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3.performance modeling

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3.performance modeling

  1. 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, IndiaAbstractPurpose – The main purpose of the present study is to develop an integrated approach combiningdata envelopment analysis (DEA) and neural network (NN) for assessment and prediction ofperformance of Indian B-schools for effective decision making as error and biasness due to humanintervention in decision making is appreciably reduced.Design/methodology/approach – DEA, being a robust mathematical tool, has been employed toevaluate the efficiency of B-schools. DEA, basically, takes into account the input and outputcomponents of a decision-making unit (DMU) to calculate technical efficiency (TE). TE is treated as anindicator for performance of DMUs and comparison has been made among them. A sensitivityanalysis 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 marketdynamism 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 ofefficiency is 0.625 with a standard deviation of 0.175 when Charnes, Cooper and Rhodes (CCR) model isused. Similarly, when the Banker, Charnes and Cooper (BCC) model is used the average score is 0.888 with astandard deviation of 0.063. The rank order correlation coefficient between the efficiency ranking obtainedthrough CCR and BCC model is 0.736 ( p ¼ 0.000) which is significant. The peer group and peer weights forthe 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 peergroup for the inefficient B-schools indicates the efficient B-schools to which the inefficient B-schools arecloser in its combination of inputs and outputs. The TE obtained through DEA is used as output variablealong with input variables considered in DEA as input and output parameters in a generalized regressionNN 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 0.08585and 0.03279 for CCR- and BCC-efficiency prediction, respectively, during testing. Now, individual schoolscan 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 topredict 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 improvingperformance of B-schools in India.Keywords Benchmarking, Data analysis, Decision making units, Neural netsPaper type Research paper Benchmarking: An International Journal Vol. 18 No. 2, 20111. Introduction pp. 221-239India has liberalized the business education market in 1990s resulting in a rapid q Emerald Group Publishing Limited 1463-5771growth of business schools offering programs at both undergraduate as well as DOI 10.1108/14635771111121685
  2. 2. BIJ post-graduate levels. The development of B-schools is largely adopting the policy of18,2 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. 3. of the confidentiality of the schools and avoidance of conflicting interests, the identities Indian businessof schools are not disclosed. However, some of the top Indian B-schools such as Indian schoolsInstitute of Management, Xavier Labour Relations Institute, Management DevelopmentInstitute, and Faculty of Management Studies (Delhi University) have been included inthe dataset.2. Literature review 223In the recent years, several studies have been undertaken for analysis of efficiency ineducation sector using DEA methodology. Each study differs in its scope, meaning, anddefinition of decision-making units (DMUs). Tomkins and Green (1988) conducted DEAanalysis 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 universitydepartments of the UK over the period 1984-1988. McMullen (1997) has applied DEA toassess the relative desirability of Association to Advanced Collegiate Schools ofBusiness-accredited MBA programs. The authors have incorporated several attributes ofMBA programs into the model for finding out most desirable program in terms of theseattributes. McMillan and Datta (1998) have assessed the relative efficiency of 45 Canadianuniversities using DEA. A subset of universities including universities from each of threecategories such as comprehensive with medical school, comprehensive without medicalschool, and primarily undergraduate are regularly found efficient while some universitiesexhibit inefficiency. But, overall efficiency for most of the universities is relatively high.Ramanathan (2001) has compared the performance of selected schools in The Netherlandsusing DEA and found that the efficiencies of the schools are closely related with theirperformance. The authors have also observed that several non-discretionary inputvariables can influence the efficiency scores but some of them are not in direct control ofmanagement of the school. Lopes and Lanzer (2002) have addressed the issue ofperformance evaluation, productivity, and quality of academic departments at a universityusing a DEA model for cross-evaluation between departments considering the dimensionsof teaching, research, and service quality. The authors have observed zero correlationbetween department teaching, research, and service and weak correlation between researchproductivity and quality. Ray and Jeon (2003) in their study employed a measure ofPareto-Koopmans global efficiency to evaluate the efficiency levels of MBA programs inBusiness Week’s top-rated list. They computed input and output-oriented radial andnon-radial efficiency measures for comparison purpose. Among three-tier groups, theschools from a higher tier group on an average are more efficient than those from lower tiersalthough variations in efficiency levels do occur within the same tier. In India,comparatively less studies have been conducted for performance evaluation of B-schoolsusing DEA. Wadhwa et al. (2005) has proposed integration of DEA and knowledgemanagement methods to evaluate the efficiency of technical education system (TES) inIndia. The authors claim that the suggested approach can assist decision makers inselecting proper institutes to further strengthen the TES in an efficient and effectivemanner. 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 themultinomial logit model, and concluded that the ANNs perform better than logit regressionsin franchising decision making. Wu et al. (1995) have applied NN approach for the decision
  4. 4. BIJ surface modeling of apparel retail operations. Tam and Kiang (1992) have discussed a back18,2 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 foreign224 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. 5. Another variation to a DEA model is the returns to scale (RTS) assumption. Constant, Indian businessdecreasing, increasing, and variable RTS assumptions may be employed. Constant returnto scale (CRS) implies that doubling inputs will exactly double outputs. Decreasing return schoolsto scale implies that doubling inputs will less-than-double outputs. Increasing return toscale implies that doubling inputs will more-than-double outputs. Thus, variable returnto scale (VRS) allows for a combination of constant, increasing, and decreasing inputsand outputs. The DEA model shown in Equation (1) assumes a CRS. The drawback with 225the CRS model is that it compares DMUs only based on overall efficiency assumingconstant RTS. It ignores the fact that different DMUs could be operating at differentscales. To overcome this drawback, Banker et al. (1984) developed a model whichconsiders variable RTS and compares DMUs purely on the basis of TE. The model can beshown 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 ;iwhere: u ¼ efficiency score. li ¼ dual variable.The difference between the CRS model (1) and the VRS model (2) is that the li isrestricted to one. This has the effect of removing the constraint in the CRS model thatDMUs must be scale efficient. Consequently, the VRS model allows variable RTS andmeasures 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 networkAn ANN is an information processing paradigm that is inspired by the way biologicalnervous systems, such as the human brain and process information. It is composed of alarge number of highly interconnected processing elements (neurons) working inconjunction to solve specific problems. ANNs, like people, learn by example. An ANN isconfigured for a specific application such as pattern recognition or data classificationthrough a learning process. Learning in biological systems involves adjustments to theconnections that exist between the neurons which is true for ANNs as well. An NNconsists 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, andan output vector as shown in Figure 1. An NN may consist of one or more neurons in eachlayer. In a network, the final layer is called the output layer and all previous layers arecalled hidden layers. In the hidden layers, the output of a layer becomes the input forthe following layer. The transfer function of a neuron converts the input to the output ofthe neuron. Multi-layer NNs are quite powerful tools used in solving many differentcomplex problems. Various types of NNs are available for different purposes. In thisstudy, a multi-layer back propagation NN architecture is adopted.
  6. 6. BIJ Teach/use18,2 W1 X W2 X Inputs Weights226 Neuron Output Wn XFigure 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 3Figure 2.A simple feed forward NN Input 4with three layers
  7. 7. together at the low and high ends of the original data range (Mostafa, 2009). An NN Indian businessconfiguration called generalized regression neural networks (GRNN) put forward schoolsby Specht (1991) is adopted to give the best possible predictions. The rationale forchoosing the GRNN configuration lies in the fact that it is a good numerical predictor anduser need not to make decisions about the structure of a net. These nets always have twohidden layers of neurons, with one neuron per training case in the first hidden layer, andthe size of the second layer determined by some facts about training data. 227 GRN architecture. A generalized regression neural (GRN) net for two independentnumeric variables is structured as shown in Figure 3 with the assumption that thereare just three training cases (Palisade Corporation, 2008). The pattern layer contains one node for each training case. Presenting a training case tothe net consists here of presenting two independent numeric values. Each neuron in thepattern layer computes its distance from the presented case. The values passed to thenumerator 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 themto generate the prediction. The distance function computed in the pattern layer neuronsuses “smoothing factors”; every input has its own “smoothing factor” value. With a singleinput, the greater the value of the smoothing factor, the more significant distant trainingcases become for the predicted value. With two inputs, the smoothing factor relates to thedistance along one axis on a plane, and in general, with multiple inputs, to one dimensionin multi-dimensional space. Training a GRN net consists of optimizing smoothing factorsto minimize the error on the training set, and the conjugate gradient descent optimizationmethod is used to accomplish that. The error measure used during training to evaluatedifferent sets of smoothing factors is the mean squared error. However, when computingthe squared error for a training case, that case is temporarily excluded from the patternlayer. This is because the excluded neuron would compute a zero distance, making otherneurons insignificant in the computation of the prediction.3.3 Data and data classificationFor solving the benchmarking problem, 49 top B-schools of India are considered usingconvenience sampling method. Data on 11 parameters as listed below are collected fromvarious secondary sources. The secondary source reference includes popular Indianmagazines like Outlook, Business World, Indian Management, and B-school directorieswhich 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. 8. BIJ The data collected on the above parameters are classified into two categories based on18,2 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 schoolTable I. 10 Fee FEE Fee collected from studentsList of parameters 11 Salary SAL Initial salary at which graduating students are placed
  9. 9. In this study, the DEA and NN has been integrated to have an efficient predicting model. Indian businessDEA, being a robust mathematical tool, has been employed to evaluate the efficiency of schoolsB-schools. DEA, basically, takes into account the input and output components of aDMU to calculate TE. TE is treated as an indicator for performance of DMUs andcomparison has been made among them. A sensitivity analysis has been carried out tostudy robustness of the ranking of schools obtained through DEA. Finally, NN is usedto predict the efficiency when changes in inputs are caused due to market dynamism so 229that effective strategies can be evolved by the managers with limited available data.4. Results and discussionThe Charnes, Cooper and Rhodes (CCR)-DEA model as discussed above is based onconstant RTS does not consider the size of B-school under consideration whilecalculating the efficiency. But in many cases the size of a unit may influence its ability toproduce services more efficiently. So, we have also considered the VRS model for ourstudy. The B-schools under consideration for our problem contain both private andgovernment institute. The input for both the category of institute differs widely, so theoutput 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 DMUis 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. TheBCC score is based on VRS assumption and measures the pure TE. The CCR scoreis based on CRS assumption and consist of non-additive combination of pure TE andscale efficiency. The table shows that in a scale of 0-1 the average score for the B-schoolsis 0.625 with a standard deviation of 0.175 when CCR model is used. Similarly, when theBCC model is used the average score is 0.888 with a standard deviation of 0.063. Therank-order correlation coefficient between the efficiency ranking obtained through CCRand BCC model is 0.736 ( p ¼ 0.000) which is significant. The above table also shows thepeer group and peer weights for the inefficient B-schools. This is useful forbenchmarking for the inefficient DMUs. They can identify the parameters in which theylack and take necessary steps for improvement. The peer group for the inefficientB-schools indicates the efficient B-schools to which the inefficient B-schools are closer inits combination of inputs and outputs. It may also be observed that in both CCR and BCCscore 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 betreated as the best school. Moreover, this school is likely to be the school which isefficient with respect to a large number of factors, and is probably a good example of anexemplary operating performer. Efficient DMUs that appear seldom in the peer set ofother inefficient DMUs are likely to possess a very uncommon input/output mix and arethus not suitable examples for other inefficient schools (Mostafa, 2009). Now, it isprudent to check the robustness of the model trough sensitivity. DEA is an extreme point technique because the efficiency frontier is formed by theactual performance of best-performing DMUs. A direct consequence of this aspect is thaterrors in measurement can affect the DEA result significantly. So, according to DEAtechnique, it is possible for a B-School to become efficient if it achieves exceptionallybetter results in terms of one output but performs below average in other outputs. Thesensitivity of DEA efficiency can be verified by checking whether the efficiency of aDMU is affected appreciably:
  10. 10. BIJ 18,2 230 oriented) Table II. Efficiency score (outputDMU CCR Rank Peer Peer weights BCC Rank Peer Peer weights 1 1.000000 1 1 – 1.000000 1 1, 1 – 2 1.000000 1 2, 1 – 1.000000 1 2, 1 – 3 0.995190 5 1, 2, 6 0.634, 0.382, 2.71 £ 102 2 1.000000 1 3, 1 – 4 1.000000 1 4, 1 – 1.000000 1 4, 1 – 5 0.877809 7 1, 4 1.051, 0.306 1.000000 1 5, 1 – 6 1.000000 1 6, 1 – 1.000000 1 6, 1 – 7 0.799198 9 2, 4, 6 0.333, 0.674, 0.455 1.000000 1 7, 1 – 8 0.844716 8 2, 4, 6 0.341, 0.548, 0.296 0.964907 9 2, 4, 17 0.570, 0.330, 0.101 9 0.618562 20 1, 2, 6 0.159, 0.631, 0.741 0.907631 16 1, 2, 5, 6 0.111, 0.429, 0.177, 0.28310 0.644462 19 4, 6 1.050, 0.491 0.898023 19 1, 2, 7 0.150, 0.508, 0.34211 0.524947 31 2, 4, 6 0.704, 0.804, 0.333 0.902703 18 2, 5, 6 0.681, 0.289, 0.03012 0.753229 10 2, 6 1.209, 1.11 £ 102 2 0.907649 15 2, 7 0.884, 0.11513 0.584787 23 4, 6 1.141, 0.471 0.881374 21 1, 2, 7 0.487, 0.393, 0.12014 0.729801 13 4, 6 0.659, 0.687 0.943011 11 2, 4, 6 0.486, 0.215, 0.29915 0.514123 32 4, 6 1.147, 0.653 0.869822 25 2 1.00016 0.526763 29 2, 4, 6 0.341, 1.090, 0.135 0.793427 47 1, 7 0.819, 0.18117 0.904431 6 4, 6 1.00 £ 102 1, 1.079 1.000000 1 17 1.00018 0.546956 26 4, 6 0.614, 1.227 0.905501 17 4, 6, 17 0.670, 0.226, 0.10419 0.568486 24 4, 6 0.621, 1.141 0.921440 13 4, 6, 7, 17 0.366, 0.286, 0.301, 4.79 £ 102 220 0.508409 33 4, 6 0.353, 1.579 0.912566 14 6, 7 0.586, 0.41421 0.556489 25 4, 6 0.634, 0.969 0.861150 28 2, 6 0.703, 0.29722 0.504688 34 4, 6 0.905, 1.010 0.872109 24 2, 6, 7 0.692, 1.07 £ 102 2, 0.29723 0.534655 27 4, 6 0.208, 1.415 0.856631 33 2, 6 0.266, 0.73424 0.679945 15 4, 6 0.580, 0.744 0.857588 31 2, 6 0.624, 0.37625 0.470277 44 4, 6 0.613, 1.356 0.843978 39 2, 4, 6 0.571, 0.136, 0.29226 0.485306 39 4, 6 0.605, 1.349 0.869303 26 2, 4, 6, 7 0.533, 6.42 £ 102 2, 0.305, 9.74 £ 102 227 0.484885 40 4, 6 0.6135, 1.239 0.831249 41 2, 6 0.703, 0.29728 0.472438 43 4, 6 1.044, 1.141 0.881026 22 2, 7 0.131, 0.86929 0.500204 36 4, 6 0.701, 1.119 0.876344 23 2, 6 0.790, 0.21030 0.487138 37 4, 6 0.567, 1.342 0.854651 34 2, 4, 6, 7 0.199, 0.238, 0.361, 0.20231 0.476137 41 4, 6 0.353, 1.572 0.860350 30 2, 6, 7 0.110, 0.579, 0.31132 0.475426 42 4, 6 0.479, 1.460 0.853220 37 2, 4, 6 0.453, 0.115, 0.431 (continued)
  11. 11. DMU CCR Rank Peer Peer weights BCC Rank Peer Peer weights 33 0.486999 38 4, 6 0.444, 1.408 0.860563 29 2, 6 0.528, 0.472 34 0.525993 30 4, 6 0.744, 0.967 0.857388 32 2, 6 0.825, 0.175 35 0.665816 17 4, 6 9.41 £ 102 3, 1.453 0.945689 10 6, 7, 17 0.703, 1.38 £ 102 2, 0.283 36 0.613720 22 4, 6 0.313, 1.064 0.829688 42 2, 6 0.354, 0.6463 37 0.457457 45 4, 6 0.835, 1.010 0.806735 45 2, 6 0.930, 6.99 £ 102 2 38 0.533847 28 4, 6 0.272, 1.508 0.883930 20 2, 6 0.236, 0.358, 5.64 £ 102 2, 0.349 39 0.617969 21 4, 6 0.224, 1.199 0.854069 36 2, 4, 6 0.079, 0.181, 0.739 40 0.675052 16 4, 6 0.488, 0.814 0.854545 35 2, 6 0.528, 0.472 41 0.435924 47 4, 6 0.260, 1.778 0.838353 40 2, 4, 6 0.302, 5.05 £ 102 2, 0.648 42 0.452255 46 4, 6 0.403, 1.446 0.813703 44 2, 6 0.485, 0.515 43 0.739848 11 4, 6 9.72 £ 102 2, 1.221 0.938403 12 6, 7, 17 0.460, 6.65 £ 102 2, 0.473 44 0.500706 35 4, 6 0.373, 1.315 0.827064 43 2, 6 0.441, 0.559 45 0.695122 14 4 1.263 0.866262 27 4, 6, 17 8.72 £ 102 3, 0.882, 0.109 46 0.738727 12 4, 6 0.244, 0.926 0.848324 38 4, 6, 17 0.250, 0.677, 0.073 47 0.355991 49 4, 6 0.969, 1.364 0.792899 48 2 1.000 48 0.662169 18 4, 6 0.071636, 1.143831 0.800977 46 2, 6 9.17 £ 102 2, 0.908 49 0.412507 48 4, 6 0.776855, 1.205363 0.784348 49 2 0.882, 0.118Notes: Avg (CCR) – 0.625297, Min – 0.355991, and SD – 0.175012; Avg (BCC) – 0.888339, Min – 0.784348, and SD – 0.062977; Pearson correlation ofCCR and BCC ¼ 0.736, p-value ¼ 0.000 Indian business schools 231 Table II.
  12. 12. BIJ . if only one input or output is omitted from DEA analysis; and18,2 . 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 is232 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.
  13. 13. Efficiency Efficiency Dropping Dropping Dropping Dropping Dropping DMU Dropping DMU Dropping DroppingDMU CCR BCC IC, CCR IC, BCC FEE, CCR FEE, BCC 1, CCR 1, BCC PP, CCR PP, BCC 1 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 – – 1.000000 1.000000 2 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 3 0.995190 1.000000 0.981913 1.000000 0.970112 1.000000 1.000000 1.000000 0.995190 1.000000 4 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 5 0.877809 1.000000 0.772174 1.000000 0.877809 1.000000 0.981736 1.000000 0.877809 1.000000 6 1.000000 1.000000 1.000000 1.000000 0.586713 1.000000 1.000000 1.000000 1.000000 1.000000 7 0.799198 1.000000 0.774525 1.000000 0.607166 1.000000 0.799198 1.000000 0.799198 1.000000 8 0.844716 0.964907 0.844716 0.964907 0.673546 0.937684 0.844716 0.964907 0.844716 0.964907 9 0.618562 0.907631 0.618562 0.907631 0.392137 0.900923 0.620586 0.907877 0.618562 0.90763110 0.644462 0.898023 0.644462 0.898023 0.433763 0.898023 0.644462 0.899259 0.644462 0.89802311 0.524947 0.902703 0.492203 0.902703 0.430246 0.902703 0.524947 0.902703 0.524947 0.90270312 0.753229 0.907649 0.522483 0.886576 0.738128 0.907649 0.753229 0.907649 0.753229 0.90764913 0.584787 0.881374 0.584787 0.881374 0.436566 0.881374 0.584787 0.888147 0.584787 0.88137414 0.729801 0.943011 0.729801 0.943011 0.423904 0.902508 0.729801 0.943011 0.729801 0.94301115 0.514123 0.869822 0.514123 0.869822 0.376683 0.869822 0.514123 0.869822 0.514123 0.86982216 0.526763 0.793427 0.526763 0.793427 0.434564 0.793427 0.526763 0.804730 0.526763 0.79342717 0.904431 1.000000 0.904431 1.000000 0.355112 0.832466 0.904431 1.000000 0.904431 1.00000018 0.546956 0.905501 0.546956 0.905501 0.262281 0.846514 0.546956 0.905501 0.546956 0.90550119 0.568486 0.921440 0.568486 0.921440 0.320073 0.879471 0.568486 0.921440 0.568486 0.92144020 0.508409 0.912566 0.508409 0.912566 0.274155 0.867030 0.508409 0.912566 0.508409 0.91256621 0.556489 0.861150 0.556489 0.861150 0.331672 0.852071 0.556489 0.861150 0.556489 0.86115022 0.504688 0.872109 0.504688 0.872109 0.324421 0.871695 0.504688 0.872109 0.504688 0.87210923 0.534655 0.856631 0.534655 0.856631 0.265378 0.834320 0.534655 0.856631 0.534655 0.85663124 0.679945 0.857588 0.679945 0.857588 0.359272 0.846154 0.679945 0.857588 0.679945 0.85758825 0.470277 0.843978 0.470277 0.843978 0.249000 0.828402 0.470277 0.843978 0.470277 0.84397826 0.485306 0.869303 0.485306 0.869303 0.270222 0.853810 0.485306 0.869303 0.485306 0.86930327 0.484885 0.831249 0.484885 0.831249 0.257981 0.822485 0.484885 0.831249 0.484885 0.83124928 0.472438 0.881026 0.472438 0.881026 0.311123 0.881026 0.472438 0.881026 0.472438 0.88102629 0.500204 0.876344 0.500204 0.876344 0.273313 0.869822 0.500204 0.876344 0.500204 0.87634430 0.487138 0.854651 0.487138 0.854651 0.260696 0.827372 0.487138 0.854651 0.487138 0.85465131 0.476137 0.860350 0.476137 0.860350 0.249919 0.838258 0.476137 0.860350 0.476137 0.860350 (continued) report Sensitivity analysis Indian business schools Table III. 233
  14. 14. BIJ 18,2 234 Table III. Efficiency Efficiency Dropping Dropping Dropping Dropping Dropping DMU Dropping DMU Dropping DroppingDMU CCR BCC IC, CCR IC, BCC FEE, CCR FEE, BCC 1, CCR 1, BCC PP, CCR PP, BCC32 0.475426 0.853220 0.475426 0.853220 0.238986 0.834320 0.475426 0.853220 0.475426 0.85322033 0.486999 0.860563 0.486999 0.860563 0.239228 0.846154 0.486999 0.860563 0.486999 0.86056334 0.525993 0.857388 0.525993 0.857388 0.288255 0.852071 0.525993 0.857388 0.525993 0.85738835 0.665816 0.945689 0.665816 0.945689 0.301387 0.849922 0.665816 0.945689 0.665816 0.94568936 0.613720 0.829688 0.613720 0.829688 0.289507 0.810651 0.613720 0.829688 0.613720 0.82968837 0.457457 0.806735 0.457457 0.806735 0.257054 0.804734 0.457457 0.806735 0.457457 0.80673538 0.533847 0.883930 0.533847 0.883930 0.255412 0.804734 0.533847 0.883930 0.533847 0.88393039 0.617969 0.854069 0.617969 0.854069 0.283359 0.822485 0.617969 0.854069 0.617969 0.85406940 0.675052 0.854545 0.675052 0.854545 0.339557 0.840237 0.675052 0.854545 0.675052 0.85454541 0.435924 0.838353 0.435924 0.838353 0.205649 0.816568 0.435924 0.838353 0.435924 0.83835342 0.452255 0.813703 0.452255 0.813703 0.230183 0.798817 0.452255 0.813703 0.452255 0.81370343 0.739848 0.938403 0.739848 0.938403 0.286491 0.835148 0.739848 0.938403 0.739848 0.93840344 0.500706 0.827064 0.500706 0.827064 0.254029 0.810651 0.500706 0.827064 0.500706 0.82706445 0.695122 0.866262 0.695122 0.866262 0.208424 0.822485 0.695122 0.866262 0.695122 0.86626246 0.738727 0.848324 0.738727 0.848324 0.318954 0.804734 0.738727 0.848324 0.738727 0.84832447 0.355991 0.792899 0.355991 0.792899 0.205402 0.792899 0.355991 0.792899 0.355991 0.79289948 0.662169 0.800977 0.662169 0.800977 0.275852 0.775148 0.662169 0.800977 0.662169 0.80097749 0.412507 0.784348 0.412507 0.784348 0.237532 0.781065 0.412507 0.784348 0.412507 0.784348
  15. 15. Indian business CCR-efficiency prediction BCC-efficiency prediction schoolsNet informationConfiguration GRNN numeric predictor GRNN numeric predictorIndependent category variables 0 0Independent numeric variables 3 (IC, IF, and FEE) 3 (IC, IF, and FEE)Dependent variable Numeric variable (CCR-eff) Numeric variable (BCC-eff) 235TrainingNumber of cases 39 39Number of trials 69 98Bad predictions (%) (30 percent tolerance) 0.0000 0.0000Root mean square error 0.009344 0.02323Mean absolute error 0.005236 0.01606Std deviation of abs. error 0.007740 0.01679TestingNumber of cases 10 10 Table IV.Bad predictions (%) (30 percent tolerance) 0.0000 0.0000 Network configurationRoot mean square error 0.08585 0.03279 for CCR and BCCMean absolute error 0.05931 0.02420 efficiency scoreStd deviation of absolute Error 0.06208 0.02212 prediction5. ConclusionsThis study is concerned with the ranking of Indian B-schools using a non-parametrictechnique and developing an NN to predict the standing of schools based on limitednumber of parameters. Both CRS and VRS are considered to obtain the efficiency scoreof DMUs. The methodology facilitates in identifying the benchmarked institutions forthe inefficient institutes. The process of benchmarking is useful in identifying the bestbusiness practices and formulating the winning strategies. The DEA methodology canbe 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 ofindividual unit, the problem associated with it is lack of transparency in data sharingand data reliability. Some of the schools may not be too enthusiastic to share the datapertaining to their resource consumption and output produced. This requires amethodology which will allow the individual schools to generate scenario with the datawithin their control and test their own performance through simulation. For thispurpose, an NN model is developed and trained to predict the performance level of theindividual B-schools based on the input level consumed. The paper integrates the DEAmodel and NN. The output obtained through DEA model is used for training the NNfor prediction of efficiency score of schools based on the input values. Like any otherstudy, 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 theinstitution, funds generation by the institution, etc. could have been incorporatedin the model for calculating efficiency score of schools. Next, some of the inputs maynot 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.
  16. 16. BIJ NN Absolute NN Absolute18,2 DMU CCR-eff prediction difference BCC-eff prediction difference 1 1.000000 0.995199 0.004801 1.000000 0.990000 0.010000 2 1.000000 0.999804 0.000196 1.000000 0.990000 0.010000 3 0.995190 0.995383 0.000190 1.000000 0.980000 0.020000236 4 1.000000 1.000000 9 £ 102 8 1.000000 0.970000 0.030000 5 0.877809 0.877809 8.5 £ 102 10 1.000000 1.000000 0.000000 6 1.000000 1.000000 2.76 £ 102 7 1.000000 1.000000 0.000000 7 0.799198 0.798370 0.000828 1.000000 0.990000 0.010000 8 0.844716 0.844631 8.5 £ 102 5 0.964907 0.970000 0.005090 9 0.618562 0.510193 0.108369 0.907631 0.840000 0.067631 10 0.644462 0.643716 0.000746 0.898023 0.890000 0.008023 11 0.524947 0.524947 1.41 £ 102 7 0.902703 0.920000 0.017300 12 0.753229 0.753229 1.4 £ 102 12 0.907649 0.950000 0.042350 13 0.584787 0.585286 0.000500 0.881374 0.880000 0.001374 14 0.729801 0.711399 0.018402 0.943011 0.880000 0.063011 15 0.514123 0.515267 0.001140 0.869822 0.880000 0.010180 16 0.526763 0.638785 0.112020 0.793427 0.800000 0.006570 17 0.904431 0.904431 3.26 £ 102 7 1.000000 0.980000 0.020000 18 0.546956 0.515410 0.031546 0.905501 0.860000 0.045501 19 0.568486 0.489394 0.079092 0.921440 0.910000 0.011440 20 0.508409 0.501404 0.007005 0.912566 0.860000 0.052566 21 0.556489 0.556487 2.26 £ 102 6 0.861150 0.860000 0.001150 22 0.504688 0.504462 0.000226 0.872109 0.890000 0.017890 23 0.534655 0.536646 0.001990 0.856631 0.870000 0.013370 24 0.679945 0.698285 0.018340 0.857588 0.870000 0.012410 25 0.470277 0.478689 0.008410 0.843978 0.860000 0.016020 26 0.485306 0.482410 0.002896 0.869303 0.860000 0.009303 27 0.484885 0.491726 0.006840 0.831249 0.860000 0.028750 28 0.472438 0.472462 2.4 £ 102 5 0.881026 0.880000 0.001026 29 0.500204 0.501399 0.001190 0.876344 0.870000 0.006344 30 0.487138 0.486487 0.000651 0.854651 0.850000 0.004651 31 0.476137 0.484822 0.008680 0.860350 0.840000 0.020350 32 0.475426 0.484047 0.008620 0.853220 0.850000 0.003220 33 0.486999 0.491297 0.004300 0.860563 0.860000 0.000563 34 0.525993 0.511250 0.014743 0.857388 0.860000 0.002610 35 0.665816 0.662770 0.003046 0.945689 0.950000 0.004310 36 0.613720 0.616240 0.002520 0.829688 0.840000 0.010310 37 0.457457 0.474462 0.017000 0.806735 0.840000 0.033270 38 0.533847 0.532308 0.001539 0.883930 0.880000 0.003930 39 0.617969 0.619263 0.001290 0.854069 0.840000 0.014069 40 0.675052 0.675232 0.000180 0.854545 0.850000 0.004545 41 0.435924 0.478165 0.042240 0.838353 0.840000 0.001650 42 0.452255 0.484692 0.032440 0.813703 0.850000 0.036300 43 0.739848 0.723855 0.015993 0.938403 0.880000 0.058403 44 0.500706 0.502156 0.001450 0.827064 0.840000 0.012940 45 0.695122 0.494601 0.200521 0.866262 0.860000 0.006262 46 0.738727 0.737289 0.001438 0.848324 0.870000 0.021680Table V. 47 0.355991 0.355991 1.3 £ 102 8 0.792899 0.800000 0.007100CCR and BCC efficiency 48 0.662169 0.674932 0.012760 0.800977 0.840000 0.039020score prediction 49 0.412507 0.435469 0.022960 0.784348 0.840000 0.055650
  17. 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 DMUsIn future study, more number of schools over a period of time may be considered forbetter insight into the problem.ReferencesBanker, R.D., Charnes, A. and Cooper, W.W. (1984), “Some models for estimating technical and scale inefficiencies in data envelopment analysis”, Management Science, Vol. 30 No. 9, pp. 1078-92.Charnes, A., Cooper, W.W. and Rhodes, E. (1978), “Measuring the efficiency of decision making units”, European Journal of Operations Research, Vol. 2 No. 6, pp. 429-44.Chiang, W., Urban, T.L. and Baldridge, G.W. (1996), “A neural network approach to mutual fund net asset value forecasting”, Omega, Vol. 24 No. 2, pp. 205-15.Dayal, I. (2002), “Developing management education in India”, Journal of Management Research, Vol. 2 No. 2, pp. 98-113.Dutta, S. and Shekhar, S. (1988), “Bond ratings: a non-conservative application of neural networks”, IEEE International Conference on Neural Networks, San Diego, CA, Vol. 2, pp. 443-50.Hoefer, P. and Gould, J. (2000), “Assessment of admission criteria for predicting students’ academic performance in graduate business programs”, Journal of Education for Business, Vol. 75 No. 4, pp. 225-9.Hu, M.Y., Zhang, G.P. and Haiyang, C. (2004), “Modeling foreign equity control in Sino-foreign joint ventures with neural networks”, European Journal of Operational Research, Vol. 159 No. 3, pp. 729-40.Johnes, G. and Johnes, J. (1993), “Measuring the research performance of UK economics departments: an application of data envelopment analysis”, Oxford Economics Papers, Vol. 4 No. 2, pp. 332-47.Kannan, S.R. (2005), “Extended bidirectional associative memories: a study on poor education”, Mathematical and Computer Modelling, Vol. 42 Nos 3/4, pp. 389-95.Kimoto, T., Asakawa, K., Yoda, M. and Takeoda, M. (1990), “Stock market prediction system with modular neural networks”, Proceedings of the International Joint Conference on Neural Networks, San Diego, CA, Vol. 1, pp. 1-6.Lopes, A.L.M. and Lanzer, E.A. (2002), “Data envelopment analysis – DEA and fuzzy sets to assess the performance of academic departments: a case study at Federal University of Santa Catarina – UFSC”, Pesquisa Operational, Vol. 22 No. 2, pp. 217-30.
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  19. 19. Whitley, R., Thomas, A. and Marceau, J. (1981), Masters of Business? Business Schools and Indian business Business Graduates in Britain and France, Tavistock, London.Wu, P., Fang, S-C., King, R.E. and Nuttle, H.L. (1995), “Decision surface modeling of apparel retail schools operations using neural network technology”, International Journal of Operations and Quantitative Management, Vol. 1 No. 1, pp. 33-47.About the authors 239S. Sreekumar is an Associate Professor in Rourkela Institute of Management Studies, Rourkela769015, India. His areas of interest include application of DEA for efficiency analysis andmulti-criteria decision making. He has 17 years of teaching experience in the areas of quantitativetechniques and information science. He has published 30 papers in various international andnational journals and conferences. He has also authored two books. S.S. Mahapatra is Professor in the Department of Mechanical Engineering, National Institute ofTechnology 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, assemblyline 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 hisresearch work. He is also currently dealing with few sponsored projects. S.S. Mahapatra is thecorresponding author and can be contacted at: mahapatrass2003@yahoo.comTo purchase reprints of this article please e-mail: reprints@emeraldinsight.comOr visit our web site for further details: www.emeraldinsight.com/reprints

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