Indian Journal of Science and Technology
Year: 2016, Volume: 9, Issue: Special Issue 1, Pages: 1-8
D. Annapoorni1* and V. Prakash2
1 Department of Statistics, S.D.N.B. Vaishnav College for Women, Chromepet, Chennai - 600044, Tamil Nadu, India; [email protected]
2 Department of Statistics, Presidency College, Kamarajar Salai, Chennai - 600005, Tamil Nadu, India; [email protected]
*Author for correspondence
Department of Statistics
Email: [email protected]
Objectives: The Government provides primary health care services to the poor and needy people through District Hospitals. Primary care is an ongoing care being focused on person over time that fulfils the health related requirements of people. This necessitates studying the efficient functioning of public hospitals. So the author concentrated and considered to analyse the performance of District Hospitals in the state of Tamil Nadu. Methods/Statistical Analysis: To attain the above objective one of the nonparametric methods namely Data Envelopment Analysis (DEA) has applied. It is a mathematical technique based on linear programming problem and it measures the relative efficiency of similar type of organizations termed as Decision Making Units (DMUs). In this study each DMU refers to the District Hospital in the state of Tamil Nadu. In DEA, normally there exists a significant correlation between the inputs and outputs. Inclusion of more number of inputs and /or outputs in DEA results in getting a more number of efficient units. Therefore, select the appropriate inputs and outputs based on the experts’ advice who know their characteristics very well. A clear understanding of the characteristics of input/output variables will nullify the above deficiency and will really results with exact number of efficient units. An attempt is made to rectify the deficiency in introducing the technique viz., Principal Component Analysis. Principal Component Analysis helps the decision maker to reduce the data structure into certain principal components which are essential for identifying efficient DMUs. It is important to note that we have used the basic BCC model for the entire analysis. Findings: The author has considered 31 DMUs for the study using BCC model. The data results with 13 DMUs out of 31 DMUs as efficient. Subsequently with the same original data 3 PCs on input and output explains 98 percent of the total variance and this has resulted with only 3 DMUs as efficient. Then we have considered 2PCs on input and output. This has resulted with 90.31 percent variance in the case of input and 95.78 percent variance in the case of output. Normally in Principal Component analysis, if the variance lies between 80 percent to-90 percent it is judged as a meaningful one. The above computations result with 2 DMUs efficient. Finally, we have attempted to identify the efficient units with the above expected variance interval 80 percent to 90 percent. This has resulted with 90 percent variance explained with 2 input variable and one output variable with 89 percent explained variance. This also resulted with only 2 efficient DMUs. It is concluded that Principal Component Analysis plays an important role in the reduction of input output variables and helps in identifying the efficient DMUs and improves the discriminating power of DEA. Application/Improvements: Introduction of PCA with DEA is definitely is an improvement which helps the decision maker to apply in wider sense and to take proper managerial decision.
Keywords: Data Envelopment Analysis, Decision Making Unit, Principal Component Analysis, Principal Components
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