Non-dominated DEA cross efficiency scores; a secondary goal approach

Subject Areas : Data Envelopment Analysis

سعید  شاه قبادی ¹ (گروه ریاضی کاربردی، واحد کرمانشاه، دانشگاه آزاد اسلامی، کرمانشاه، ایران.)
عباس  قماشی ² (گروه ریاضی کاربردی، واحد کرمانشاه، دانشگاه آزاد اسلامی، کرمانشاه، ایران.)
فرهاد  مرادی ³ (گروه ریاضی، واحد سنندج، دانشگاه آزاد اسلامی، سنندج، ایران.)

Received: 2022-06-12 Accepted : 2022-07-20 Published : 2022-06-01

Keywords: Multi-Objective Optimization, Data Envelopment Analysis (DEA), cross-efficiency evaluation,

Abstract :

Data envelopment analysis (DEA) is a non-parametric programming method for evaluating the relative efficiency of a set of peer decision-making units (DMUs) with multiple inputs and multiple outputs. The DEA cross-efficiency method is a well-known method that use to evaluate and ranking a set of peer decision-making units. Whenever a DMU intends to evaluate other DMUs, it faces the problem of non-uniqueness optimal weights of DEA models. Because different weights give us different cross-scores and subsequently different cross-efficiencies scores and this will confuse the decision-maker to make an ultimate decision. The main drawback of this method is the alternate optimal solution set of the DEA model. The main purpose of this study is to propose an approach to this problem to generate non-dominated DEA cross-efficiency scores. We propose a linear programming secondary goal model to select a set of optimal weights for each DMU. Our proposed method is not only simpler than other methods presented with the same purpose, but also does not go beyond the main method.

References:

REFERENCES

 

Aldamak, A. and S. Zolfaghari (2017). "Review of efficiency ranking methods in data envelopment analysis." Measurement 106: 161-172.

Amin, G. R. and M. Toloo (2004). "A polynomial-time algorithm for finding ε in DEA models." Computers & Operations Research 31(5): 803-805.

Charnes, A., W. W. Cooper and E. Rhodes (1978). "Measuring the efficiency of decision making units." European Journal of Operational Research 2(6): 429-444.

Chen, Y. W., M. Larbani and Y. P. Chang (2009). "Multiobjective data envelopment analysis." Journal of the Operational Research Society 60(11): 1556-1566.

Cook, W. D. and L. Seiford (2009). "Data envelopment analysis (DEA) - Thirty years on." European Journal of Operational Research 192(1): 1-17.

Cooper, W. W., L. M. Seiford and K. Tone (2007). Data envelopment analysis a comprehensive text with models, applications, references and DEA-solver software. New York (Estados Unidos, Springer.

Hosseinzadeh Lotfi, F., G. Jahanshahloo, M. Vaez-Ghasemi and Z. Moghaddas (2013). "Modified Malmquist Productivity Index Based on Present Time Value of Money." Journal of Applied Mathematics 2013: 607190.

Hosseinzadeh Lotfi, F., G. R. Jahanshahloo, M. Vaez-Ghasemi and Z. Moghaddas (2013). "Evaluation progress and regress of balanced scorecards by multi-stage Malmquist Productivity Index." Journal of Industrial and Production Engineering 30(5): 345-354.

Izadikhah, M. and R. Farzipoor Saen (2019). "Solving voting system by data envelopment analysis for assessing sustainability of suppliers." Group Decision and Negotiation 28(3): 641-669.

Kao, C. and H. T. Hung (2005). "Data envelopment analysis with common weights: the compromise solution approach." Journal of the Operational Research Society 56(10): 1196-1203.

Kornbluth, J. S. H. (1991). "Analysing Policy Effectiveness Using Cone Restricted Data Envelopment Analysis." Journal of the Operational Research Society 42(12): 1097-1104.

Lotfi, F. H., A. Ebrahimnejad, M. Vaez-Ghasemi and Z. Moghaddas Data envelopment analysis with R, Springer.

Pourhabib Yekta, A., S. Kordrostami, A. Amirteimoori and R. Kazemi Matin (2018). "Data envelopment analysis with common weights: the weight restriction approach." Mathematical Sciences 12(3): 197-203.

Roll, Y., W. D. Cook and B. Golany (1991). "Controlling Factor Weights in Data Envelopment Analysis." IIE Transactions 23(1): 2-9.

Shahghobadi, S. (2020). "Utilization of performance indicators in data envelopment analysis to increase the efficiency discrimination of units." Computers & Industrial Engineering 145: 106535.

Soltanifar, M. and S. Shahghobadi (2013). "Selecting a benevolent secondary goal model in data 

envelopment analysis cross-efficiency evaluation by a voting model." Socio-Economic Planning Sciences 47(1): 65-74.

Soltanifar, M. and S. Shahghobadi (2014). "Survey on rank preservation and rank reversal in data envelopment analysis." Knowledge-Based Systems 60: 10-19.

Sun, J., J. Wu and D. Guo (2013). "Performance ranking of units considering ideal and anti-ideal DMU with common weights." Applied Mathematical Modelling 37(9): 6301-6310.

Zohrehbandian, M., A. Makui and A. Alinezhad (2010). "A compromise solution approach for finding common weights in DEA: an improvement to Kao and Hung's approach." Journal of the Operational Research Society 61(4): 604-610.