DATA ENVELOPMENT ANALYSIS A TECHNIQUE FOR MEASURING EFFICIENCY

Universities play an important role in the social and economical development of a country. Therefore, governments usually provide the financial resources universities need. On the other hand, universities should be efficient in satisfying the government's conditions of functional resources. Finding a transparent and systematic way to distributing the funds to each university is a major challenge for government. With participation in higher education amongst young people rising, governments around the world have been faced with increasing pressure on their finances, giving rise to the need to operate universities with a higher degree of efficiency. Data Envelopment Analysis (DEA) is a powerful method widely used in the evaluation of performance of Decision Making Units (DMUs). These can be business units, government agencies, police departments, hospitals, educational institutions, and even people DEA have been used in the assessment of athletic, sales and student performance). This paper provides an introduction to DEA and some important methodological extensions that have improved its effectiveness as a productivity analysis tool. Data Envelopment Analysis (DEA) techniques are used to estimate technical and scale efficiency of individual Saudi Arabia universities 2010. The purpose of this paper is to present basic principles of DEA and evaluate its application possibilities to assess the performance of nineteen Saudi Arabia universities. DEA is a choice between constant returns to scale CRS and variable returns to scale VRS. The CRS efficiency score represents technical efficiency, which measures inefficiencies due to input/output configuration and as well as size of operations. On the other hand, the VRS efficiency score represent pure technical efficiency, that is, a measure of efficiency without scale efficiency. The results found that the number of universities with maximum relative efficiency was ten out of nineteen universities when CRS was used. The number of universities with maximum relative efficiency was fifteen out of nineteen universities when VRS was used. The percentage of inefficiency was determined for each inefficient university, together with the extent of inputs that could be reduced and the extent of outputs that could be increased in these universities in order for them to be fully efficient.


INTRODUCTION
Data Envelopment Analysis has become a popular tool for evaluating the efficiency of decision making units. Data Envelopment Analysis (DEA) is a nonparametric mathematical programming approach to the measurement of efficiency that was introduced in the operations research literature by Charnes, Cooper, and Rhodes (1978) and Banker, Charnes, and Cooper (1984). The nonparametric approach has been widely applied to educational production. Using linear programming, an observed decision making unit (DMU) is evaluated relative to the production frontier, which consists of combinations of observed production possibilities using minimal assumptions.
The primary advantage of the approach is the ability to handle multiple inputs and multiple outputs, particularly in the case when input prices are unavailable. One important application of (DEA) is to the analysis of educational production. Many states have undergone legal challenges because school districts are not providing educational services efficiently and outcomes are not adequate. Reform has moved away from traditional issues like equity to adequacy and efficiency. The important policy implication is that school districts need to spend their money more wisely and increase their outcomes to acceptable levels. One popular technique that has been used for measuring efficiency in education is DEA. DEA is used to measure the performance of educational production in nineteen Saudi Arabia universities. The results found that the number of universities with maximum relative efficiency was fifteen out of nineteen universities when VRS model was used. DEA is most useful when a comparison is sought against "best -practice" Decision Making Units (DMUs).

DATA ENVELOPMENT ANALYSIS AND UNIVERSITIES
With participation in higher education amongst young people rising, governments around the world have been faced with increasing pressure on their finances, giving rise to the need to operate universities with a higher degree of efficiency. The higher education sectors of many countries obtain at least some of their income from public funds making it essential, in the interests of accountability, to measure the efficiency of the institutions which comprise these sectors. The series of application of DEA in education started with the article by Charnes et al in 1981. Thereafter several studies have applied DEA in measuring the efficiency of schools. The series of application of DEA in education started with the article by Bessent and Bessent (1980) used DEA in measuring the relative efficiency of education programs in an urban school district and to identify those that are less efficient than others with respect to the Pareto optimality criterion. The study demonstrated how DEA can be used in improving programs, terminating programs, initiating new programs, or discontinuing inefficient programs. Vargas and Bricker (2000) combined the Charnes, Cooper and Rhodes CCR output oriented model of DEA and Factor Analysis to evaluate the performance of academic units of a university's graduate programs relative to their counterparts nationally. Factor analysis and constructed outputs can be deduced from the observable outputs, and can be expressed as a linear combination of observed and random components. Ng and Li (2000) presented study attempted to examine the effectiveness of education reform implemented in china. The study focused on the research performance of the institutions, individual institution efficiency is computed by the method of DEA. The study found that research performance of institutions across regions has improved, although the institutions as a whole have remained inefficient. Moreno and Tadepalli (2002) proposed DEA for evaluating the efficiency of academic departments at a public university. The study provided the DEA as a single measure of efficiency for academic unit, and identified the causes behind the inefficiencies exhibited by poor performing. Afonso and Aubyn (2005) addressed the efficiency in education and health sectors for a sample of organization for economic co-operation and development (OECD) countries by applying two alternative non -parametric methodologies Free Disposable Hull and DEA. Those are two areas where public expenditure is of great importance so that findings have strong implications in what concerns public sector efficiency. Johns (2006) applied DEA to Economics graduates from United Kingdom universities in order to assess teaching efficiency. The results suggested that the efficiencies derived from DEA performed at an aggregate level include both institution and individual components, and are therefore misleading. Thus the unit of analysis in a Data Envelopment Analysis is highly important. Ruggiero (2006) applied DEA to aggregated data and show that aggregation can lead to unbiased efficiency estimates. These results represent an important contribution to the Data Envelopment Analysis literature, and performance evaluation using aggregate data can produce reliable results, even when measurement error is substantial.  examined the possibility of measuring efficiency in the context of higher education. The paper begins by exploring the advantage and drawbacks of the various methods for measuring efficiency in the higher education context. The ease with which DEA can handle multiple inputs and multiple outputs makes it an attractive choice of technique for measuring the efficiency of higher education institutions (HEIs), yet its drawbacks cannot be ignored. Johnes and Li YU (2008) this study used DEA to examine the relative efficiency in the productivity research of 109 Chinese regular universities in 2003 and 2004. Output variables measure the impact productivity of research; input variables reflect staff, students, capital and resources. Mean efficiency is just over 90% when all inputs and outputs variables are included in the model, and this falls to just over 80% when student -related input variables are excluded from the model. The rankings of universities across models and time periods are highly significantly correlated. Emrouznejad and et.al. (2008) presented an extensive; if not nearly complete, listing of DEA research covering theoretical developments as well as "real -world" applications from inception to the year 2007. Kao and Hung (2008) applied data envelopment analysis (DEA) to assess the relative efficiency of the academic departments at National Cheng Kung University in Taiwan. The outputs considered are total credit-hours, publications, and external grants; and the inputs utilized by the departments are personal, operating expenses, and floor space. Toth (2009) aimed to determine the relationship between the efficiency of European higher education's systems and the degree of state support as well as the family's socio-economic background. The study found that the GDP per capita has the most considerable influence on what results the countries achieve in higher education relative to their inputs, and the degree of the state contribution is negatively correlated to the efficiency measure. For solving this problem, two major trends were formed: stochastic (based on probability) analysis and the so-called Data Envelopment Analysis (DEA) requiring mathematical programming. Rayeni and Saljooghi (2010) computed disaggregate performance measures of universities. The traditional models for data envelopment analysis (DEA) type performance measurement are based on thinking about production as a "black box". Network DEA models consider processed which represent the main component of the system being studied. Chen and Chen (2011) presented Inno-Qual performance system (IQPS) which is adopted by using data envelopment analysis (DEA) to evaluate the Inno-Qual efficiency of 99 Taiwanese universities. The found that over half (73%) of the universities are highly inefficient in improving the Inno-Qual performance. Lopez and et.al (2011) measured the technical efficiency of the state universities of Mexico using DEA. Some of the conclusions that can be obtained from the analysis of the results are not necessarily the institutions with greater public financing obtained the highest scores of efficiency, in the case of the Private Universities (UP), will depend on the conditions under which is to receive pupils to first year, in terms of teaching staff and resources. Agha and et.al (2011) evaluated the relative technical efficiencies of academic departments at Islamic University in Gaza during the years 2004-2005. The study applied DEA to assess the relative technical efficiency of the academic departments. The study found that the average efficiency score is 68.5% and that there are 10 efficient departments out of the 30 studied. Monaco (2012) provided an assessment of levels of technical efficiency in university education among Italian universities and, subsequently, analyzes the environmental factors which may justify different levels of technical efficiency. In particular, the study examined the relationship between levels of technical efficiency and choices of university dropout. Therefore, the study estimated technical efficiency of Italian universities applying DEA on data collected by the National Evaluation Committee (CNVSU), relative to the academic year 2009/10. Sav (2012) estimated and compared operating efficiencies of publicly owned associate degree granting colleges in the United States using data envelopment analysis (DEA) and stochastic frontier analysis (SFA). Comparisons are based on panel data for 698 colleges over four academic years, 2005-09. Included are both constant and variable returns to scale DEA estimates along with half and truncated normal inefficiency SFA estimates. This paper provided DEA and SFA estimates of operating efficiencies for 698 publicly owned and operated two-year colleges accredited to offer associate degrees in the U.S. Antonio and et.al (2012) proposed an approach to measure the institutional efficiency in Mexican University combining analytic hierarchy process (AHP) with data envelopment analysis (DEA). Both methods are frequently used independently. The use of the two methodologies as an evaluation tool is novel and very useful in institutional efficiency studies. Rahimi and Behmanesh (2012) purposed, combination of data envelopment analysis (DEA) and requisite data mining techniques same as Artificial Neural Network (ANN) and Decision Tree (DT) are employed in order to enhance the power of predicting the DMUs evaluation performance because of their well-known efficiency and thereby to present precise decision rules for improving their efficiency.

Pareto-Koopmans Efficiency
Formalization of the efficiency concept began with Pareto in 1927. Pareto efficiency (optimality) is attained by any DMU if and only if none of its inputs or outputs can be improved without worsening some of its other inputs or outputs [Charnes et al., 1994].
Koopmans, 1951 adapted Pareto efficiency to the production process by defining optimality as the productive efficiency analog to the efficiency measure developed by Pareto. So, he introduced the first definition of technical efficiency. Koopmans efficiency occurs when no output can be increased without decreasing another output given the resource constraints. In other words, an input-output vector is technically efficient if and only if increasing any output or decreasing any input is possible only by decreasing some other output or increasing some other input.

Farrell Efficiency
The first measure of technical efficiency was proposed by Debreu, 1951. Despite the theoretical relevance of this study, efficiency was not quantified in it. This task was undertaken by Farrell, 1957, who considered the pioneer in the measurement of technical efficiency as he measured the efficiency of agricultural production in the United States.
Farrell proposed that the efficiency consists of two components: technical efficiency, which reflects the ability to obtain maximal output from a given set of inputs (or the ability to produce a given physical output with a minimum quantity of inputs), and allocative (price) efficiency, which reflects the ability to use inputs in optimal proportions given their respective prices. A combination of technical and allocative efficiency yields a measure of total economic (overall) efficiency.
Farrell's Technical-Efficiency measurement method was able to consider more than one output or more than one input simultaneously. His approach allowed an analyst to measure the productivity in terms of a single input that produces two separate outputs or two inputs used to produce a single output. It was able to plot the efficiency rating of organizations in relation to one another, and created an efficiency frontier, or set of best performers. These best performers could be plotted on the efficient frontier, since they use their inputs most efficiently to create outputs. This approach however has a limitation of working only for two inputs/outputs simultaneously [Sav 2012].
The relative technical efficiency of any DMU is calculated by forming the ratio of a weighted sum of outputs to a weighted sum of inputs, where the weights (multipliers) for both outputs and inputs are to be selected in a manner that calculates the Pareto efficiency measure of each DMU subject to the constraint that no DMU can have a relative efficiency score greater than unity [Lopez and et.al 2011].
The efficiency score in the presence of multiple input and output factors is defined as: where u i : weight of output i; i=1, 2, … y ij : quantity of output i derived from unit j.
v k : weight of input k; k=1, 2, … x kj : quantity of input k used by unit j.
In the process, DEA assigns an efficiency score, ranging between zero and one, to each unit by comparing the efficiency score of each unit with that of its peers. It identifies a frontier comprising best performers. Those units that lie on the frontier, achieving an unity efficiency score since they have the most appropriate combinations of input and output variables, are recognized as efficient, and those that do not, with efficiency scores of less than one are referred to as inefficient ones, which means that a linear combination of other units from the sample could produce the same vector of outputs using a smaller vector of inputs.

Data Envelopment Analysis Models
Since 1978 h k : the measure of productivity or efficiency of decision making unit "k" in the set of j = 1, 2, …., n decision-making units (DMUs) rated relative to the others. y rk : the amount of output "r" produced by DMU "k" during the period of observation.
x ik : the amount of resource input "i" used by DMU "k" during the period of observation. y rj : the amount of service output "r" produced by DMU "j" during the period of observation.
x ij : the amount of resource input "i" used by DMU "j" during the period of observation. The objective function of the model maximizes the ratio of weighted outputs to weighted inputs for the DMU under consideration subject to the condition that the similar ratios for all DMUs be less than or equal to one. The kth DMU is the base DMU in the above model. The optimal value of the objective function of the model is the data envelopment analysis efficiency score assigned to the kth DMU.
It is difficult to solve the above model because of its fractional objective function.
However, if either the denominator or numerator of the ratio is forced to be equal to one, then the objective function will become linear, and a linear programming problem can be obtained.
Linear form of CCR model is given as follows: h k : the measure of productivity or efficiency of decision making unit "k" in the set of j = 1, 2, …., n decision-making units (DMUs) rated relative to the others. y rk : the amount of output "r" produced by DMU "k" during the period of observation.
x ik : the amount of resource input "i" used by DMU "k" during the period of observation. y rj : the amount of service output "r" produced by DMU "j" during the period of observation.
x ij : the amount of resource input "i" used by DMU "j" during the period of observation.  ..., , 2 , 1 ; where k: the decision making unit being evaluated in the set of j = 1, 2, …, n decision making units.
y rk : the amount of output "r" produced by DMU "k" during the period of observation.
x ik : the amount of resource input "i" used by DMU "k" during the period of observation. y rj : the amount of service output "r" produced by DMU "j" during the period of observation.
x ij : the amount of resource input "i" used by DMU "j" during the period of observation.
θ: the efficiency score. performed on the assumption that all the defined inputs affect the process of production using an input-oriented approach. The CRS efficiency score represents technical efficiency, which measures inefficiencies due to input/output configuration and as well as size of operations. On the other hand, the VRS efficiency score represent pure technical efficiency, that is, a measure of efficiency without scale efficiency. The study used CRS, and VRS models to measure the efficiency of Kingdom of Saudi Arabia universities.
DEA is a non-parametric linear programming technique that computes a comparative ratio of outputs to inputs for each unit, which is reported as the relative efficiency score.
The efficiency score is usually expressed as either a number between 0-1 or 0-100%. A decision-making unit with a score less than 100% is deemed inefficient relative to other units.

Results:
In this study the DEA when input orientation is performed with CRS and VRS.
The study choosing between CRS and VRS is to run the performance models under each assumption and compare the efficiency scores. The nineteen Saudi Arabian universities were tested under constant returns to scale CRS and variable returns to scale VRS.
Comparing the two runs reveals different efficiency scores, thus confirming the presence of variable returns to scale among Saudi Arabian universities.
In Table 4     analysis was carried out according to the relative efficiency score. This efficiency may be a convenient method to rank policy alternatives in the case of an absence of information -44 -on stated preferences on outcomes, as well as negative environmental impacts. The results found that the number of universities with maximum relative efficiency was ten out of nineteen universities (52%) when CRS was used. The number of universities with maximum relative efficiency was fifteen out of nineteen universities (78%) when VRS was used. The percentage of inefficiency was determined for each inefficient university, together with the extent of inputs that could be reduced and the extent of outputs that could be increased in these universities in order for them to be fully efficient. The paper proposes a methodology based on DEA, a non parametric benchmarking technique, specifically developed to assess the relative efficiency of alternative water pricing policies. For this purpose a ranking analysis was carried out according to the relative efficiency score. This efficiency may be a convenient method to rank policy alternatives in the case of an absence of information on stated preferences on outcomes, as well as negative environmental impacts.