Using lexicographic parametric programming for identifying efficient hyperpalnes in DEA

Subject Areas : Data Envelopment Analysis

فرهاد  حسین زاده لطفی ¹ (Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran)
ف.  رضایی بالف ² (Department of Mathematics, Islamic Azad University, Qaemshahr, Iran)
A.  تقوی ³ (Department of Mathematics, Islamic Azad University, Qaemshahr, Iran)

Received: 2015-08-25 Accepted : 2015-08-25 Published : 2009-10-01

Keywords: Data envelopment analysis, efficiency analysis, Lexicographic, Parametric programming, Efficient hyperplanes,

Abstract :

This paper investigates a procedure for identifying all efficient hyperplanes of production possibility set (PPS). This procedure is based on a method which recommended by Pekka J. Korhonen[8]. He offered using of lexicographic parametric programming method for recognizing all efficient units in data envelopment analysis (DEA). In this paper we can find efficient hyperplanes, via using the parameterization of the right hand side vector of the envelopment problem of each efficient unit.

References:

[1] Banker R.D., Charnes A., Cooper W. W., Some models for estimating technical and scale inefficiencies in Data Envelopment Analysis, Management Science, 30, 1078-1092, 1984.

[2] Charnes A., Cooper W. W., and Rhodes E., Measuring the efficiency of decision making units, European Journal of Operational Research, 2, 429-444, 1978.

[3] Charnes A., Cooper W. W., Rhodes E., Short communication: Measuring efficiency of decision making units, European Journal of Operational Research, 3,339, 1979.

[4] Halme M., Joro T., Korhonen P., Salo S., Wallenius J., A value efficiency approach to incorporating preference information in data envelopment analysis, Management Science, 45, 103-15, 1999.

[5] Jahanshahloo G. R., Hosseinzadeh Lotfi F., Sohraiee S., characteristics of Defining Hyperplanes of Variable Returns to Scale Technology in DEA.

[6] Jahanshahloo G. R., Hosseinzadeh Lotfi F., Zhiani Rezai H., Rezai Balf F.,  Finding Strong Defining Hyper planes Of Production Possibility Set, European Journal of Operational Research, 177, 42-54, 2007.

 [7] Korhonen P., Halme M., Using lexicographic parametric programming for searching a nondominated set in multiple objective linear programming, Journal of Multi-Criteria Decision Analysis, 5, 291-300, 1996.

[8] Korhonen P., Antti Siitari P., Using lexicographic parametric programming for identifying efficient units in DEA, Computers and operations Research, 34, 2177-2190, 2007.

[9] Zohrehbandian M., Jahanshahloo G. R., Hosseinzadeh Lotfi F., Finding the piecewise linear frontier production function in Data Envelopment Analysis, Applied Mathematics and Computation, 163 (1), 483-488, 2005.