Efficiency distribution and expected efficiencies in DEA with imprecise data

Document Type : Research Paper

Author

Satellite Research Institute, Iranian Space Research Center, Tehran, Iran

Abstract

Several methods have been proposed for ranking the decision-making units (DMUs) in data envelopment analysis (DEA) with imprecise data. Some methods have only used the upper bound efficiencies to rank DMUs. However, some other methods have considered both of the lower and upper bound efficiencies to rank DMUs. The current paper shows that these methods did not consider the DEA axioms and may be unable to produce a rational ranking. We show that considering the imprecise data as stochastic and using the expected efficiencies to rank DMUs give better results. Indeed, we propose a new ranking approach, based on considering the DEA axioms for imprecise data that removes the existing drawbacks. Some numerical examples are provided to explain the content of the paper.

Keywords

Main Subjects


Asosheh, A., Nalchigar, S., Jamporazmey, M. (2010). Information technology project evaluation: An integrated data envelopment analysis and balanced scorecard approach. Expert Systems With Applications, 37, 5931–5938.
Baghery, M.,  Yousefi, S., Jahangoshai Rezaee, M. (2016). Risk measurement and prioritization of auto parts manufacturing processes based on process failure analysis, interval data envelopment analysis and grey relational analysis. Journal of Intelligent Manufacturing, DOI: 10.1007/s10845-016-1214-1.
Charnes, A., Cooper, W.W., Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2, 429–444.
Chen, Y., Cook, W. D., Du, J., Hu, H., & Zhu, J. (2017). Bounded and discrete data and Likert scales in data envelopment analysis: application to regional energy efficiency in China. Annals of Operations Research, 255(1–2), 347–366.
Cooper, W.W., Park, K.S., & Yu, G. (1999). IDEA and AR-IDEA: Models for dealing with imprecise data in DEA. Management Science, 45, 597–607.
Cooper, W.W., Park, K.S., Yu, G. (2001). IDEA (imprecise data envelopment analysis) with CMDs (column maximum decision making units). Journal of the Operational Research Society, 52(2), 176–181.
Despotis, D.K., & Smirlis, Y.G. (2002). Data envelopment analysis with imprecise data. European Journal of Operational Research, 140, 24–36.
Ebrahimi, B., Khalili, M. (2018). A new integrated AR-IDEA model to find the best DMU in the presence of both weight restrictions and imprecise data. Computers & Industrial Engineering, 125, 357-363.
Ebrahimi, B., Rahmani, M., Khakzar Bafruei, M. (2014). Comments on "Information technology project evaluation: An integrated data envelopment analysis and balanced scorecard approach" and a new ranking algorithm. Data Envelopment Analysis and Decision Science, Doi: 10.5899/2014/dea-00077.
Ebrahimi, B., Rahmani, M. (2017). An improved approach to find and rank BCC-efficient DMUs in data envelopment analysis (DEA). Journal of Industrial and Systems Engineering, 10(2), 25-34.
Ebrahimi, B., Rahmani, M., Ghodsypour S.H. (2017). A new simulation-based genetic algorithm to efficiency measure in IDEA with weight restrictions. Measurement, 108, 26-33.
Ebrahimi, B., Tavana, M., Rahmani, M. et al. (2018). Efficiency measurement in data envelopment analysis in the presence of ordinal and interval data. Neural Computing and Applications, 30, 1971–1982.
Farzipoor Saen, R. (2007). Suppliers selection in the presence of both cardinal and ordinal data. European Journal of Operational Research, 183, 741–747.
He, F., Xu, X., Chen, R., Zhu, L. (2016). Interval efficiency improvement in DEA by using ideal points. Measurement, DOI: http://dx.doi.org/10.1016/j.measurement.2016.02.062.
Kao, C. (2006). Interval efficiency measures in data envelopment analysis with imprecise data. European Journal of Operational Research, 174, 1087–1099.
Karsak, E.E., Dursun, M. (2014). An integrated supplier selection methodology incorporating QFD and DEA with imprecise data. Expert Systems with Applications, 41, 6995–7004.
Khalili-Damghani, K., Tavana, M., Haji-Saami, S. (2015). data envelopment analysis model with interval data and undesirable output for combined cycle power plant performance assessment. Expert Systems with Applications, 42, 760–773.
Khalili, M., Camanho, A.S., Portela, M., Alirezaee, M. (2010). The measurement of relative efficiency using data envelopment analysis with assurance regions that link inputs and outputs. European Journal of Operational Research, 203, 761–770.
Kim, S.H., Park, C.K., Park, K.S. (1999). An application of data envelopment analysis in telephone offices evaluation with partial data. Computers & Operations Research, 26, 59–72.
Lee, Y.K., Park, K.S., Kim, S.H. (2002). Identification of inefficiencies in an additive model based IDEA (imprecise data envelopment analysis). Computers & Operations Research, 29, 1661-1676.
Marbini, A.H., Emrouznejad, A., Agrell, P.J. (2014). Interval data without sign restrictions in DEA. Applied Mathematical Modelling, 38, 2028–2036.
Olesen, O.B., Petersen, N.C. (2016). Stochastic Data Envelopment Analysis—A review. European Journal of Operational Research, 251 (1), 2-21.
Park, K.S. (2004). Simplification of the transformations and redundancy of assurance regions in IDEA (imprecise DEA). Journal of the Operational Research Society, 55, 1363-1366.
Park, K.S. (2007). Efficiency bounds and efficiency classifications in DEA with imprecise data. Journal of the Operational Research Society, 58, 533–540.
Park, K.S. (2010). Duality, efficiency computations and interpretations in imprecise DEA. European Journal of Operational Research, 200, 289–296.
Toloo, M. (2014). Selecting and full ranking suppliers with imprecise data: A new DEA method. The International Journal of Advanced Manufacturing Technology, 74, 1141–1148.
Toloo, M., Keshavarz, E., & Hatami-Marbini, A. (2018). Dual-role factors for imprecise data envelopment analysis. Omega, 77, 15–31.
Toloo, M., & Nalchigar, S. (2011). A new DEA method for supplier selection in presence of both cardinal and ordinal data. Expert Systems with Applications, 38(12), 14726–14731.
Wang, Y.M., Greatbanks, R., Yang, J.B. (2005). Interval efficiency assessment using data envelopment analysis. Fuzzy Sets and Systems, 153, 347–370.
Zhu, J. (2003). Imprecise data envelopment analysis (IDEA): A review and improvement with an application. European Journal of Operational Research, 144, 513–529.
Zhu, J. (2004). Imprecise DEA via standard linear DEA models with a revisit to a Korean mobile telecommunication company. Operations Research, 52, 323–329.