18 No. 2, 2011
1. Introduction pp. 221-239
India has liberalized the business education market in 1990s resulting in a rapid q Emerald Group Publishing Limited
1463-5771
growth of business schools offering programs at both undergraduate as well as DOI 10.1108/14635771111121685
2. BIJ post-graduate levels. The development of B-schools is largely adopting the policy of
18,2 self-sustainability and maximum of them are self-funded operated by private promoters.
Most of the recruiters in India consider qualification in management as an added
advantage. It caused demand in management education leading to an intense
competition among the B-schools in the country. The low investment for entry and
flourishing market has engineered the growth of B-schools throughout the country.
222 Mintzberg (1973) has pointed that the management school gives students degrees but it
hardly teach them how to manage. Therefore, such degrees can barely be considered as
prerequisites for managing firms in professional manner. On the contrary, Whitley et al.
(1981) have advocated that many employers perceive holders of business education
degree obviously distinguishes from those who do not possess it. Generally, students
feel that getting a management degree from a reputed school may act as a formal way to
batter career planning. Indian B-schools play a major role for providing career
opportunity for around 68 percent of the Indian population who are in the 22-27 years age
group. The quality of education imparted in Indian B-schools is reasonably good enough
and many firms in the globe prefer Indian management graduates as a result of
globalization and liberalization of the market economy. As a business strategy,
manpower of cross-cultural nature may have edge over competitors (Sahay and Thakur,
2007). Dayal (2002) emphasized on changing the structure of management education in
India and suggested a strategy for institutional development for upgrading the quality
of the academic program. The Indian B-schools should understand the emerging context
of the economy, the industries, business and their needs and work out what they are
delivering today and what they are expected to deliver tomorrow (Sahay and Thakur,
2008). In this context, it is important for each of the Indian B-schools to know where one
stands and design programs and pedagogy which will meet the future business needs.
The new B-schools can set well-established institutes as their peers and follow them to
become competitive. Although there is an unprecedented growth of schools in recent
times, assessment on performance and efficiency of them is found to a limited extent in
the literature. Measuring efficiency levels of the B-schools is an important issue for
prospective students, parents, employers, and program administrators. Ranking of them
can provide useful guidelines to all the stake holders involved in management education
(Ojha, 2005). Some magazines like Outlook, Business World, Indian Management, etc.
publish the annual report on the ranks of the Indian B-schools. However, ranking
mechanism and sample size is questionable in such efforts.
In this paper, a non-parametric technique called data envelopment analysis (DEA) is
adopted to rank Indian B-schools based on their efficiency score. The scores can suggest
inefficient and low-performing schools in an effective manner. Though the concept of
benchmarking is good for improving the performance of individual unit, the problem
associated with it is lack of transparency in data sharing. Therefore, methodology which
will allow the individual schools to generate scenario with the data within their control
and perform at the desired level is highly desirable. To address this problem, a neural
network (NN) model is developed and trained to predict the performance level of the
individual B-schools. The proposed model, in this paper, integrates the DEA and NN
models to predict the performance of Indian B-schools. The data necessary for this study
are collected from standard weekly business magazines and journals. The data sources
employ professional surveying agencies for data collection. Therefore, data are
considered to be reliable although collected from secondary sources. For the purpose
3. of the confidentiality of the schools and avoidance of conflicting interests, the identities Indian business
of schools are not disclosed. However, some of the top Indian B-schools such as Indian schools
Institute of Management, Xavier Labour Relations Institute, Management Development
Institute, and Faculty of Management Studies (Delhi University) have been included in
the dataset.
2. Literature review 223
In the recent years, several studies have been undertaken for analysis of efficiency in
education sector using DEA methodology. Each study differs in its scope, meaning, and
definition of decision-making units (DMUs). Tomkins and Green (1988) conducted DEA
analysis to test the performance of 20 accounting departments in UK. Johnes and Johnes
(1993) investigated the use of DEA in the assessment of performance of university
departments of the UK over the period 1984-1988. McMullen (1997) has applied DEA to
assess the relative desirability of Association to Advanced Collegiate Schools of
Business-accredited MBA programs. The authors have incorporated several attributes of
MBA programs into the model for finding out most desirable program in terms of these
attributes. McMillan and Datta (1998) have assessed the relative efficiency of 45 Canadian
universities using DEA. A subset of universities including universities from each of three
categories such as comprehensive with medical school, comprehensive without medical
school, and primarily undergraduate are regularly found efficient while some universities
exhibit inefficiency. But, overall efficiency for most of the universities is relatively high.
Ramanathan (2001) has compared the performance of selected schools in The Netherlands
using DEA and found that the efficiencies of the schools are closely related with their
performance. The authors have also observed that several non-discretionary input
variables can influence the efficiency scores but some of them are not in direct control of
management of the school. Lopes and Lanzer (2002) have addressed the issue of
performance evaluation, productivity, and quality of academic departments at a university
using a DEA model for cross-evaluation between departments considering the dimensions
of teaching, research, and service quality. The authors have observed zero correlation
between department teaching, research, and service and weak correlation between research
productivity and quality. Ray and Jeon (2003) in their study employed a measure of
Pareto-Koopmans global efficiency to evaluate the efficiency levels of MBA programs in
Business Week’s top-rated list. They computed input and output-oriented radial and
non-radial efficiency measures for comparison purpose. Among three-tier groups, the
schools from a higher tier group on an average are more efficient than those from lower tiers
although variations in efficiency levels do occur within the same tier. In India,
comparatively less studies have been conducted for performance evaluation of B-schools
using DEA. Wadhwa et al. (2005) has proposed integration of DEA and knowledge
management methods to evaluate the efficiency of technical education system (TES) in
India. The authors claim that the suggested approach can assist decision makers in
selecting proper institutes to further strengthen the TES in an efficient and effective
manner. A number of successful business applications of artificial neural networks (ANNs)
have been discussed in the literature, particularly in financial services (Tam and Kiang,
1992), transportation services (Nordmann and Luxhoj, 2000), telecommunications
(Mozer et al., 1999), etc. Lu et al. (1996) have compared the effectiveness of NNs and the
multinomial logit model, and concluded that the ANNs perform better than logit regressions
in franchising decision making. Wu et al. (1995) have applied NN approach for the decision
4. BIJ surface modeling of apparel retail operations. Tam and Kiang (1992) have discussed a back
18,2 propagation NN application in predicting bankruptcy of financial institutions based on
financial ratios. Dutta and Shekhar (1988) have applied NNs to a generalization problem of
predicting the corporate bond ratings. Chiang et al. (1996) have discussed a back
propagation NN approach to mutual fund net asset value forecasting. Hu et al. (2004) have
found that ANN can perform better than logistic regression in the modeling of foreign
224 equities. Kimoto et al. (1990) have applied modular NNs to develop a buying and selling
timing prediction system for stocks on the Tokyo Stock Exchange using a high-speed
learning method called supplementary learning. Odom and Sharda (1990) have developed
an NN model using back propagation for prediction of bankruptcy and compared results
with discriminant analysis. It is claimed that ANN model performs better than discriminant
analysis which is generally used for such type of problems. In education sector, some ANN
models have been reported for prediction of academic performance of educational
institutions considering qualitative as well as quantitative criteria (Hoefer and Gould, 2000;
Kannan, 2005; Naik and Ragothaman, 2004; Wang, 1994). However, the application of NNs
to model qualitative and intangible aspects of different services is not addressed adequately
in the literature of education. It may be apposite to extend implementation of NNs to address
more general and theoretical issues in service sector, such as education.
3. Methodology
3.1 Data envelopment analysis
DEA, introduced by Charnes et al. (1978), computes efficiency score of each unit by
comparing the efficiency score of each unit with that of its peers. Geometrically, a
frontier can be constructed comprising of best performers. The units lying on the
frontier are said to be efficient, and other units are treated as inefficient.
Algebraically, the DEA model can be written as:
Pn Xn Xm
ur yrj0
max hj0 ¼ Pr¼1 m subject to ur yrj0 2 vi xij0 # 0 ur ; vi $ 0 ;r; i ð1Þ
i¼1 vi xij0 r¼1 i¼1
where:
hj0 ¼ relative efficiency of target DMU j0.
r ¼ 1, 2,. . .n the number of outputs.
i ¼ 1, 2,. . .m the number of inputs.
j ¼ 1, 2,. . .s the number of DMUs.
ur ¼ weight attached to the output r.
vi ¼ weight attached to the input i.
yrjo ¼ quantity of rth output produced by the DMU Jo.
xijo ¼ quantity of ith input consumed by the DMU Jo.
The DEA models may have any of the two orientations viz. input orientation and
output orientation. Input orientation means how much inputs can be reduced while
maintaining the same level of output. But output orientation of DEA is characterized
by how much output can be increased while keeping the level of inputs constant.
The latter orientation is more relevant for many service providers where the objective
is to maximize the output maintaining the same level of inputs.
5. Another variation to a DEA model is the returns to scale (RTS) assumption. Constant, Indian business
decreasing, increasing, and variable RTS assumptions may be employed. Constant return
to scale (CRS) implies that doubling inputs will exactly double outputs. Decreasing return
schools
to scale implies that doubling inputs will less-than-double outputs. Increasing return to
scale implies that doubling inputs will more-than-double outputs. Thus, variable return
to scale (VRS) allows for a combination of constant, increasing, and decreasing inputs
and outputs. The DEA model shown in Equation (1) assumes a CRS. The drawback with 225
the CRS model is that it compares DMUs only based on overall efficiency assuming
constant RTS. It ignores the fact that different DMUs could be operating at different
scales. To overcome this drawback, Banker et al. (1984) developed a model which
considers variable RTS and compares DMUs purely on the basis of TE. The model can be
shown as below:
min u
Xn
subject to li xji 2 uxjj0 # 0 ;j
i¼1
X n ð2Þ
li yrj 2 yjj0 $ 0 ;r
i¼1
li ¼ 1 ;i
where:
u ¼ efficiency score.
li ¼ dual variable.
The difference between the CRS model (1) and the VRS model (2) is that the li is
restricted to one. This has the effect of removing the constraint in the CRS model that
DMUs must be scale efficient. Consequently, the VRS model allows variable RTS and
measures only TE for each DMU. Thus, a DMU to be considered as CRS efficient,
it must be both scale and technical efficient. For a DMU to be considered VRS efficient,
it only needs to be technically efficient.
3.2 Neural network
An ANN is an information processing paradigm that is inspired by the way biological
nervous systems, such as the human brain and process information. It is composed of a
large number of highly interconnected processing elements (neurons) working in
conjunction to solve specific problems. ANNs, like people, learn by example. An ANN is
configured for a specific application such as pattern recognition or data classification
through a learning process. Learning in biological systems involves adjustments to the
connections that exist between the neurons which is true for ANNs as well. An NN
consists of a network of neurons. Each neuron is associated with an input vector,
a weight vector corresponding to the input vector, a scalar bias, a transfer function, and
an output vector as shown in Figure 1. An NN may consist of one or more neurons in each
layer. In a network, the final layer is called the output layer and all previous layers are
called hidden layers. In the hidden layers, the output of a layer becomes the input for
the following layer. The transfer function of a neuron converts the input to the output of
the neuron. Multi-layer NNs are quite powerful tools used in solving many different
complex problems. Various types of NNs are available for different purposes. In this
study, a multi-layer back propagation NN architecture is adopted.
6. BIJ Teach/use
18,2 W1
X
W2
X
Inputs Weights
226 Neuron Output
Wn
X
Figure 1.
A typical neuron
Teaching input
A typical NN is shown in Figure 2. There are three layers – a layer of “input” units is
connected to a layer of “hidden” units, which is connected to a layer of “output” units.
The behavior of the output units depends on the activity of the hidden units and the
weights between the hidden and output units. The architectures of ANN may be single
layer or multi-layer. In the single-layer organization, all units are connected to one
another. It constitutes the most general case and is of more potential computational
power than hierarchically structured multi-layer organizations.
As discussed, NNs are capable of learning complex relationships in data. The problems
NNs are used for can be divided in two general groups: classification problems in which
one tries to determine what type of category an unknown item falls into and numeric
problems where one attempts to predict a specific numeric outcome (Palisade Corporation,
2008). There are many computer software packages available for building and analysing
NNs. In this work, Neural Tools Version 5.0 by Palisade Corporation (2008) is used.
This software automatically scales all input data. Scaling involves mapping each variable
to a range with minimum and maximum values of 0 and 1. A non-linear scaling function
known as “tanh” is used as activation function. This function tends to squeeze data
Input Hidden Output
Input 1
Input 2
Output
Input 3
Figure 2.
A simple feed forward NN Input 4
with three layers
7. together at the low and high ends of the original data range (Mostafa, 2009). An NN Indian business
configuration called generalized regression neural networks (GRNN) put forward schools
by Specht (1991) is adopted to give the best possible predictions. The rationale for
choosing the GRNN configuration lies in the fact that it is a good numerical predictor and
user need not to make decisions about the structure of a net. These nets always have two
hidden layers of neurons, with one neuron per training case in the first hidden layer, and
the size of the second layer determined by some facts about training data. 227
GRN architecture. A generalized regression neural (GRN) net for two independent
numeric variables is structured as shown in Figure 3 with the assumption that there
are just three training cases (Palisade Corporation, 2008).
The pattern layer contains one node for each training case. Presenting a training case to
the net consists here of presenting two independent numeric values. Each neuron in the
pattern layer computes its distance from the presented case. The values passed to the
numerator and denominator nodes are functions of the distance and the dependent value.
The two nodes in the summation layer sum its inputs, while the output node divides them
to generate the prediction. The distance function computed in the pattern layer neurons
uses “smoothing factors”; every input has its own “smoothing factor” value. With a single
input, the greater the value of the smoothing factor, the more significant distant training
cases become for the predicted value. With two inputs, the smoothing factor relates to the
distance along one axis on a plane, and in general, with multiple inputs, to one dimension
in multi-dimensional space. Training a GRN net consists of optimizing smoothing factors
to minimize the error on the training set, and the conjugate gradient descent optimization
method is used to accomplish that. The error measure used during training to evaluate
different sets of smoothing factors is the mean squared error. However, when computing
the squared error for a training case, that case is temporarily excluded from the pattern
layer. This is because the excluded neuron would compute a zero distance, making other
neurons insignificant in the computation of the prediction.
3.3 Data and data classification
For solving the benchmarking problem, 49 top B-schools of India are considered using
convenience sampling method. Data on 11 parameters as listed below are collected from
various secondary sources. The secondary source reference includes popular Indian
magazines like Outlook, Business World, Indian Management, and B-school directories
which publish the annual report on the ranks of the Indian B-schools (Table I).
Output
Figure 3.
A simple GRN
Inputs Pattern Summation architecture
later layer
8. BIJ The data collected on the above parameters are classified into two categories based on
18,2 their nature for DEA and NN application. The criteria of selection of inputs and
outputs are quite subjective; there is no specific rule for determining the procedure for
selection of inputs and outputs (Ramanathan, 2001). The classification of input and
output is done as follows (Sreekumar and Patel, 2007):
Input:
228 X1: IC
X2: IF
X3: FEE
Output:
Y1: II
Y2: PP
Y3: IL
Y4: RS
Y5: SS
Y6: FS
Y7: ECA
Y8: SAL
S. no. Parameter Abbreviation Explanation
1 Intellectual capital IC Faculty/student ratio, teaching experience of faculty,
corporate experience of faculty/students, PhD/students
ratio, faculty with PhD (abroad), books, research papers,
and cases
2 Industry interface II Revenue from consultancy, revenue from management
development programs, seminars, and workshops
3 Infrastructure and IF Area (in acres), built-up area, computers per batch,
facilities amphitheatre class room, library books, electronic
database, residential facilities, single occupancy room,
and MDP hostel
4 International linkage IL Student exchange program and faculty exchange
program
5 Placement PP Percentage of student placed, median salary, maximum
performance salary, minimum salary, percentage of students placed
abroad, and return on investment
6 Extra curricular ECA National-level events organized and awards won
activities by students
7 Recruiters RS Application of knowledge of subject/skills,
satisfaction analytical skills, communication and presentation
skills, creativity, proactive attitude, and ability to
work in team
8 Students satisfaction SS Satisfaction of ongoing students from the school
9 Faculty satisfaction FS Based on present faculty of the school
Table I. 10 Fee FEE Fee collected from students
List of parameters 11 Salary SAL Initial salary at which graduating students are placed
9. In this study, the DEA and NN has been integrated to have an efficient predicting model. Indian business
DEA, being a robust mathematical tool, has been employed to evaluate the efficiency of schools
B-schools. DEA, basically, takes into account the input and output components of a
DMU to calculate TE. TE is treated as an indicator for performance of DMUs and
comparison has been made among them. A sensitivity analysis has been carried out to
study robustness of the ranking of schools obtained through DEA. Finally, NN is used
to predict the efficiency when changes in inputs are caused due to market dynamism so 229
that effective strategies can be evolved by the managers with limited available data.
4. Results and discussion
The Charnes, Cooper and Rhodes (CCR)-DEA model as discussed above is based on
constant RTS does not consider the size of B-school under consideration while
calculating the efficiency. But in many cases the size of a unit may influence its ability to
produce services more efficiently. So, we have also considered the VRS model for our
study. The B-schools under consideration for our problem contain both private and
government institute. The input for both the category of institute differs widely, so the
output orientation model is used. It may be noted that the Banker, Charnes and Cooper
(BCC) model allows variable RTS and measures only TE for each DMU whereas a DMU
is considered as CCR efficient if it is both scale and technical efficient.
The relative efficiency score of B-schools are analysed and presented in Table II. The
BCC score is based on VRS assumption and measures the pure TE. The CCR score
is based on CRS assumption and consist of non-additive combination of pure TE and
scale efficiency. The table shows that in a scale of 0-1 the average score for the B-schools
is 0.625 with a standard deviation of 0.175 when CCR model is used. Similarly, when the
BCC model is used the average score is 0.888 with a standard deviation of 0.063. The
rank-order correlation coefficient between the efficiency ranking obtained through CCR
and BCC model is 0.736 ( p ¼ 0.000) which is significant. The above table also shows the
peer group and peer weights for the inefficient B-schools. This is useful for
benchmarking for the inefficient DMUs. They can identify the parameters in which they
lack and take necessary steps for improvement. The peer group for the inefficient
B-schools indicates the efficient B-schools to which the inefficient B-schools are closer in
its combination of inputs and outputs. It may also be observed that in both CCR and BCC
score there are multiple numbers of DMUs with efficiency score unity leading to tie case.
The school which appears maximum number of times as peer in the above table may be
treated as the best school. Moreover, this school is likely to be the school which is
efficient with respect to a large number of factors, and is probably a good example of an
exemplary operating performer. Efficient DMUs that appear seldom in the peer set of
other inefficient DMUs are likely to possess a very uncommon input/output mix and are
thus not suitable examples for other inefficient schools (Mostafa, 2009). Now, it is
prudent to check the robustness of the model trough sensitivity.
DEA is an extreme point technique because the efficiency frontier is formed by the
actual performance of best-performing DMUs. A direct consequence of this aspect is that
errors in measurement can affect the DEA result significantly. So, according to DEA
technique, it is possible for a B-School to become efficient if it achieves exceptionally
better results in terms of one output but performs below average in other outputs. The
sensitivity of DEA efficiency can be verified by checking whether the efficiency of a
DMU is affected appreciably:
12. BIJ .
if only one input or output is omitted from DEA analysis; and
18,2 .
dropping one efficient DMU at a time from DEA analysis.
Initially the input “intellectual capital” is dropped from the analysis and TE of DMUs is
calculated, then input “FEE” is dropped, and similarly the outputs “placement performance”
is dropped from both CCR and BCC model. At the second level, the efficient unit DMU1 is
232 dropped to calculate the CCR and BCC efficiency. The results of both the stage are tabulated
in Table III. The table shows that dropping the input “IC” and outputs “PP” one-by-one
causes no significant change in the TE score of DMUs and efficient units are remaining
efficient as such. Change in efficiency score is observed when the input “FEE” is dropped
from the analysis. DMU6 is becoming inefficient when “FEE” is not considered for CCR
efficiency. This indicates that “FEE” is an important input for such schools. At the second
level of analysis, some of the efficient DMUs are dropped one-by-one. It is observed that the
efficient units are remaining efficient as such when DMU1 is dropped from the DEA
analysis but DMU3 becomes an efficient unit for CCR efficiency whereas there is no change
efficiency status for BCC score.
Finally, GRNN model is used to predict efficiency score of DMUs. The prediction
results help the managers to use the available data for strategic decision making when
the data for benchmarking is not shared by DMUs under consideration. The prediction
can also generate various scenarios to guide the managers/administrators for effective
decision making. In addition, human error is avoided during prediction process. Both
CCR- and BCC-efficiency scores are predicted using GRNN model. The three inputs
considered for prediction purpose are IC, IF, and FEE. As mentioned earlier, Neural
Tools version 5.0 (Palisade Corporation, 2008) is used for building the network due to its
flexibility and extensive capabilities. In general, 75 percent of the data is considered for
training for mapping good relationship between inputs and outputs and 25 percent is
used for testing. In this study, 39 cases are used for training the network chosen
randomly from dataset to provide variation during training and ten cases for testing.
The model is used to predict the output for the entire dataset of 49 B-schools. The
network configuration setting is shown in Table IV. The network is run till a reasonable
root mean square error is attained during training period. The number of epochs to
obtain error within tolerance limit happens to be 69 and 98, respectively, for CCR- and
BCC-efficiency prediction during training of the network. Once the network is well
trained, it can be used for testing purpose as generalization capability of the network is
ensured. It can be observed that root mean square error is 0.009344 and 0.02323 for
CCR- and BCC-efficiency prediction, respectively, during training. Similarly, root mean
square error is 0.08585 and 0.03279 for CCR- and BCC-efficiency prediction, respectively,
during testing. The prediction results are shown in Table V. It can be observed that
maximum absolute difference in CCR-efficiency score and the NN prediction is 0.108369
which occurs for DMU9. Similarly, maximum absolute difference in BCC-efficiency
score and the NN prediction is 0.067631 which occurs again for DMU9. For rest of the
cases, the absolute difference between either for CCR or BCC and neural network
prediction is much smaller. The NN prediction of efficiency scores is compared with
scores obtained through DEA using CCR and BCC in Figure 4. It is noted that the pattern
is perfectly followed in both type of prediction.
15. Indian business
CCR-efficiency prediction BCC-efficiency prediction
schools
Net information
Configuration GRNN numeric predictor GRNN numeric predictor
Independent category variables 0 0
Independent numeric variables 3 (IC, IF, and FEE) 3 (IC, IF, and FEE)
Dependent variable Numeric variable (CCR-eff) Numeric variable (BCC-eff) 235
Training
Number of cases 39 39
Number of trials 69 98
Bad predictions (%) (30 percent tolerance) 0.0000 0.0000
Root mean square error 0.009344 0.02323
Mean absolute error 0.005236 0.01606
Std deviation of abs. error 0.007740 0.01679
Testing
Number of cases 10 10 Table IV.
Bad predictions (%) (30 percent tolerance) 0.0000 0.0000 Network configuration
Root mean square error 0.08585 0.03279 for CCR and BCC
Mean absolute error 0.05931 0.02420 efficiency score
Std deviation of absolute Error 0.06208 0.02212 prediction
5. Conclusions
This study is concerned with the ranking of Indian B-schools using a non-parametric
technique and developing an NN to predict the standing of schools based on limited
number of parameters. Both CRS and VRS are considered to obtain the efficiency score
of DMUs. The methodology facilitates in identifying the benchmarked institutions for
the inefficient institutes. The process of benchmarking is useful in identifying the best
business practices and formulating the winning strategies. The DEA methodology can
be quite useful for Indian B-schools in identifying their position relative to their peers,
and in formulating strategies for improvement by right mix of inputs and outputs.
Although the concept of benchmarking is good for improving the performance of
individual unit, the problem associated with it is lack of transparency in data sharing
and data reliability. Some of the schools may not be too enthusiastic to share the data
pertaining to their resource consumption and output produced. This requires a
methodology which will allow the individual schools to generate scenario with the data
within their control and test their own performance through simulation. For this
purpose, an NN model is developed and trained to predict the performance level of the
individual B-schools based on the input level consumed. The paper integrates the DEA
model and NN. The output obtained through DEA model is used for training the NN
for prediction of efficiency score of schools based on the input values. Like any other
study, this paper also has several limitations giving opportunity for further research.
The paper considers 11 parameters relevant for improving quality of Indian B-schools.
The other pertinent factors like quality of inputs (students), investment pattern in the
institution, funds generation by the institution, etc. could have been incorporated
in the model for calculating efficiency score of schools. Next, some of the inputs may
not be fully under the control of management leading to practically infeasible target.
Again as the DEA gives the relative efficiency score, so it gets affected by sample size.
17. 1.2 Indian business
1
schools
0.8 CCR-EFF
Efficiency
0.6 NN-CCR 237
0.4 BCC-EFF
0.2 NN-BCC
Figure 4.
Comparison of NN
0 predictions with
1 5 9 13 17 21 25 29 33 37 41 45 49
DEA results
DMUs
In future study, more number of schools over a period of time may be considered for
better insight into the problem.
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About the authors 239
S. Sreekumar is an Associate Professor in Rourkela Institute of Management Studies, Rourkela
769015, India. His areas of interest include application of DEA for efficiency analysis and
multi-criteria decision making. He has 17 years of teaching experience in the areas of quantitative
techniques and information science. He has published 30 papers in various international and
national journals and conferences. He has also authored two books.
S.S. Mahapatra is Professor in the Department of Mechanical Engineering, National Institute of
Technology Rourkela, India. He has more than 20 years of experience in teaching and research.
His current area of research includes multi-criteria decision making, quality engineering, assembly
line balancing, group technology, neural networks, and non-traditional optimization and simulation.
He has published more than 40 papers in referred journals. He has written few books related to his
research work. He is also currently dealing with few sponsored projects. S.S. Mahapatra is the
corresponding author and can be contacted at: mahapatrass2003@yahoo.com
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