Computing the efficiency interval of decision making units (DMUs) having interval inputs and outputs with the presence of negative data

Subject Areas : Statistics

M.  Rostamy-Malkhalifeh ¹ (Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran Corresponding author)
F.  seyed Esmaeili ² (Department of Mathematics, South Tehran Branch, Islamic Azad University, Tehran, Iran)

Received: 2015-10-09 Accepted : 2016-02-09 Published : 2016-02-01

Keywords: تحلیل پوششی داده ها, داده های بازه ای, داده های منفی, ارزیابی کارایی,

Abstract :

The basic assumption in data envelopment analysis patterns (DEA) (such as the CCR andBCC models) is that the value of data related to the inputs and outputs is a precise andpositive number, but most of the time in real conditions of business, determining precisenumerical value is not possible in for some inputs or outputs. For this purpose, differentmodels have been proposed in DEA for imprecise data over recent years and also severalresearches have been conducted on DEA that are able to evaluate efficiency with negativedata. The negative interval DEA pattern which has been introduced and used in the presentstudy, addresses uncertainty both in inputs and outputs and provides user with more stableand reliable results for decision making.Now, in this paper a model is presented that is able to compute efficiency interval of unitswith interval input and output that while some indicators can also be negative and then weprove that the efficiency interval that this model gives us is more precise compared toefficiency interval of models previously proposed and finally, ten decision making units(DMUs) with the negative imprecise (interval) data are investigated by the proposed modeland the results of the proposed model are compared with the results of the previous models.

References:

[1] Charnes A, Cooper WW, Rhodes E., Measuring the efficiency of decision making units, European Journal of Operational Research; 2:429- 440, (1978).

[2] Cooper, W. W., Park, K. S., Pastor, J. T., (1999). RAM: A Range Adjusted Measure of Inefficiency for use with Additive Models and Relations to other Models and in DEA. Journal of Productivity Analysis, 11(1):5– 42.

[3] Seyed Esmaeili, F., RostamyMalkhalifeh, M. (2014). The Efficiency of MSBM Model with Imprecise Data (Interval). International Journal of Data Envelopment Analysis, 00216, 343-350.

[4] Sharp, J. A., Meng, W., & Liu, W. (2006). A modified slacks-based measure model for data envelopment analysis with ‘natural’ negative outputs and inputs. Journal of the Operational Research Society, 58, 1672–1677.

[5] Silva Portela, M. C. A., Thanassoulis, E., & Simpson, G. (2004). Negative data in DEA: A directional distance approach applied to bank branches. Journal of the Operational Research Society, 55, 1111– 1121.

[6] Wang, Y.M., Greatbanks, R.& Yang, B. (2005) Interval Efficiency Assessment Usin Data Envelopment Analysis; Fuzzy Sets and Systems 153 ,347-370