References
1. Charnes, A., Cooper, W.W., and Rhodes, E. Measuring
the eciency of decision making units", European
Journal of Operational Research, 2, pp. 429-444 (1978).
2. Tavana, M. and Khalili-Damghani, K. A new twostage
Stackelberg fuzzy data envelopment analysis
model", Measurement, 53, pp. 277-296 (2014).
3. Banihashemi, S., Tohidi, G., and Sanei, M. Sensitivity
analysis of ecient and inecient units in
integer-valued data envelopment analysis", International
Journal of Mathematical Modelling & Computations,
4, pp. 45-53 (2014).
4. Banker, R.D., Charnes, A., and Cooper, W.W. Some
models for estimating technical and scale ineciencies
in data envelopment analysis", Management Science,
30, pp. 1078-1092 (1984).
5. Bogetoft, P. and Hougaard, J.L. Eciency evaluations
based on potential (non-proportional) improvements",
Journal of Productivity Analysis, 12, pp. 233-
247 (1999).
6. Diabat, A., Shetty, U., and Pakkala, T. Improved
eciency measures through directional distance formulation
of data envelopment analysis", Annals of
Operations Research, 229, pp. 325-346 (2015).
7. Kao, C. Eciency improvement in data envelopment
analysis", European Journal of Operational Research,
73, pp. 487-494 (1994).
8. Chen, T.-H., Bao, C.-P., and Chang, S.-Y. Another
view of eciency improvement in data envelopment
analysis", Journal of the Chinese Institute of Industrial
Engineers, 26, pp. 109-114 (2009).
9. Khoshfetrat, S. and Daneshvar, S. Improving weak
eciency frontiers in the fuzzy data envelopment
analysis models", Applied Mathematical Modelling, 35,
pp. 339-345 (2011).
10. Akbarian, D. On characterizing weak dening hyperplanes
(weak Facets) in DEA with constant returns
to scale technology", arXiv preprint arXiv:1409.7546,
(2014).
11. Hadi-Vencheh, A., Jablonsky, J., and Esmaeilzadeh,
A. The slack-based measure model based on supporting
hyperplanes of production possibility set", Expert
Systems with Applications, 42, pp. 6522-6529 (2015).
12. Jahanshahloo, G.R., Lot, F.H., and Zohrehbandian,
M. Finding the piecewise linear frontier production
function in data envelopment analysis", Applied Mathematics
and Computation, 163, pp. 483-488 (2005).
13. Korhonen, P. Searching the ecient frontier in data
envelopment analysis", In Aiding Decisions with Multiple
Criteria, Springer, pp. 543-558 (2002).
14. Jahanshahloo, G.R., Hosseinzadeh, F., Rezai, H.Z.,
and Balf, F.R. Finding strong dening hyperplanes
of production possibility set", European Journal of
Operational Research, 177, pp. 42-54 (2007).
N. Ebrahimkhani Ghazi et al./Scientia Iranica, Transactions E: Industrial Engineering 25 (2018) 2852{2866 2865
15. Yu, P. and Zeleny, M. The set of all nondominated
solutions in linear cases and a multicriteria simplex
method", Journal of Mathematical Analysis and Applications,
49, pp. 430-468 (1975).
16. Hosseinzadeh, F., Jahanshahloo, G.R., Mozaari, M.,
and Gerami, J. Finding DEA-ecient hyperplanes
using MOLP ecient faces", Journal of Computational
and Applied Mathematics, 235, pp. 1227-1231 (2011).
17. Charnes, A., Cooper, W.W., Lewin, A.Y., Morey,
R.C., and Rousseau, J. Sensitivity and stability
analysis in DEA", Annals of Operations Research, 2,
pp. 139-156 (1984).
18. Forghani, A. and Naja, E. Sensitivity analysis in
two-stage DEA", Iranian Journal of Optimization, 07,
pp. 872-886 (2015).
19. Khalili-Damghani, K. and Taghavifard, B. Sensitivity
and stability analysis in two-stage DEA models with
fuzzy data", International Journal of Operational Research,
17, pp. 1-37 (2013).
20. Huang, Z., Li, S., and Rousseau, J. Determining rates
of change in data envelopment analysis", Journal of the
Operational Research Society, 48, pp. 591-593 (1997).
21. Jahanshahloo, G.R., Hosseinzadeh, F., Shoja, N.,
Sanei, M., and Tohidi, G. Sensitivity and stability
analysis in DEA", Applied Mathematics and Computation,
169, pp. 897-904 (2005).
22. Ebrahimkhani, N., Hosseinzadeh, F., Rostamy-
Malkhalifeh, M., Jahanshahloo, G., and Namin, M.A.
An improved approach on sensitivity and stability
analysis in DEA", International Journal of Applied
Mathematics and StatisticsTM, 56, pp. 75-84 (2017).
23. Kordrostami, S., Pourjafar, S., and Pourjafar, H. A
geometric method in data envelopment analysis to
obtain the region of eciency", Indian Journal of
Science and Technology, 6, pp. 4116-4122 (2013).
24. Zamani, P. and Borzouei, M. Finding stability regions
for preserving eciency classication of variable
returns to scale technology in data envelopment analysis",
Journal of Industrial Engineering International,
12, pp. 499-507 (2016).
25. Farrell, M.J. The measurement of productive e-
ciency", Journal of the Royal Statistical Society. Series
A (General), 120, pp. 253-290 (1957).
26. Kerstens, K. and Vanden^a Eeckaut, P., Technical E-
ciency Measures on DEA and FDH: A Reconsideration
of the Axiomatic Literature, In Universite Catholique
de Louvain, Center for Operations Research and
Econometrics (CORE) (1995).
27. Colwell, R.J. and Davis, E.P. Output and productivity
in banking", The Scandinavian Journal of Economics,
S111-S129 (1992).
28. Lovell, C.K. and Schmidt, P. A comparison of alternative
approaches to the measurement of productive e-
ciency", In Applications of Modern Production Theory:
Eciency and Productivity, Springer, pp. 3-32 (1988).
29. Pahlavan, R., Omid, M., and Akram, A. Application
of data envelopment analysis for performance assessment
and energy eciency improvement opportunities
in greenhouses cucumber production", Journal of
Agricultural Science and Technology, 14, pp. 1465-1475
(2012).
30. Coelli, T. A multi-stage methodology for the solution
of orientated DE models", Operations Research Letters,
23, pp. 143-149 (1998).
31. Portela, M.C.A.S., Borges, P.C., and Thanassoulis, E.
Finding closest targets in non-oriented DEA models:
the case of convex and non-convex technologies", Journal
of Productivity Analysis, 19, pp. 251-269 (2003).
32. Post, T. and Spronk, J. Performance benchmarking
using interactive data envelopment analysis", European
Journal of Operational Research, 115, pp. 472-
487 (1999).
33. Russell, R.R. Measures of technical eciency", Journal
of Economic Theory, 35, pp. 109-126 (1985).
34. Frei, F.X. and Harker, P.T. Projections onto ecient
frontiers: theoretical and computational extensions to
DEA", Journal of Productivity Analysis, 11, pp. 275-
300 (1999).
35. Golany, B., Phillips, F., and Rousseau, J. Models
for improved eectiveness based on DEA eciency
results", IIE Transactions, 25, pp. 2-10 (1993).
36. Baek, C. and Lee, J.-D. The relevance of DEA benchmarking
information and the least-distance measure",
Mathematical and Computer Modelling, 49, pp. 265-
275 (2009).
37. Sayin, S. An algorithm based on facial decomposition
for nding the ecient set in multiple objective linear
programming", Operations Research Letters, 19, pp.
87-94 (1996).
38. Jahanshahloo, G., Lot, F.H., and Akbarian, D.
Finding weak dening hyperplanes of PPS of the
BCC model", Applied Mathematical Modelling, 34, pp.
3321-3332 (2010).
39. Seiford, L.M. and Zhu, J. Context-dependent data
envelopment analysis-measuring attractiveness and
progress", Omega, 31, pp. 397-408 (2003).
40. Sh. Banihashemi, M.S., Abri, A.GH., and Sourani, F.
Finding 'Improvement region' for the inecient units
in data envelopment analysis", Applied Mathematics
& Information Sciences, Appl. Math. Inf. Sci., 10, pp.
1169-1176 (2016).
41. Cherchye, L. and Van Puyenbroeck, T. A comment on
multi-stage DEA methodology", Operations Research
Letters, 28, pp. 93-98 (2001).
2866 N. Ebrahimkhani Ghazi et al./Scientia Iranica, Transactions E: Industrial Engineering 25 (2018) 2852{2866