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Data envelopment analysis (DEA) is a useful management tool for measuring the relative efficiency of decision making units (DMUs) which consumes multiple inputs to produce multiple outputs. Although precise input and output data are fundamentally indispensable in classical DEA models, real-world problems often involve random and/or rough input and output data. We present a chance-constrained DEA model with random and rough (random-rough) input and output data and propose a deterministic equivalent model with quadratic constraints to solve the model. The main contributions of this paper are fourfold: (3.1) we propose a DEA model for problems characterized by random-rough variables; (3.2) we transform the proposed chance-constrained model with random-rough variables into a deterministic equivalent non-linear form that could be simplified as a deterministic model with quadratic constraints; (3.3) we perform sensitivity analysis to investigate the stability and robustness of the proposed model; and (3.4) we use a numerical example to demonstrate the feasibility and richness of the obtained solutions.
Keywords: Data envelopment analysis, chance-constrained programming, random and rough data, alpha-optimistic, alpha-pessimistic
Shiraz, Rashed Khanjani 1 ; Tavana, Madjid 1 ; Di Caprio, Debora 1
@article{RO_2018__52_1_259_0,
author = {Shiraz, Rashed Khanjani and Tavana, Madjid and Di Caprio, Debora},
title = {Chance-constrained data envelopment analysis modeling with random-rough data},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {259--284},
publisher = {EDP-Sciences},
volume = {52},
number = {1},
year = {2018},
doi = {10.1051/ro/2016076},
mrnumber = {3812480},
zbl = {1397.90222},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ro/2016076/}
}
TY - JOUR AU - Shiraz, Rashed Khanjani AU - Tavana, Madjid AU - Di Caprio, Debora TI - Chance-constrained data envelopment analysis modeling with random-rough data JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2018 SP - 259 EP - 284 VL - 52 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ro/2016076/ DO - 10.1051/ro/2016076 LA - en ID - RO_2018__52_1_259_0 ER -
%0 Journal Article %A Shiraz, Rashed Khanjani %A Tavana, Madjid %A Di Caprio, Debora %T Chance-constrained data envelopment analysis modeling with random-rough data %J RAIRO - Operations Research - Recherche Opérationnelle %D 2018 %P 259-284 %V 52 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ro/2016076/ %R 10.1051/ro/2016076 %G en %F RO_2018__52_1_259_0
Shiraz, Rashed Khanjani; Tavana, Madjid; Di Caprio, Debora. Chance-constrained data envelopment analysis modeling with random-rough data. RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 1, pp. 259-284. doi: 10.1051/ro/2016076
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