Stability of the Classification of Returns to Scale FDH Models in the Presence of Undesirable Data

Subject Areas : Business Strategy

Leila  Jalaei ¹ (Arak Branch, Islamic Azad University, Arak, Iran)
Dariush  Akbarian ² (Department of Mathematics, Arak Branch, Islamic Azad University, Arak, Iran)

Received: 2014-02-13 Accepted : 2014-09-13 Published : 2016-07-01

Keywords: DEA, FDH, Stability, undesirable data, Returns-to-Scale, Polynomial-Time Algorithms,

Abstract :

This paper deals with the estimation of returns to scale (RTS) in free disposal hull (FDH) models for undesirable data and provides some stability intervals for preserving the RTS classification. It has been shown that the proposed stability intervals can be obtained via a polynomial-time algorithm based on the calculation of certain ratios of inputs and outputs, without solving any mathematical programming problem. The results of the study have been proved via some lemmas and theorems for undesirable data and have been illustrated by numerical example.

References:

[1] Liu, W.B., W. Meng, X.X. Li and D.Q., DEA models with undesirable inputs and outputs, Annals of Operations Research Zhang (2010), 173, 177-194.

[2] R.D. Banker, A. Charnes, W.W. Cooper, Some models for estimating technicall and scale efficiencies in data envelopment analysis, Management Science 30 (1984) 1078–1092.

[4] W.W. Cooper, L.M. Sieford, K. Tone, Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA Solver Software, Kluwer Academic Publishers, 2000.

[5] D. Deprins, L. Simar, H. Tulkens, Measuring labor-efficiency in post offices, in: M. Marchand, P. Pestieau, H. Tulkens (Eds.), The Performance of Public.

[6] R. Fare, S. Grosskopf, C.A.K. Lovell and S. Yaisawarang, Derivation of shadow prices for undesirable outputs: a distance function approach, Rev. Econ. Statist, (1993), 75, (2) 374-380.

[7] R. Fare, S. Grosskopf, Estimating of returns to scale using data envelopment analysis: A comment, European Journal of Operational Research 79 (3) (1995) 379–382.

[8] R. Fare. and S. Grosskopf Modeling undesirable factors in e_ciency evaluation: Comment, European Journal of Operational Research, (2004),  157, 242-245.

[9] B. Golany. and Y. Roll An application procedure for DEA, Omega: The International Journal of Management Science, (1989),  17, 237-250

 [10] B. Golany, G. Yu, Estimating returns to scale in DEA, European Journal of Operational Research 103 (1) (1997) 28–37.

[11] G.R. Jahanshahloo, F. Hosseinzadeh Lotfi, M. Zohrehbandian, Notes on sensitivity and stability of the classification of returns to scale in data envelopment analysis, Journal of Productivity Analysis 23 (2005) 309–313.

[12] G.R. Jahanshahloo, M. Soleimani-damaneh, Estimating returns-to-scale in data envelopment analysis: A new procedure, Applied Mathematics and Computation 150 (1) (2004) 89–98.

[13] G.R. Jahanshahloo, M. Soleimani-damaneh, M. Rostamy-Malkhalifeh, An enhanced procedure for estimating returns-to-scale in DEA, Applied Mathematics and Computation 171 (2005) 1226–1238.

[14] K. Kerstens, P. Vanden Eeckaut, Estimating returns-to-scale using nonparametric deterministic technologies: A new method based on goodnessof- fit, European Journal of Operational Research 113 (1999) 206–214.

[15] Koopmans, T.C. Analysis of production as an e_cient combination of activities, in: T.C. Koopmans (Ed.), Activity Analysis of Production and Allocation, Cowles Commission, Wiley, New York(1951), 33-97

[16] Liu, W.B., W. Meng, X.X. Li and D.Q. Zhang (2010), DEA models with undesirable inputs and outputs, Annals of Operations Research(2010), 173, 177-194.

[17] Liu, W.B. and J. Sharp, DEA models via goal programming, In G. Westerman(Ed.), Data envelopment analysis in the public and private sector. Deutscher Universitats-Verlag. (1999).

[18] Lovell, C.A.K., J.T. Pastor and J.A Turner, Measuring macroeconomic   performance in the OECD: a comparison of European and non-European countries, European Journal of Operational Research, (1995),  87, 507-518.

[19] V.V. Podinovski, On the linearisation of reference technologies for testing returns to scale in FDH models, European Journal of Operational Research 152 (3) (2004) 800–802.

[20] Pastor, J.T., Translation invariance in data envelopment analysis, Annals of Operations Research, (1996),  66, 93-102.

[21] L.M. Seiford, J. Zhu, Sensitivity and stability of the classifications of returns to scale in data envelopment analysis, Journal of Productivity Analysis 12 (1999) 55–75.

[22] Seiford, L.M. and J. Zhu Modeling undesirable factors in e_ciency evaluation, European Journal of Operational research, (2002),  142, 16-20.

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

[24]M.Soleimani-damaneh, A.Mostafaee Stability of the classification of return to scale in FDH models Original Research Article European Journal of Operation Research, Volume 196, Issue 3, 1 August 2009, pages 1223-1228

[25] M. Soleimani-damaneh, G.R. Jahanshahloo, M. Reshadi, On the estimation of returns to scale in FDH models, European Journal of Operational Research 174 (2) (2006) 1055–1059.

[26] M. Soleimani-damaneh, M. Reshadi, A polynomial-time algorithm to estimate returns to scale in FDH models, Computers and Operations Research 34 (7) (2007) 2168–2176.

[27] Tulkens H. On FDH efficiency analysis: Some methodological issues and applications to retail banking, courts and urban transit. Journal of Productivity Analysis 1993;4:183-210.

[28] M. Zarepisheh, M. Soleimani-damaneh, Global Variation of Outputs with Respect to the Variation of Inputs in Performance Analysis; Generalized RTS, European Journal of Operational Research 186 (2008) 786–800.

[29] M. Zarepisheh, M. Soleimani-damaneh, A Dual Simplex-based Method for Determination of the Right and Left Returns to Scale in DEA. European Journal of Operational Research, in press.

[30] M. Zarepisheh, M. Soleimani-damaneh, L. Pourkarimi, Determination of returns to scale by CCR formulation without chasing down alternative optimal solutions, Applied Mathematics Letters 19 (9) (2006) 964–967.

[31] Yu, M.M. Measuring physical e_ciency of domestic airports in Taiwan with undesirable outputs and environment factors, Journal of Air Transport Man-agement, (2004),  10, 295-303.