Mixed input and output orientations of Data Envelopment Analysis with Linear Fractional Programming and Least Distance Measures
AbstractData Envelopment Analysis (DEA) is an optimization technique to evaluate the efficiency of Decision- Making Units (DMU’s) together with multiple inputs and multiple outputs on the strength of weighted input and output ratios, where as Linear fractional programming is used to obtain DEA frontier. The efficiency scores of DMU obtained through either input orientation or output orientation DEA model will provide only local optimum solution. However, the mixed orientation of input and output variables will provide the global optimal solution for getting the efficient DMUs in DEA. This study has proposed the relationships of a mixed orientation of input and output variables using fractional linear programming along with Least-Distance Measure (LDM). Both constant returns to scale (CRS) and variable returns to scale (VRS) are considered for the comparative study.
A Charnes, W.W.cooper, B. Golany and L . Seiford, Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions, Journal of econometrics , vol. 30, no. 1, pp. 91–‘107, 1985.
A. Ebrahimnejad, M. Tavana , F. H. lotfi, R. Shahverdi, and M. yousfpour, A three-stage data envelopment analysis model with application to banking industry Measurement , vol. 49, pp. 308–‘319, 2014.
Abbott, M., and Doucouliagos. C, The efficiency of Australian universities: a data envelopment analysis, Economics of Education review, vol. 22, no. 1, pp. 89–97, 2003.
Arsham, H., and Kahn, A. B , A complete algorithm for linear fractional programs, Computers and Mathematics with Applications, vol. 20,no. 7,pp. 11–23, 1990.
Baek, C., and Lee, J. D, The relevance of DEA benchmarking information and the least-distance measure, Mathematical and Computer Modelling, vol. 49, no. 1, pp. 265–275, 2009.
Banker, Rajiv D., A, Charnes, and W. W. Cooper, Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management science, vol. 30, no. 9, pp. 1078–‘11092, 1984.
Charnes, A., and Cooper, W. W , Programming with linear fractional functionals, Naval Research logistics quarterly, vol. 9, no. 3-4, pp. 181–‘186, 1962.
Charnes, A., Cooper, W. W., and Rhodes,E.,
Measuring the efficiency of decision-making units, European journal of operational research, vol. 3,no. 4 pp. 339–351, 1978.
Charnes, A., Cooper, W. W., and Thrall, R. M., A structure for classifying and characterizing efficiency and inefficiency in data envelopment analysis, Journal of Productivity Analysis, vol. 2,no. 3 pp. 197–237, 1991.
Emrouznejad, A., Parker, B. R., and Tavares, G., Evaluation of research in efficiency and productivity: A survey and analysis of the first 30 years of scholarly literature in DEA, Socio-economic planning sciences, vol. 42,no. 3 pp. 151–157, 2008.
Jablonsky, Josef. A slack based model for measuring super-efficiency in data envelopment analysis, Multiple Criteria Decision Making,vol. 5, pp. 101–112, 2006.
Kao, Chiang, and Shiuh-Nan Hwang, Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan, European Journal of Operational Research,vol. 185,no. 1 pp. 418–429, 2008.
Kao, Chiang, Efficiency decomposition in network data envelopment analysis with slacks-based measures, Omega, vol. 45, pp. 1–6, 2014.
Shaban, M., Kavida, V., and Shah. A, Evaluating Efficiency of Commercial Banks in India: Using DEA Model, Pacific Business Review International, vol. 5, pp. 9–18, 2013.
Morita, Hiroshi, Koichiro Hirokawa, and Joe Zhu. A slack-based measure of efficiency in context-dependent data envelopment analysis, Omega,vol. 33,no. 4 pp. 357–362, 2005.
Morita, H., and Avkiran, N. K., Selecting inputs and outputs in data envelopment analysis by designing statistical experiment (¡ Special Issue¿ Operations Research for Performance Evaluation), Journal of the Operations Research Society of Japan, vol. 52,no.2
pp. 163–173, 2009.
Von Neumann, John. , ”A model of general economic equilibrium.” Readings in the Theory of Growth, Palgrave Macmillan UK,pp. 1–9, 1971.
O .Brien, G. C., and Wu, L., Alternative transformations and duality of linear fractional programming, In Operations Research/Management Science at Work (pp. 333-350), Springer US -2002.
Park, K. S, Duality, efficiency computations and interpretations in imprecise DEA, European Journal of Operational Research,vol. 200,no. 1 pp. 289–296, 2010.
Rty, T. Efficient facet based efficiency index: A variable returns to scale specification, Journal of Productivity Analysis,vol. 17,no. 1-2 pp. 62–82, 2002.
s. j. Sadjadi, H. Omrani, S. Abdollahzadeh, M.Alinaghian, and M. Hodammadi. A robust super-efficiency data envelopment analysis model for ranking of provincial gas companies in Iran, Expert Systems with Applications, vol. 38,no. 9 pp.10875–10881, 2011.
Schaible, S., Fractional programming, In Handbook of global optimization in Springer US., pp. 495–608, 1995.
Schaible, S., and Shi, J. , Fractional programming: the sum-of-ratios case, Optimization Methods and Software, vol. 18,no. 2 pp. 219–229, 2003.
Schaible, Siegfried, Analyse und Anwendungen von Quotientenprogrammen: e. Beitr. zur Planung mit Hilfe d, nichtlinearen Programmierung. Vol. 42. Hain, 1978.
Shahooth, K., and Battall, A. H., Using data envelopment analysis to measure cost efficiency with an application on Islamic banks, Scientific Journal of Administrative Development, vol. 4, pp. 134–156, 2006.
Seiford, Lawrence M., and Joe Zhu. Infeasibility of super-efficiency data envelopment analysis models, INFOR:Information Systems and Operational Research,vol. 37,no. 2 pp. 174–187, 1999.
Stancu-Minasian, I. M., Fractional programming: theory, methods, and applications Springer Science and Business Media, vol. 409,2012.
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