A generalized DEA model for inputs (outputs) estimation under inter-temporal dependence
RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 5, pp. 1791-1805.

This paper extended the inverse Data Envelopment Analysis (DEA) to the framework of dynamic DEA. The following question is studied under inter-temporal dependence assumption: among a set of decision making units (DMUs), to what extent should the input (output) levels of the DMU change if the efficiency index of a DMU remains unchanged, yet the output (input) levels change? This question is answered using (periodic weak) Pareto solutions of multiple-objective linear programming (MOLP) problems in the framework of dynamic DEA. In this study, unlike other proposed methods, the simultaneous increase and decrease of the various input (output) levels are considered under inter-temporal dependence. In addition, a numerical example with real data is provided to illustrate the objective of this research.

DOI : 10.1051/ro/2018100
Classification : 90C05, 90C29, 90C39, 90C90, 90B50, 47N10
Mots-clés : Data Envelopment Analysis (DEA), inverse DEA, multiple-objective linear programming (MOLP), inter-temporal dependence, (Periodic weak) Pareto solution
Ghobadi, Saeid 1

1
@article{RO_2019__53_5_1791_0,
     author = {Ghobadi, Saeid},
     title = {A generalized {DEA} model for inputs (outputs) estimation under inter-temporal dependence},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {1791--1805},
     publisher = {EDP-Sciences},
     volume = {53},
     number = {5},
     year = {2019},
     doi = {10.1051/ro/2018100},
     mrnumber = {4018322},
     zbl = {1431.90093},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro/2018100/}
}
TY  - JOUR
AU  - Ghobadi, Saeid
TI  - A generalized DEA model for inputs (outputs) estimation under inter-temporal dependence
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2019
SP  - 1791
EP  - 1805
VL  - 53
IS  - 5
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ro/2018100/
DO  - 10.1051/ro/2018100
LA  - en
ID  - RO_2019__53_5_1791_0
ER  - 
%0 Journal Article
%A Ghobadi, Saeid
%T A generalized DEA model for inputs (outputs) estimation under inter-temporal dependence
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2019
%P 1791-1805
%V 53
%N 5
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ro/2018100/
%R 10.1051/ro/2018100
%G en
%F RO_2019__53_5_1791_0
Ghobadi, Saeid. A generalized DEA model for inputs (outputs) estimation under inter-temporal dependence. RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 5, pp. 1791-1805. doi : 10.1051/ro/2018100. http://www.numdam.org/articles/10.1051/ro/2018100/

G.R. Amin and S. Al-Muharrami, A new inverse data envelopment analysis model for mergers with negative data. IMA J. Manage. Math. 29 (2016) 137–149. | MR | Zbl

G.R. Amin, A. Emrouznejad and S. Gattoufi, Minor and major consolidations in inverse DEA: definition and determination. Comput. Ind. Eng. 103 (2017) 193–200. | DOI

G.R. Amin, A. Emrouznejad and S. Gattoufi, Modelling generalized firms’ restructuring using inverse DEA. J. Prod. Anal. 48 (2017) 51–61. | DOI

L. Dong Joon, Inverse DEA with frontier changes for new target setting. Eur. J. Oper. Res. 254 (2016) 510–516. | DOI | MR | Zbl

M. Ehrgott, Multicriteria Optimization. Springer Berlin, Berlin (2005). | MR | Zbl

A. Emrouznejad, An alternative DEA measure: a case of oecd countries. Appl. Econ. Lett. 10 (2003) 779–782. | DOI

A. Emrouznejad and E. Thanassoulis, A mathematical model for dynamic efficiency using data envelopment analysis. Appl. Math. Comput. 160 (2005) 363–378. | DOI | Zbl

A. Emrouznejad and E. Thanassoulis, Measurement of productivity index with dynamic DEA. Int. J. Oper. Res. 8 (2010) 247–260. | DOI | Zbl

A. Emrouznejad, G.-L. Yang and G.R. Amin, A novel inverse DEA model with application to allocate the CO2 emissions quota to different regions in chinese manufacturing industries. J. Oper. Res. Soc. 70 (2019) 1079–1090. | DOI

S. Fallah-Fini, K. Triantis and A.L. Johnson, Reviewing the literature on non-parametric dynamic efficiency measurement: state-of-the-art. J. Prod. Anal. 41 (2014) 51–67. | DOI

R. Färe and S. Grosskopf, Intertemporal production Frontiers: With Dynamic DEA. Kluwer Academic Publishers, Dordrecht (1996).

S. Gattoufi, G.R. Amin and A. Emrouznejad, A new inverse DEA method for merging banks. IMA J. Manage. Math. 25 (2014) 73–87. | Zbl

S. Ghobadi, Inputs and outputs estimation in inverse DEA, Iran. J. Optim. 9 (2017) 119–129.

S. Ghobadi and S. Jahangiri, Inverse DEA: review, extension and application. Int. J. Technol. Decis. Making 14 (2015) 805–824. | DOI

S. Ghobadi, G.R. Jahanshahloo, F. Hoseinzadeh Lotfi and M. Rostami-Malkhalifeh, Dynamic inverse DEA in the presence of fuzzy data. Adv. Environ. Biol. 8 (2014) 139–151.

S. Ghobadi, G.R. Jahanshahloo, F. Hoseinzadeh Lotfi and M. Rostami-Malkhalifeh, Efficiency measure under inter-temporal dependence. Int. J. Technol. Decis. Making 17 (2018) 657–675. | DOI

A. Hadi-Vencheh and A.A. Foroughi, A generalized DEA model for inputs/outputs estimation. Math. Comput. Model. 43 (2006) 447–457. | DOI | MR | Zbl

A. Hadi-Vencheh, A.A. Foroughi and M. Soleimani-Damaneh, A DEA model for resource allocation. Econ. Model. 25 (2008) 983–993. | DOI

A. Hadi-Vencheh, A. Hatami-Marbini, Z. Ghelej Beigi and K. Gholami, An inverse optimization model for imprecise data envelopment analysis. Optimization 64 (2015) 2441–2452. | DOI | MR | Zbl

G.R. Jahanshahloo, F. Hoseinzadeh Lotfi, M. Rostami-Malkhalifeh and S. Ghobadi, Using enhanced russell model to solve inverse data envelopment analysis problems. Sci. World J. 2014 (2014) 1–10. | DOI

G.R. Jahanshahloo, F.H. Lotfi, N. Shoja, G. Tohidi and S. Razavyan, Input estimation and identification of extra inputs in inverse DEA models. Appl. Math. Comput. 156 (2004) 427–437. | DOI | MR | Zbl

G.R. Jahanshahloo, F.H. Lotfi, N. Shoja, G. Tohidi and S. Razavyan, The outputs estimation of a dmu according to improvement of its efficiency. Appl. Math. Comput. 147 (2004) 409–413. | DOI | MR | Zbl

G.R. Jahanshahloo, F.H. Lotfi, N. Shoja, G. Tohidi and S. Razavyan, Sensitivity of efficiency classifications in the inverse DEA models. Appl. Math. Comput. 169 (2005) 905–916. | DOI | MR | Zbl

G.R. Jahanshahloo, M. Soleimani-Damaneh and S. Ghobadi, Inverse DEA under inter-temporal dependence using multiple-objective programming. Eur. J. Oper. Res. 240 (2015) 447–456. | DOI | MR | Zbl

G.R. Jahanshahloo, M. Soleimani-Damaneh and M. Reshadi, On the pareto (dynamically) efficient paths. Int. J. Comput. Math. 63 (2006) 629–633. | MR | Zbl

S. Lertworasirikul, P. Charnsethikul and S.C. Fang, Inverse data envelopment analysis model to preserve relative efficiency values: the case of variable returns to scale. Comput. Ind. Eng. 61 (2011) 1017–1023. | DOI

H.T. Lin, An efficiency-driven approach for setting revenue target. Decis. Support Syst. 49 (2010) 311–317. | DOI

J. Nemoto and M. Goto, Dynamic data envelopment analysis: modeling intertemporal behavior of a firm in the presence of productive inefficiencies. Econ. Lett. 64 (1999) 51–56. | DOI | Zbl

J.K. Sengupta, Dynamics of data envelopment analysis: theory of systems efficiency. J. Oper. Res. Soc. 47 (1996) 14–21. | Zbl

M. Soleimani-Damaneh, An enumerative algorithm for solving nonconvex dynamic DEA models. Optim. Lett. 7 (2013) 101–115. | DOI | MR | Zbl

T. Sueyoshi and K. Sekitani, Returns to scale in dynamic DEA. Eur. J. Oper. Res. 16 (2005) 536–544. | DOI | MR | Zbl

K. Tone and M. Tsutsui, Dynamic DEA: a slacks-based measure approach. Omega 38 (2010) 145–156. | DOI

K. Tone and M. Tsutsui, Dynamic DEA with network structure: a slacksbased measure approach. Omega 42 (2014) 124–131. | DOI

Q.L. Wei, J.Z. Zhang and X.S. Zhang, An inverse DEA model for inputs/outputs estimate. Eur. J. Oper. Res. 121 (2000) 151–163. | DOI | MR | Zbl

H. Yan, Q.L. Wei and G. Hao, DEA models for resource reallocation and production input/output estimation. Eur. J. Oper. Res. 136 (2002) 19–31. | DOI | MR | Zbl

X. Zhang and J. Cui, A project evaluation system in the state economic information system of china: an operation research practice in public sectore. Int. Trans. Oper. 6 (1999) 441–452. | DOI

Cité par Sources :