In this paper, for evaluating the efficiency in a three-stage DEA structure we use the additive and the multiplicative cooperative models that comply with the cooperation paradigm in the organizations, where for improving efficiency of system, stages cooperate together. Since the overall efficiency from the cooperative models may not be unique and consequently the stages’ efficiencies, then we combine them with the Nash bargaining game approach that besides maximizing efficiency scores for stages and the whole system, provides a unique and fair efficiency decomposition. Second order programming relaxation of the proposed nonlinear models are given in contrast to the parametric linear models in the literature. Finally, the effectiveness of the proposed models are illustrated with two numerical examples.
Keywords: Cooperative models, data envelopment analysis, three-stage models, Nash bargaining game, conic relaxation
@article{RO_2021__55_6_3677_0,
author = {Golsefid, Narges Torabi and Salahi, Maziar},
title = {Efficiency decomposition in a three-stage network structure: {Cooperative} {DEA,} {Nash} bargaining game models and conic relaxations},
journal = {RAIRO. Operations Research},
pages = {3677--3699},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {6},
doi = {10.1051/ro/2021170},
mrnumber = {4350869},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2021170/}
}
TY - JOUR AU - Golsefid, Narges Torabi AU - Salahi, Maziar TI - Efficiency decomposition in a three-stage network structure: Cooperative DEA, Nash bargaining game models and conic relaxations JO - RAIRO. Operations Research PY - 2021 SP - 3677 EP - 3699 VL - 55 IS - 6 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2021170/ DO - 10.1051/ro/2021170 LA - en ID - RO_2021__55_6_3677_0 ER -
%0 Journal Article %A Golsefid, Narges Torabi %A Salahi, Maziar %T Efficiency decomposition in a three-stage network structure: Cooperative DEA, Nash bargaining game models and conic relaxations %J RAIRO. Operations Research %D 2021 %P 3677-3699 %V 55 %N 6 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2021170/ %R 10.1051/ro/2021170 %G en %F RO_2021__55_6_3677_0
Golsefid, Narges Torabi; Salahi, Maziar. Efficiency decomposition in a three-stage network structure: Cooperative DEA, Nash bargaining game models and conic relaxations. RAIRO. Operations Research, Tome 55 (2021) no. 6, pp. 3677-3699. doi: 10.1051/ro/2021170
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