Interactive multiobjective DEA target setting using lexicographic DDF
RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 6, pp. 1703-1722.

In this paper, a new interactive multiobjective target setting approach based on lexicographic directional distance function (DDF) method is proposed. Lexicographic DDF computes efficient targets along a specified directional vector. The interactive multiobjective optimization approach consists in several iteration cycles in each of which the Decision Making Unit (DMU) is presented a fixed number of efficient targets computed corresponding to different directional vectors. If the DMU finds one of them promising, the directional vectors tried in the next iteration are generated close to the promising one, thus focusing the exploration of the efficient frontier on the promising area. In any iteration the DMU may choose to finish the exploration of the current region and restart the process to probe a new region. The interactive process ends when the DMU finds its most preferred solution (MPS).

DOI : 10.1051/ro/2019105
Classification : 90B50, 90C29, 90B30
Mots-clés : DEA, target setting, interactive multiobjective optimization, lexicographic directional distance function, most preferred solution
@article{RO_2020__54_6_1703_0,
     author = {Soltani, Narges and Lozano, Sebasti\'an},
     title = {Interactive multiobjective {DEA} target setting using lexicographic {DDF}},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {1703--1722},
     publisher = {EDP-Sciences},
     volume = {54},
     number = {6},
     year = {2020},
     doi = {10.1051/ro/2019105},
     mrnumber = {4150239},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro/2019105/}
}
TY  - JOUR
AU  - Soltani, Narges
AU  - Lozano, Sebastián
TI  - Interactive multiobjective DEA target setting using lexicographic DDF
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2020
SP  - 1703
EP  - 1722
VL  - 54
IS  - 6
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ro/2019105/
DO  - 10.1051/ro/2019105
LA  - en
ID  - RO_2020__54_6_1703_0
ER  - 
%0 Journal Article
%A Soltani, Narges
%A Lozano, Sebastián
%T Interactive multiobjective DEA target setting using lexicographic DDF
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2020
%P 1703-1722
%V 54
%N 6
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ro/2019105/
%R 10.1051/ro/2019105
%G en
%F RO_2020__54_6_1703_0
Soltani, Narges; Lozano, Sebastián. Interactive multiobjective DEA target setting using lexicographic DDF. RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 6, pp. 1703-1722. doi : 10.1051/ro/2019105. http://www.numdam.org/articles/10.1051/ro/2019105/

[1] J. Aparicio, A survey on measuring efficiency through the determination of the least distance in data envelopment analysis. J. Centrum Cathedra 9 (2016) 143–167. | DOI

[2] J. Aparicio, J.L. Ruiz and I. Sirvent, Closest targets and minimum distance to the Pareto-efficient frontier in DEA. J. Prod. Anal. 28 (2007) 209–218. | DOI

[3] J. Aparicio, J.M. Cordero and J.T. Pastor, The determination of the least distance to the strongly efficient frontier in Data Envelopment Analysis oriented models: Modelling and computational aspects. Omega 71 (2017) 1–10. | DOI

[4] R. Benayoun, J. Montgolfier, J. Tergny and O. Laritchev, Linear programming with multiple objective functions: step method (STEM). Math. Prog. 1 (1971) 366–375. | DOI | MR | Zbl

[5] P. Bogetoft and K. Nielsen, Internet based benchmarking. Group Decis. Negotiation 14 (2005) 195–215. | DOI

[6] R.G. Chambers, Y. Chung and R. Färe, Benefit and Distance Functions. J. Econ. Theory 70 (1996) 407–419. | DOI | Zbl

[7] A. Ebrahimnejad and F. Hosseinzadeh Lofti, Equivalence relationship between the general combined-oriented CCR model and the weighted minimax MOLP formulation. J. King Saud Univ. – Sci. 24 (2012) 47–54. | DOI

[8] A. Ebrahimnejad and M. Tavana, An interactive MOLP method for identifying target units in output-oriented DEA models: the NATO enlargement problem. Measurement 52 (2014) 124–134. | DOI

[9] M.P. Estellita Lins, L. Angulo-Meza and A.C. Moreira Da Silva, A multi-objective approach to determine alternative targets in data envelopment analysis. J. Oper. Res. Soc. 55 (2004) 1090–1101. | DOI | Zbl

[10] A.M. Geoffrion, J.S. Dyer and A. Feinberg, An interactive approach for multi-criterion optimization with an application to the operation of an academic department. Part I. Manage. Sci. 19 (1972) 357–368. | Zbl

[11] J. Gerami, An interactive procedure to improve estimate of value efficiency in DEA. Expert Syst. App. 137 (2019) 29–45. | DOI

[12] B. Golany, An interactive MOLP procedure for the extension of DEA to effectiveness analysis. J. Oper. Res. Soc. 39 (1988) 725–734. | DOI | Zbl

[13] E. Gutiérrez, S. Lozano and S. Furió, Evaluating efficiency of international container shipping lines: a bootstrap DEA approach. Maritime Econ. Logistics 16 (2014) 55–71. | DOI

[14] E. Gutiérrez and S. Lozano, Efficiency assessment and output maximization possibilities of European small and medium sized airports. Res. Transp. Econ. 56 (2016) 3–14. | DOI

[15] M. Halme, T. Joro, P. Korhonen, S. Salo and J. Wallenius, A value efficiency approach to incorporating preference information in data evelopment analysis. Manage. Sci. 45 (1999) 103–115. | DOI | Zbl

[16] F. Hosseinzadeh Lotfi, G.R. Jahanshahloo, M. Soltanifar, A. Ebrahimnejad and S.M. Mansourzadeh, Relationship between MOLP and DEA based on output-orientated CCR dual model. Expert Syst. App. 37 (2010) 4331–4336. | DOI

[17] F. Hosseinzadeh Lotfi, G.R. Jahanshahloo, A. Ebrahimnejad, M. Soltanifar and S.M. Mansourzadeh, Target setting in the general combined-oriented CCR model using an interactive MOLP method. J. Comput. Appl. Math. 234 (2010) 1–9. | DOI | MR | Zbl

[18] T. Joro, P. Korhonen and J. Wallenius, Structural comparison of data envelopment analysis and multiple objective linear programming. Manage. Sci. 44 (1998) 962–970. | DOI | Zbl

[19] P. Korhonen and J. Wallenius, A pareto race. Naval Res. Logistics 35 (1988) 615–623. | DOI | Zbl

[20] P. Korhonen, R. Tainio and J. Wallenius, Value efficiency analysis of academic research. Eur. J. Oper. Res. 130 (2001) 121–132. | DOI | Zbl

[21] P. Korhonen, M. Soismaa and A. Siljamäki, On the use of value efficiency analysis and some further developments. J. Prod. Anal. 17 (2002) 49–65. | DOI

[22] P. Korhonen, S. Stenfors and M. Syrjänen, Multiple objective approach as an alternative to radial projection in DEA. J. Prod. Anal. 20 (2003) 305–321. | DOI

[23] P.J. Korhonen, A. Dehnokhalaji and N. Nasrabadi, A lexicographic radial projection onto the efficient frontier in Data Envelopment Analysis. Eur. J. Oper. Res. 265 (2018) 1005–1012. | DOI | MR | Zbl

[24] S. Lozano and L. Calzada-Infante, Computing gradient-based stepwise benchmarking paths. Omega 81 (2018) 195–207. | DOI

[25] S. Lozano and E. Gutiérrez, A multiobjective approach to fleet, fuel and operating cost efficiency of European airlines. Comput. Ind. Eng. 61 (2011) 473–481. | DOI

[26] S. Lozano and N. Soltani, DEA target setting using lexicographic and endogenous Directional Distance Function approaches. J. Prod. Anal. 50 (2018) 55–70. | DOI

[27] S. Lozano and N. Soltani, Efficiency assessment using a multidirectional DDF approach. Int. Trans. Oper. Res. 27 (2020) 2064–2080. | DOI | MR

[28] S. Lozano and G. Villa, Determining a sequence of targets in DEA. J. Oper. Res. Soc. 56 (2005) 1439–1447. | DOI | Zbl

[29] S. Lozano and G. Villa, Multiobjective target setting in data envelopment analysis using AHP. Comput. Oper. Res. 36 (2009) 549–564. | DOI | MR | Zbl

[30] S. Lozano and G. Villa, Gradual technical and scale efficiency improvement in DEA. Ann. Oper. Res. 173 (2010) 123–136. | DOI | MR | Zbl

[31] N. Malekmohammadi, F. Hosseinzadeh Lotfi and A.B. Jaafar, Target setting in data envelopment analysis using MOLP. Appl. Math. Modell. 35 (2011) 328–338. | DOI | MR | Zbl

[32] M. Moradi Dalini and A.A. Noura, Relation between Imprecise DESA and MOLP Methods. Iran. J. Manage. Stud. 11 (2018) 23–36.

[33] H. Nakayama, Y. Sawaragi, Satisfying trade-off method for multiobjective programming. An interactive decision analysis, edited by M. Grauer and A.P. Wierzbicki. In Vol. 229 of Lecture Notes in Economics and Mathematical Systems. Springer, Heidelberg (1984) 113–122. | DOI | MR | Zbl

[34] G.T. Post and J. Spronk, Performance benchmarking using interactive data envelopment analysis. Eur. J. Oper. Res. 115 (1999) 472–487. | DOI | Zbl

[35] R.E. Steuer and E.U. Choo, An interactive weighted Tchebycheff procedure for multiple objective programming. Math. Prog. 26 (1983) 326–344. | DOI | MR | Zbl

[36] M. Tavana, A. Ebrahimnejad, F.J. Santos-Arteaga, S.M. Mansourzadeh and R. Kazemi Matin, A hybrid DEA-MOLP model for public school assessment and closure decision in the City of Philadelphia. Soc.-Econ. Planning Sci. 61 (2018) 70–89. | DOI

[37] E. Thanassoulis and R.G. Dyson, Estimating preferred target input–output levels using data envelopment analysis. Eur. J. Oper. Res. 56 (1992) 80–97. | DOI | Zbl

[38] K. Wang, Y. Xian, C.Y. Lee, Y.M. Wei and Z. Huang, On selecting directions for directional distance functions in a non-parametric framework: a review. Ann. Oper. Res. 278 (2019) 43–76. | DOI | MR

[39] A.P. Wierzbicki, The use of reference objectives in multiobjective optimization, edited by G. Fandel and T. Gal. In Vol. 177 of Lecture Notes in Economics and Mathematical Systems. Springer, Heidelberg (1980) 468–486. | DOI | MR | Zbl

[40] B.Y.H. Wong, M. Luque and J.B. Yang, Using interactive multiobjective methods to solve DEA problems with value judgements. Comput. Oper. Res. 36 (2009) 623–636. | DOI | MR | Zbl

[41] J.B. Yang, Gradient projection and local region search for multiobjective optimisation. Eur. J. Oper. Res. 112 (1999) 432–459. | DOI | Zbl

[42] J.B. Yang and D.L. Xu, Interactive minimax optimisation for integrated performance analysis and resource planning. Comput. Oper. Res. 46 (2014) 78–90. | DOI | MR

[43] J.B. Yang, B.Y.H. Wong, D.L. Xu and T.J. Stewart, Integrating DEA-oriented performance assessment and target setting using interactive MOLP methods. Eur. J. Oper. Res. 195 (2009) 205–222. | DOI | Zbl

[44] J.B. Yang, D.L. Xu and S. Yang, Integrated efficiency and trade-off analyses using a DEA-oriented interactive minimax reference point approach. Comput. Oper. Res. 39 (2012) 1062–1073. | DOI | MR | Zbl

[45] J. Zhu, Data envelopment analysis with preference structure. J. Oper. Res. Soc. 47 (1996) 136–150. | DOI | Zbl

[46] S. Zionts and J. Wallenius, An interactive programming method for solving the multiple criteria problem. Manage. Sci. 22 (1976) 652–663. | DOI | Zbl

Cité par Sources :