Estimation of undesirable outputs and desirable inputs along with efficiency improving for DMUs with interval data

Subject Areas : Statistics

Farhad taher ¹ , Behrouz Daneshian ² , ghasem Tohidi ³ , Farhad Hosseinzadeh lotfi ⁴ , Farzin Modarres Khiyabani ⁵

1 - Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran
2 - Department of Mathematic, Islamic Azad University, Central Tehran Branch, Tehran, Iran.
3 - Department of Mathematic, Islamic Azad University, Central Tehran Branch, Tehran, Iran.
4 - Department of Mathematic, Islamic Azad University, Science and Research Branch, Tehran, Iran.
5 - Department of Mathematic, Islamic Azad University, Tabriz Branch, Tehran, Iran.

Received: 2019-07-13 Accepted : 2020-10-19 Published : 2021-03-01

Keywords: داده‌های نامطلوب, DEA, داده‌های بازه‌ای, IDEA, MOLP,

Abstract :

Some researchers deals to estimation of some of the influences factors in efficiency score in which the DMU, maintains or improves its current efficiency level. This problems are considered in a general framework which is called inverse DEA. This paper studies the inverse data envelopment analysis. The issue of input or output estimation has been examined with improvement in unit efficiency.Therefore, in this paper, by increasing the level of undesirable inputs and the level of desired outputs of decision-making units along with improvements in the efficiency of the decision-maker, the level of changes in the level of desired inputs and the level of undesirable outputs is estimated. To do this, we consider the data as Interval data and then use the inverse DEA method using a multi-objective linear programming model (MOLP), so that the unit performance under evaluation is improved. The following is an applied example of the proposed method.

References:

[1] Charnes, Abraham, William W. Cooper, and Edwardo Rhodes. "Measuring the efficiency of decision making units." European journal of operational research 2.6 (1978): 429-444.

 

[2] Banker, Rajiv D., Abraham Charnes, and William Wager Cooper. "Some models for estimating technical and scale inefficiencies in data envelopment analysis." Management science 30.9 (1984): 1078-1092.

 

[3] Amirteimoori, Alireza, and Sohrab Kordrostami. "An alternative clustering approach: a DEA-based procedure." Optimization 62.2 (2013): 227-240.

 

[4] Esmaeilzadeh, A., and A. Hadi-Vencheh. "A new method for complete ranking of DMUs." Optimization 64.5 (2015): 1177-1193.

 

[5] Färe R, Grosskopf S, Lovell CK, Pasurka C. Multilateral productivity comparisons when some outputs are undesirable: a nonparametric approach. The review of economics and statistics. (1989):90-8.

 

[6] Chung, Yangho H., Rolf Färe, and Shawna Grosskopf. "Productivity and undesirable outputs: a directional distance function approach." journal of Environmental Management 51.3 (1997): 229-240.

 

[7] Seiford, Lawrence M., and Joe Zhu. "Modeling undesirable factors in efficiency evaluation." European journal of operational research 142.1 (2002): 16-20.

 

[8] Jahanshahloo GR, Lotfi FH, Shoja N, Tohidi G, Razavyan S. Undesirable inputs and outputs in DEA models. Applied mathematics and computation. (2005);169(2):917-25.

 

[9] Pathomsiri S, Haghani A, Dresner M, Windle RJ. Impact of undesirable outputs on the productivity of US airports. Transportation Research Part E: Logistics and Transportation Review. (2008);44(2):235-59.

 

[10] Tao, Xueping, Ping Wang, and Bangzhu Zhu. "Provincial green economic efficiency of China: A non-separable input–output SBM approach." Applied energy 171 (2016): 58-66.

 

[11] Eyni, M., Ghasem Tohidi, and S. Mehrabeian. "Applying inverse DEA and cone constraint to sensitivity analysis of DMUs with undesirable inputs and outputs." Journal of the Operational Research Society 68.1 (2017): 34-40.

 

[12] Hadi-Vencheh A, Hatami-Marbini A, Ghelej Beigi Z, Gholami K. An inverse optimization model for imprecise data envelopment analysis. Optimization. (2015);64(11):2441-54.

 

[13] Wei, Quanling, Jianzhong Zhang, and Xiangsun Zhang. "An inverse DEA model for inputs/outputs estimate." European Journal of Operational Research 121.1 (2000): 151-163.

 

[14] Jahanshahloo GR, Vencheh AH, Foroughi AA, Matin RK. Inputs/outputs estimation in DEA when some factors are undesirable. Applied Mathematics and Computation. (2004);156(1):19-32.

 

[15] Navabakhsh M, Lotfi FH, Allahviranloo T, Balf FR, Rezai HZ. The outputs estimation and improvement of efficiency on interval data in DEA. Int. J. Contemp. Math. Sciences. (2007);2(4): 195-201.

 

[16] Despotis, D. K., & Smirlis, Y. G. Data envelopment analysis with imprecise data. European Journal of Operational Research. (2002): 140(1), 24-36.

 

[17] Taher F, Daneshiyan B, Tohidi G,  Lotfi F. H, Modarres F. Estimating Undesirable Outputs and Desirable Inputs for Decision Making Units with Interval Data in Data Envelopment Analysis. Accept Journal of the Operations Research Society of China (JORC).(2019)