Kinaci, H., Najjari, V. (2019). A New Model for the Secondary Goal in DEA. Sahand Communications in Mathematical Analysis, 14(1), 173-183. doi: 10.22130/scma.2018.74414.315

Harun Kinaci; Vadoud Najjari. "A New Model for the Secondary Goal in DEA". Sahand Communications in Mathematical Analysis, 14, 1, 2019, 173-183. doi: 10.22130/scma.2018.74414.315

Kinaci, H., Najjari, V. (2019). 'A New Model for the Secondary Goal in DEA', Sahand Communications in Mathematical Analysis, 14(1), pp. 173-183. doi: 10.22130/scma.2018.74414.315

Kinaci, H., Najjari, V. A New Model for the Secondary Goal in DEA. Sahand Communications in Mathematical Analysis, 2019; 14(1): 173-183. doi: 10.22130/scma.2018.74414.315

^{1}Erciyes University, Faculty of Economics and Administrative Sciences, Business Department, Kayseri, Turkey.

^{2}Young Researchers and Elite Club, Maragheh branch, Islamic Azad University, Maragheh, Iran.

Abstract

The purpose of the current paper is to propose a new model for the secondary goal in DEA by introducing secondary objective function. The proposed new model minimizes the average of the absolute deviations of data points from their median. Similar problem is studied in a related model by Liang et al. (2008), which minimizes the average of the absolute deviations of data points from their mean. By using two well known data sets, which are also used by Liang et al.(2008), and Greene (1990) we compare the results of the proposed new model and several other models.

[1] I. Alp, Performance of evaluation of Goalkeepers of World Cup, G.U. Journal of Science, 19 (2006), pp. 119-125.

[2] I. Alp and A. Sozen, Efficiency Assessment of Turkey's Carbonization Index, Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 33 (2011), pp. 1678-1691.

[3] T.R. Anderson, K.B. Hollingsworth, and L.B. Inman, The fixed weighting nature of a cross-evaluation model, J. of Prod. Anal., 18 (2002), pp. 249-255.

[4] T. Anderson and G. Sharp, A New Measure of Baseball Batters Using DEA, Ann. of Oper. Res., 73 (1997), pp. 141-155.

[5] J. Doyle and R. Green, Efficiency and cross efficiency in DEA: Derivations, meanings and the uses, J. of the Oper. Res. Soc., 45 (1994), pp. 567-578.

[6] W. Greene, A Gamma-distributed Stochastic Frontier Model, Journal of Econometrics, J. of Econ., 46 (1990), pp. 141-163.

[7] L. Liang, J. Wu, W.D. Cook, and J.Zhu, Alternative secondary goals in DEA cross-efficiency evaluation, Int. J. Prod. Econ., 113 (2008), pp. 1025-1030.

[8] R. Lin, Z. Chen, and W. Xiong, An Iterative Method for Determining Weights in Cross Efficiency Evaluation, Comp. and Ind. Engineering, 101 (2016), pp. 91-102.

[9] M. Mercan, A. Reisman, R. Yoalan, and A.B. Emel, The Effect of Scale and Mode of Ownership on the Financial Performance of the Turkish Banking Sector: Results of A DEA Based Analysis, Soc.-Econ. Plan. Sciences, 37 (2003), pp. 185-202.

[10] H.H. Orkcu and H. Bal, Goal Programming Approaches for Data Envelopment Analysis Cross-Efficiency Evaluation, Applied Math. and Comp., 218 (2011), pp. 346-356.

[11] G. Tohidi, M. Khodadadi, and E. Rostamian, Improving the Selection Symmetric Weights as a Secondary Goal in DEA Cross-Efficiency Evaluation, Int. J. of Math. Modelling and Computations, 3 (2013), pp. 149-155.

[12] M.D. Troutt, Derivation of the maximin efficiency ratio model from the maximum decisional efficiency principle, Ann. of Oper. Research, 73 (1997), pp. 323-338.

[13] T.R. Sexton, The methodology of data envelopment analysis, In Silkman, R.H. (Ed.) Measuring efficiency: An assessment of Data Envelopment Analysis, San Francisco: Jossey-Bass, (1986), pp. 7-29.

[14] A. Sozen and I. Alp, and A. Ozdemir, Assessment Of Operational And Environmental Performance Of The Thermal Power Plants In Turkey By Using Data Envelopment Analysis, E. Policy (Soc. A), 38 (2010), pp. 6194-6203.

[15] Y.M. Wang and K.S. Chin, Some alternative models for DEA cross-efficiency evaluation, Int. J. of Prod. Econ., 128 (2010a), pp. 332-338.

[16] Y.M. Wang and K.S. Chin, A neutral DEA model for cross-efficiency evaluation and its extension, Expert Sys. with App., 37 (2010b), pp. 3666-3675.

[17] J. Wu, J. Chu, J. Sun, Q. Z, and L. Liang, Extended Secondary Goal Models for Weights Selection in DEA Cross-Efficiency Evaluation, Comp. and Ind. Engineering, 93 (2016), pp. 143-151.

[18] J. Zhu, Data envelopment analysis vs. principal component analysis: An illustrative study of economic performance of Chinese cities, E. J. of Oper. Res., 111 (1998), pp. 50-61.