1Department of Mathematics, Zabol Branch, Islamic Azad University, Zabol, Iran
2Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Data envelopment analysis (DEA) is a non-parametric technique for evaluation of relative efficiency of decision making units described by multiple inputs and outputs. It is based on solving linear programming problems. Since 1978 when basic DEA model was introduced many its modifications were formulated. Among them are two or multi-stage models with serial or parallel structure often called network DEA models that are widely discussed in professional community in the last years. The exact known inputs and outputs are required in these DEA models. However, in the real world, the concern is systems with interval (bounded) data. When we incorporate such interval data into multi-stage DEA models, the resulting DEA model becomes a non-linear programming problem. In this study, we suggest an approach to measure the efficiency of series and parallel systems with interval data that preserves the linearity of DEA model. Also, the interval DEA models are proposed to measure the lower and upper bounds of the efficiency of each DMU with interval data.
Ashrafi, A. Jaafer, A.B. (2011). Efficiency Measurement of Series and Parallel Production Systems with Interval Data By Data Envelopment Analysis, Australian Journal of Basic and Applied Sciences, 5(11): 1435-1443.
Beasley, J. (1995). Determining teaching and research efficiencies. Journal of the Operational Research Society, 46, 441–452.
Charnes, A., Cooper, W. W., & Rhodes, E. (1978) Measuring the efficiency of decision making units. European Journal of Operational Research, 2, 429–444.
Cook, W. D., & Seiford, L. M. (2009).Data envelopment analysis (DEA) – Thirty years on. European Journal of Operational Research, 192, 1–17.
Da Cruz, N. F. Carvalho, P. & Marques, R. C. (2013). Disentangling the cost efficiency of jointly provided water and wastewater services. Utilities Policy, 24, 70–77.
Emrouznejad, A., Parker, B. R., & Tavares, G. (2008). 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, 42, 151–157.
Fure, R., Grabowski, R., Grosskopf, S., & Kraft, S. (1997). Efficiency of a fixed but allocable input: A non-parametric approach. Economics Letters, 56, 187–193.
Kao, C., & Lin, P. H. (2011). Qualitative factors in data envelopment analysis: A fuzzy number approach. European Journal of Operational Research, 211, 586–593.
Kao, C., & Lin, P. H. (2012).Efficiency of parallel production systems with fuzzy data. Fuzzy Sets and Systems, 198, 83–98.
Liu, J. S., Lu, L. Y. Y., Lu, W. M., & Lin, B. J. Y. (2013a). A survey of DEA applications. Omega, 41, 893–902.
Liu, J. S., Lu, L. Y. Y., Lu, W. M., & Lin, B. J. Y. (2013b). Data envelopment analysis 1978–2010: A citation-based literature survey. Omega, 41, 3–15
Matthews, K. (2013). Risk management and managerial efficiency in Chinese banks: A network DEA framework. Omega, 41, 207–215.
Rogge, N., & Jaeger, S. (2012).Evaluating the efficiency of municipalities in collecting and processing municipal solid waste: A shared input DEA-model. Waste Management, 32, 1968–1978.
Seiford, L. M. (1996). Data envelopment analysis: The evolution of the state of the art (1978–1995). Journal of Productivity Analysis, 7, 99–138.
Tsutsui, M., & Goto, M. (2009). A multi-division efficiency evaluation of U.S. electric power companies using a weighted slacks-based measure. Socio-Economic Planning Sciences, 43, 201–208.
Zhou, P., Ang, B. W., & Poh, K. L. (2008). A survey of data envelopment analysis in energy and environmental studies. European Journal of Operational Research, 189, 1–18.