PERFORMANCE MEASUREMENT OF EDUCATIONAL INSTITUTIONS USING FUZZY DATA ENVELOPMENT ANALYSIS

Abstract

Data envelopment analysis (DEA) was first introduced by Charnes et. al. [77] in 1978. In a very short period of time DEA has evolved as a powerful tool for measuring the performance of decision making units (DMUs). DEA is a data-oriented linear programming based non-parametric approach for measuring the performance of a set of peer entities called DMUs, which utilize multiple inputs to produce multiple outputs. Examples include the performance assessment problems of educational institutions, hospitals, libraries, banks, transport sectors, airlines etc. In literature, several parametric and non-parametric approaches are available for evaluating the performances of DMUs. Stochastic frontier analysis (SFA) [10], Distribution free approach (DFA) [53], Thick frontier approach (TFA) [54] are known as parametric approaches which require explicit specification of production fron tier. Data envelopment analysis (DEA) [101] and Free disposal hull (FDH) [106] are known as non-parametric approaches which do not require any specification of production frontier. Among these approaches, DEA is one of the most popular approach because it does not require any prior assumptions concerning the internal operations of a DMU. DEA is useful for assessing the relative efficiencies of DMUs with multiple inputs and outputs. DEA provides information for the identifi cation of efficient and inefficient DMUs, as well as the suggestions for improvements of inefficient DMUs to become efficient. DEA has several advantages; however DEA also has some limitations. DEAisbased onfrontiers and sensitivity analysis. Sensitivity analysis shows that even little changes in inputs and outputs can shift the efficiency frontiers. Due to senistivity analysis, it becomes very important to measure accurate input-output data in DEA. In real-world applications, input-output data is complex and volatile; getting accurate input-output data is not an easy task. In some situa tions, the input and output data is available in imprecise form, implying that the inputs and outputs are uncertain. Education and research play an important role in development of any Nation. After The United States of America and China, India has the third-largest higher education system in the world. Cur rently, in India there are more than 700-degree granting institutions and 35500 affiliated colleges with 20 million students. Among these institutions, which one is the best? This can be the ques tion of intense debate. DEA can answer this question impressively. To understand the DEA and its application to the real-life situations, education sector in India is taken in this work. A numerous researches of DEA can be found in the field of education sector. Input-output data can be crisp and uncertain both. Uncertainty in the input- output data can be represented with the help of intervals, ordinal relations, fuzzy numbers etc. The fuzzy set (FS) theory is an important tool to handle the fluctuations/uncertainties in real life problems. FS theory is an extension of the classical crisp set theory. Mathematically, the concept of FS theory was developed by Zadeh [406]. In general, in DEA, input-output data is considered in the form of crisp. But in real-life situations, it is not an easy task to obtain the input-output data accurately. Data is collected by humans, machines, or by both humans and machines. Sometimes, there could be some fluctuation or uncertainty in the input- output data collected due to human or machine error. To deal with the uncertainty in data, the concept of fuzzy DEA (FDEA) comes into existence. FDEA is a data-oriented technique to evaluate the performance of DMUs in a fuzzy environment. Theaimofthis thesis is to (i) develop basic understanding of DEA and its applications to the field of education, (ii) extend DEA to uncertain environment with real-life application, (iii) develop fuzzy multi-objective DEA approach for measuring the performance of DMUs, (iv) analyze the cause of the inefficiency of DMUs in a decision process with the help of a two-stage relational network DEA model, (v) measure the efficiencies of education sector in India. Chapter-wise summary of thesis is given as below: The Chapter 1 serves as an introduction to the rest of the thesis. This chapter covers some fundamental definitions, operations, and DEA models in both crisp and fuzzy environments. It also gives a brief overview of DEA, fuzzy DEA, fully fuzzy DEA, fuzzy multi-objective DEA, network DEA, and efficiency in the education sector. It discusses the various DEA techniques in crisp and fuzzy environments. It reviews the literature in the education sector for choosing the input-output variables for educational institutions. In Chapter 2, 61 educational institutions in India, established before 1980, are considered for performance evaluation with the help of CCR and BCCDEAmodelsfortheyears2016-17and2017 18. In this study, 2 input variables ( Student-faculty ratio, financial resources) and 4 output variables (Growth index, Publications, Patent details, Perception) are used. The input and output data has been collected from the NIRF website [288] launched by the Govt. of India in 2015. The ranking is done on the basis of the efficiency scores of the institutions. To rank the efficient institutions super efficiency DEA model is applied. Finally, some suggestions and concluding remarks are given for inefficient institutions to make them efficient. In Chapter 3, a multi-objective optimization approach is developed for performance evaluation of DMUswiththehelpofDEAmodelsinfuzzyenvironment. The conventional DEA models mostly use deterministic/crisp data for input and output parameters. However, in real situations, input and output data cannot always be obtained accurately because of vagueness. Such vagueness in input and output data can be tackled with fuzzy numbers. So, the aim of the current study is to extend the crisp DEA to fuzzy DEA (FDEA). In this study, the input and output data are considered as fuzzy numbers (FNs), particularly the triangular fuzzy numbers (TFNs). Then a multi-objective approach is developed to solve the FDEA model to measure the performance efficiencies of DMUs. The weighted sum method is adopted to solve the developed fuzzy multi-objective DEA (FMODEA) model. The weighted sum method is very easy to handle MOOPs with some limitations but in this study due to the nature of the problem weighted sum method is one of the most suited methods. A solution approach is proposed for solving the developed FMODEA model for each DMU. The solution obtained for each DMU is the efficiency score for each DMU. Further, the DMUs are ranked according to the efficiency scores obtained. The proposed method is applied to a numerical example to determine the efficiency scores of 5 DMUs for fuzzy data which is taken from Guo and Tanaka [153] and the results of the proposed approach are compared with existing approach. The efficiencies of 13 IIMs in India with two fuzzy inputs: number of students and number of faculty members; two fuzzy outputs: number of students went for placement and higher studies, and number of publications are measured with the proposed models to ensure the acceptability of the proposed approach in the real-world. In Chapter 4, the fuzzy optimistic and fuzzy pessimistic models are proposed to determine the relative performance efficiencies of DMUs using α- cut approach. A hybrid fuzzy optimistic pessimistic approach is proposed to discriminate model which represents a better decision process for the judgment of organizations in real world problems. In support of the developed fuzzy optimistic and pessimistic DEA models, we have given two theorems. These theorems show the advantage of the proposed models over the existing models. Further, we offer two ranking approaches for integrating optimistic and pessimistic efficiencies simultaneously. The ranking of DMUs is done with the help of the proposed ranking approaches. The proposed methods are applied to a numerical example to determine the efficiencies, and total deviation of 5 DMUs for fuzzy data which is taken from Guo and Tanaka [153]. The efficiencies of 13 IIMs in India with two fuzzy inputs: number of students and number of faculty members; two fuzzy outputs: number of students went for placement and higher studies, and number of publications are measured with the proposed models to ensure the approaches’ acceptability in real-world applications. There are 13 IIMs that have been ranked. The best performer with high levels of efficiencies (or low levels of inefficiencies) and the worst performer with low levels of efficiencies (or high levels of inefficiencies) relative to the other IIMs in both optimistic and pessimistic situations are determined from the overall performance assessment using the hybrid FDEA approach. In Chapter 5, the left and right-end FFDEA models are proposed to determine the relative per formance efficiencies of DMUs in the term of left and right-ends using α- cut approach. It also proposes a ranking approach to rank the DMUs. The proposed ranking approach is compared with geometric average method [388]. The proposed methods have been applied to two numerical ex amples (i) to determine the performance efficiencies of 5 DMUs which is taken from Guo and Tanaka [153], and (ii) to ensure the acceptability of methods in real life applications. The per formance efficiencies of 13 IIMs in India are determined. The inefficiency percentage of 13 IIMs is [inefficiency percentage = Dk HighestDk ×100%]for some α-values are calculated and the DMUs are ranked accordingly. The input inefficiency percentage represents the degree to which the input should be changed to become fully efficient. In Chapter 6, we applied network DEA model to understand the performance of DMUs. In general, DEA works like a black box that does not provide any adequate detail to identify the spe cific reason for inefficiency in DMUs. The motivation of this study is to analyze the cause of the inefficiency of DMUs in a decision process with the help of a two-stage relational network DEA model. In the current study, a two-stage relational network DEA model is applied to measure the performance of DMUs for the whole process and each stage independently. In general, past studies used conventional DEA models in education sectors to analyze the performances of educational in stitutions. In the current study, by considering quantitative attributes to measure the performance of IIMs by using network DEA, we develop a procedure that captures both quality and quantity. Finally, Chapter 7 presents conclusions, summary of findings of the thesis and future research directions in DEA. It also presents the recommendations for the policy considerations along with some suggestions for improvements.