tion(u,v)o for which to VobXtain a linear programming problem that is equivalent to thei linieoar fractional programming prob-
lem. i
International Journal of Scientific & Engineering Research, Volume 4, Issue 8, August-2013 215
ISSN 2229-5518
An Application of Data Envelopment Analysis for
Measuring the Efficiency of Minority Institutions
Dr.R.P.Sreedevi
Abstract—This paper describes the technical efficiency and efficiency differences among 19 Minority Technical institutions under JNTUH of Andhra Pradesh in India by a linear programe based technique, Data Envelopment analysis. In this context, it is absolutely essential to assess the quality education offered by the technical institutions with specific reference to the reliability of how and when the learning takes place. Technical Education System (TES) is a growing field that is bringing a paradigm shift in new future directives. To strengthen TES there is a need to effectively assess various institutes. The identification of strongest and weakest functions is important quality education and hence to achieve high standards. DEA efficiency evaluation method identifies the functions that improve the quality of education and bring improvements in the system. The function is identification is based on knowledge based evaluation and it provides valuable inputs for further DEA exercise. In this application the final decision is based on the evaluation of a number of alternatives in terms of various outputs and inputs. The suggested approach can assist decision makers in selecting proper institutes to further strengthen the TES is an efficient and effective manner
Index Terms— CCR Model, DMUS, DEA,Technical Education, Literature, Ranks, Relative Efficiency, Technical Efficiency, Peer count
—————————— ——————————
Education System plays a pivotal role for socio-economic devel- opment in any country since it deals with knowledge develop- ment and dissemination, technology transfer, education and col- laborative works with industries. The demand and opportunities in education has resulted in an overwhelming increase in number of educational technical institutes especially in the developing countries like India. The technical institutes in India are currently facing a stiff competition because of opening of the off-shore campus of foreign universities. Highly competitive environment makes quality as a key variable for attracting primary customers (students).
The concept of quality while applied to education sector is not well defined. Definitions of quality in education follow the general definitions of quality. The term has been defined in many ways like “excellence in education”, “value addition in educa- tion”, “fitness of educational outcome and experience for use”, “defect avoidance in the education process”, and “meeting or exceeding customer’s expectations of education”. Variations in conceptualizations of quality as well as performance in education pose extreme difficulty while formulating a single and compre- hensive quality definition. Moreover, educational services are supposed to be intangible, heterogeneous, and In separable from the administrator’s point of view whereas it is variable and per- ishable for the customers’ viewpoint. Further, in this highly com- petitive environment, students have become more discriminating in their selection and more demanding in regard to choosing ap- propriate colleges and universities that suits their expectations as well as perceptions. It is also important for the institutions to un- derstand what the incoming students expect from the institution of their choice. Because, if student’s perceptions meet the extent of expectation while studying in an institute; according to students viewpoint the institute would be highly appreciated and that message would be conveyed to the junior batch of students com- munity. Therefore, the issue of survival of the institute and the retention of the students has become an area of critical concern for
most colleges and universities. Therefore, the administrators of the educational institutions should focus more on improvement of overall quality of education through continuous improvement programmes Usually, technical institutions exhibit highly process oriented and a multi- stakeholder situation leading to a difficulty in aggregating the functional variables (inputs and outputs) for the evaluation of education quality. Therefore, it is desirable to use a tool that is capable of relating customers’ perception (input) to the desired performance (output) of the education system so that strategic decision-making can be made easier. It is one such technique that aggregates the input and output components in order to obtain an overall performance measure through compari- son of a group of decision units. It evaluates performance of Deci- sion-Making Units (DMUs) by finding out the relative efficiency of the units under consideration. The DMUs can be business units (points of sales, bank branches, dealers, franchisees, etc.), gov- ernment agencies, police departments, hospitals, educational in- stitutions and even human beings on assessment of athletic, sales and student performance, etc. The major advantages of DEA may be listed as:
it can handle multiple input and multiple output models
it does not require the functional relationship between inputs and outputs
it identifies the possible peers as the role models (benchmarks)
it determines the possible sources of inefficiency
it is independent of units of measurement of various parame- ters.
In this study, an attempt has been made to assess the efficiency of the Minority institutions using various quality dimensions of ed- ucation through application of DEA. This study seeks to measure the relative efficiency of 19 educational institutions under JNTUH in Andhra Pradesh, India.
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International Journal of Scientific & Engineering Research, Volume 4, Issue 8, August-2013 216
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based on computation of Technical Efficiency (TE) using DEA with various input and output specifications (Agasisti and Bianco, 2006). A comparative study on efficiency of private universities and public universities in the USA using DEA has been carried out by Rhodes and Southwick (1986) considering each individual university as a DMU[18]. Tomkins and Green (1988) have used DEA to test the performance of individual departments of a university considering both teaching and research activities and compared the results with the ranking obtained by means of elemental analysis of staff/student ra- tio[19]. McMullen (1997) applied DEA in order to assess the relative desirability of Association to Advance Collegiate Schools of Business (AACSB) accredited MBA programmes [12]. McMillan and Datta (1998) used DEA to assess the rela- tive efficiency of 45 Canadian universities and found that a subset of universities comprising of three categories such as comprehensive with medical school, comprehensive without medical school and primarily undergraduate universities are regularly found to be efficient. In an attempt to compare the performance of selected schools in the Netherlands, Rama- nathan (2001) studied the effect of several non- discretionary input variables which are not under direct control of man- agement on efficiency scores[15]. Calhoun (2003) employed DEA to compare relative efficiencies of private and public In- stitutions of Higher Learning (IHL) using a sample of 1323 four-year old institutions and introduced a new way for clus- tering institutions based on revenue management. Data envel- opment analysis (DEA), occasionally called frontier analysis, was first put forward by Charnes, Cooper and Rhodes in
1978[5]. It is a performance measurement technique which,
can be used for evaluating the relative efficiency of decision- making units (DMU's) in organizations. Examples of such units to which DEA has been applied are: banks, police sta-
tions, hospitals, tax offices, prisons, defense bases (army, navy, air force), schools and university departments. One advantage of DEA is that it can be applied to non-profit making organiza- tions. Since the technique was first proposed much theoretical and empirical work has been done. Many studies have been published dealing with applying DEA in real-world situations. Obviously there are many more unpublished studies, e.g.
done internally by companies or by external consultants.
Data Envelopment Analysis is a relatively new “data oriented” approach for evaluating the performance of a set of peer enti- ties called Decision Making Units (DMUS) which convert mul- tiple inputs into multiple outputs. The definition of a DMU is generic and flexible. Recent years have seen a great variety of application of DEA for use in evaluation the performances of many different kinds of entities engaged in many different activities in many different contexts in many different coun- tries. These DEA applications have used DMUS of various forms to evaluate the performance of entities, such as hospi- tals, US Air force wings, Universities, Cities and Courts, busi- ness firms, and others, including the performance of countries, regions etc. Because it requires very few assumptions, DEA has also opened up possibilities for use in cases which have been resistant to other approaches because of the complex (of- ten un known ) nature of the relations between the multiple inputs and multiple outputs involved in DMUS.
As pointed out in Cooper, Seiford and Tone (2000), DEA has also been used to supply new insights into activities (and enti- ties ) that have previously been evaluated by other methods. DEA studies of the efficiency of different legal organization forms such as “stock” vs “mutual” insurance companies have shown that previous studies have fallen short in their attempt to evaluate the potentials of these different forms of organiza- tions. Similarly a use of DEA has suggested reconsideration of previous studies of the efficiency with which pre and post merger activities have been conducted in banks that were studied by DEA.
Since DEA in its present form was first introduced in 1978, researchers in a number of fields have quickly recognized that it is an excellent and easily used methodology for modeling operational process for performance evaluation. This has been accomplished by other developments. For instance, ZHU (2002) provides performance evaluation and benchmarking. DEA’S empirical orientation and the absence of a need for the numerous a prior assumption.
In their originating study, Charnes Cooper and Rhodes (1978) described DEA as a mathematical programming model ap- plied to observational data provides a new way of obtaining empirical estimates of relations. Such as the production func- tions and / or efficient production possibility surfaces – that are corner stones of modern economics.
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International Journal of Scientific & Engineering Research, Volume 4, Issue 8, AMugausxt-2h013(u, v) =
∑U r Yro
r Max
V X
ho (u2,1v7) =
∑U r Yro
r
V X
ISSN 2229-5518
For instance, consider what one wants to mean by “efficiency”
or more generally, what one wants to mean by saying that one
∑ i io
i
∑ i io
i
DMU is more efficient than another DMU. This is accom-
plished in a straight forward manner by DEA without requir-
ing explicitly formulated assumption and variation with vari-
ous types of models such as linear and non- linear regression
models.
Relative efficiency in DEA accords with the following defini-
tions, which has the advantage of avoiding the need for as-
Where xij = the observed amount of input of the ith type of the
j th DMU (xij > 0, i= 1,2,…..m, j= 1,2,…..n) and yrj = the observed
amount of output of the rth type for the j th DMU (yrj > 0, r =
1,2,….s, j = 1,2,…..n ).
The variables ur and vi are the weights to be deter-
mined by the above programming problem. However, this
problem has an infi∑niteUnuYmber of solutions since if (u*,v*) is
r ro
signing a prior measures of relative importance to any output .
Definition1.1 (Efficiency- extended Pareto-Koopmans defini-
tion):
Efficiency is attained by any DMU iff none of its inputs or
outputs can be improved without worsening some of its other
inputs or outputs.
In most management are social science applications the theo-
retically possible levels of efficiency will not be known. The
preceding definition is therefore replaced by emphasizing its
uses with only the information that is empirically available as
in the following definition.
Definition 1.2(relative efficiency):
A DMU is to be rated as fully (100%) efficient on the basis of
available evidence iff the performance of other DMUS does
not show that some of its inputs or outputs can be improved
without worsening some of its other inputs or outputs.
Charnes, Cooper and Rhodes introduced a measure of effi- ciency for each DMU that is obtained as a maximum of a ratio of weighted outputs to weighted inputs. The weights for the ratio are determined by the restriction that the similar ratios for every DMU have to be less than or equal to unity, thus re- ducing thus reducing multiple inputs and outputs to a single “virtual” input and “virtual” output without requiring pre assigned weights. The efficiency measure is then a function of the weights of the “virtual” input-output combination. For- mally the efficiency measure for DMU0 can be calculated by solving the following mathematical programming problem:
∑U r Yro
optimal then ( αu*,αrv* ), one can select a representative solu-
tion(u,v)o for which to VobXtain a linear programming problem that is equivalent to thei linieoar fractional programming prob-
lem. i
The paper initially illustrates DEA by taking a sample of 19
Minority Technical Institutions under JNTUH in Andhra Pra-
desh, India using a graphical (pictorial) approach to DEA. This
is very useful when attempting to explain DEA to those in the
management area. There is a mathematical approach to DEA
that can be adopted which is illustrated using Linear Pro-
gramming technique. Our analysis uses 2 output measures,
namely pass percentage of students and students placed and 3
input measures namely, intake of students, faculty and infra-
structure in the various Technical Institutions. To compare
these institutions and measure their performance a commonly
used method is CCR model which takes output measure and
divides it by the corresponding input measure. In this case, we
analyze the effectiveness of colleges by taking inputs and con-
verting them (with varying degrees of efficiency) into outputs.
Out of 19 Minority Institutions only three has been emerged as
efficient and the remaining institutions experienced input
losses due to over all technical efficiency. The relative efficien-
cy can be further analyzed to improve the performance.
The Technical Efficiency variation for the 16
Minority institutions has the following bounds.
0.716 ≤ λ (CRTS) ≤ 0.948
The Technical Efficiency variation for Efficient Institutions is
1.000.
Max
ho (u, v) =
r
∑Vi X io
i
Subjected to
For DMU2 the technical efficiency is 0.770 ≈ 0.8. According to
the “returns to scale constant “ its current outputs with only
80% of inputs is produced, it means 20% of inputs are freely
disposed or cost lessly disposed.
For DMU 11, the technical efficiency is 0.948 ≈ 0.9. As per “re-
turns to scale constant” it is experienced that 10% of input
∑U r Yrj
r ≤ 1
∑Vi X ij
i
Max
r = 1,2,.......s;
∑U r Yro
r
losses are due to over all technical efficiency. In other words j = 1,2,.......n; i = 1,2,....t.h..ims DMU could have combined 90 percent of its current in- puts to produce the current outputs, has been over all tech-
nical efficient.
Ranks will be allotted based on peer count. The Efficient
DMUs will be awarded ranks based on their peer count. The
U r , Vih≥o (0u, v)fo=r a∑ll UVi &XYr
Efficient DMU with highest peer count will be awarded first,
i r rio
Max
ho (u, v) =
ri
V X
the next highest will be second as it follows.
∑ i io
i
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International Journal of Scientific & Engineering Research, Volume 4, Issue 8, August-2013 218
ISSN 2229-5518
Table: Technical Efficiency Score & Ranks of DMUS
leges were established using graphical analysis initially and then the case was formulated as an Linear Programming Prob- lem which was solved using Solver. As this research is con- fined only to two inputs measure and three output measures, it cannot be generalized unless it is extended to more inputs and output measures. This study provides scope for further research using multiple input and output measures to assess the effectiveness of educational institutions in the service sec- tor and other industrial sectors.
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Education is the basic human requirement and one should
take effort to choose the best educational institute. Selection of
academic institute depends upon several attributes related to
infrastructure, faculty strength, student quality, administra-
tion, research and developmental activities, training and
placement and many others. However, relative priority of
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educational systems for assessing the effectiveness of educa-
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JNTUH in Andhra Pradesh, India were analyzed for effective-
ness using Data Envelopment Analysis(DEA). The efficient
frontier were identified and the relative efficiency of the col-
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International Journal of Scientific & Engineering Research, Vo lume 4, Issue 8, August-2013
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219
[12] M.S. Khan, S.S Mahapatra, Service quality evaluation of technical institutions using data envelopment analysis, International Journal of Productivity and Quality Management, Vol3, No. 1, 2008.
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