A goal programming procedure for ranking decision making units in DEA

Document Type: Research Articles

Authors

1 Department of Mathematics, Islamic Azad University, Science and Research Branch, Tehran, Iran.

2 Department of Mathematics, Islamic Azad University, Arak Branch, Arak Branch, Iran.

Abstract

This research proposes a methodology for ranking decision making units by
using a goal programming model.We suggest a two phases procedure. In phase
1, by using some DEA problems for each pair of units, we construct a pairwise
comparison matrix. Then this matrix is utilized to rank the units via the goal
programming model.

[1] N. Adler, L. Friedman, Z. Sinuany-Stern, Review of ranking methods in
data envelopment analysis context, European J. Operational Research 140
(2002) 249{265.
[2] P. Andersen, N.C. Petersen, A procedure for ranking ecient units in data
envelopment analysis, Management Sci. 39 (1993) 1261{1264.

[3] V. Belton, An IDEA-integrating data envelopment analysis with multiple
criteria analysis In: Goicochea, A., Duckstein, L., Zionts, S. (Eds.),
Proceedings of the Ninth International Conference on Multiple Criteria
Decision Making: Theory and Applications in Business, Industry and
Commerce. Springer Verlag, Berlin, (1992) 71{79.
[4] V. Belton and S.P. Vickers, Demystifying DEA -a visual interactive
approach based on multiple criteria analysis, J. Opl. Res. Soc. 44 (1993),
883{896.
[5] C-T. Chang, A modi ed goal programming model for piecewise linear
functions, Euro. J. Operatational Research 139 (2002) 62{67.
[6] A. Charnes, W. W. Cooper and E. Rhodes, Measuring the eciency of
decision making units, Euro. J. Operatational Research 2 (1978) 429{444.
[7] A. Charnes, W. W. Cooper, Management Model and Industrial
Application of Linear Programming, vol. 1, Wiley, New York, (1961).
[8] G.X. Chen and M. Deng, A cross-dependence based ranking system for
ecient and inecient units in DEA, Expert Sys. Appl. 38 (2011) 9648{
9655.
[9] W.D. Cook and M. Kress, Data envelopment model for aggregating
preference ranking, Management Sci. 36 (1990) 1302{1310.
[10] W. D. Cook, M. Kress and L. Seiford, Prioritization models for frontier
decision making units in DEA, Euro. J. Operatational Research 59 (1992)
319{323.
[11] J.R. Doyle and R.H Green, Data envelopment analysis and multiple
criteria decision making. Omega 21 (1993) 713{715.
[12] P.C. Fishburn, Expected utility: an anniversary and a new era. J. Risk
and Uncertainty, 1 (1988) 267{283.
[13] R.B. Flavell, A new goal programming, Omega 4 (1976) 731{732.
[14] A. Hadi-Vencheh and M.N. Mokhtarian, On the issue of non-zero weights
in preference voting and aggregation, Math. Sci. J. 5, (2010) 11{19.
[15] N. Hibiki and T. Sueyoshi, DEA sensitivity analysis by changing a
reference set: Regional contribution to Japanese industrial development,
Omega 27 (1999) 139{153.

[16] J.P. Ignizio, Introduction to Linear Goal Programming, Sage, Beverly,
Hills, CA (1985).
[17] M. Izadikhah, Ranking units with interval data based on ecient and
inecient frontiers, Math. Sci. J. 3(2007) 49{57.
[18] G.R. Jahanshahloo, F. Hosseinzadeh Lot , N. Shoja, G. Tohidi and S.
Razavyan, Ranking using l1-norm in data envelopment analysis, Appl.
Math. Comput. 153 (2004) 215{224.
[19] G.R. Jahanshahloo, H.V. Junior, F. Hosseinzadeh Lot and D. Akbarian,
A new DEA ranking system based on changing the reference set, Euro. J.
Operatational Research 181 (2007) 331{337.
[20] G.R. Jahanshahloo, F. Hosseinzadeh Lot , M. Khanmohammadi, M.
Kazemimanesh and V. Rezaie, Ranking of units by positive ideal DMU
with common weights, Expert Sys. Appl. 37 (2010) 7483{7488.
[21] G.R. Jahanshahloo, M. Rostamy-Malkhalifeh and S. Izadi-Boroumand,
A comment on Supply chain DEA: production possibility set and
performance evaluation model", Math. Sci. J. 7 (2011) 79{87.
[22] R.L. Keeney and H. Rai a, Decision Making with Multiple Objectives.
Wiley, New York, (1976).
[23] R.L. Keeney, Decision analysis: an overview, Operations Research, 30
(1982) 803{838.
[24] M. khodabakhshi and N. Aryavash, Input congestion, technical ineciency
and output reduction in fuzzy data envelopment analysis, Math. Sci. J. 6
(2011) 45{60.
[25] Y.J. Lai and C.L. Hwang, Fuzzy Multiple Objective Decision Making-
Methods and Applications, Springer-Verlag, (1994).
[26] S. M. Lee, Goal Programming for Decision Analysis, Auerbach,
Philadelphia, PA, (1972).
[27] S. Li, G. R. Jahanshahloo and M. Khodabakhshi, A super-eciency model
for ranking ecient units in data envelopment analysis, Appl. Math.
Comput. 184 (2007) 638{648.
[28] F-H.F. Liu and H.H. Peng, Ranking of units on the DEA frontier with
common weights, Computers and Operations Research, 35 (2008) 1624{
1637.

[29] S. Mehrabian, M.R. Alirezaee and G.R. Jahanshahloo, A complete
eciency ranking of decision making units in data envelopment analysis,
Computational Optimization and Appl., 14 (1999) 261{266.
[30] M. Oral, O. Kettani and P. Lang, A methodology for collective evaluation
and selection of industrial RD projects. Management Sci. 37 (1991) 871-
885.
[31] F. Rezai Balf, H. Zhiani Rezai, G.R. Jahanshahloo and F. Hosseinzadeh
Lot , Ranking ecient DMUs using the Tchebyche norm, Appl. Math.
Mod. 36 (2012) 46{56.
[32] C. Romero, Extended lexicographic goal programming: A unifying
approach, Omega 29 (2001) 63{71.
[33] T.L. Saaty, The Analytic Hierarchy Process. McGraw-Hill, New York,
(1980).
[34] M.J. Schniederjans, Goal Programming: Methodology and Applications,
Kluwer, Boston, MA, (1995).
[35] L.M. Seiford and J. Zhu, Infeasibility of super eciency data envelopment
analysis models, INFOR, 37 (1999) 174{187.
[36] T.R. Sexton, R.H. Silkman and A.J. Hogan, Data envelopment analysis:
Critique and extensions, in: R.H. Silkman (Ed.), Measuring Eciency: An
Assessment of Data Envelopment Analysis, Jossey-Bass, San Francisco,
CA, (1986) 73{105.
[37] Z. Sinuany-Stern and A. Mehrez, Discrete multiattribute utility approach
to project selection. J. Opl. Res. Soc. 38 (1987) 1135{1139.
[38] Z. Sinuany-Stern, A. Mehrez and Y. Hadad, An AHP/DEA methodology
for ranking decision making units. Intl. Trans. Op. Res.. 7 (2000) 109{124.
[39] T. J. Stewart, Data envelopment analysis and multiple criteria decision
making: a response. Omega, 22 (1994) 205{206.
[40] M. Tamiz, D. Jones and C. Romero, Goal programming for
decision making: An overview of the current state-of-the-art, Euro. J.
Operatational Research 111 (1998) 567{581.
[41] B. Vitoriano and C. Romero, Extended interval goal programming, J. Opl.
Res. Soc. 50 (1999) 1280{1283.

[42] Y-M. Wang, Y. Luo and L. Liang, Ranking decision making units by
imposing a minimum weight restriction in the data envelopment analysis.
J. Comput. Appl. Math. 223 (2009) 469-484.
[43] Y-M. Wang, Y. Luo and Y-X. Lan, Common weights for fully ranking
decision making units by regression analysis. Expert Sys. Appl. 38 (2011)
9122{9128.
[44] Y-M. Wang and T.M.S. Elhag, A goal programming method for obtaining
interval weights from an interval comparison matrix. Euro. J. Operational
Research, 177 (2007) 458{471.
[45] J. Zhu, Super-eciency and DEA sensitivity analysis, Euro. J. Operational
Research, 129 (2001) 443{455.