TY - JOUR
T1 - An epsilon-free approach for finding the most efficient unit in DEA
AU - Toloo, Mehdi
N1 - Funding Information:
The research was supported by the Czech Science Foundation (GACR project 14-31593S) and through European Social Fund within the project CZ.1.07/2.3.00/20.0296.
PY - 2014/7/1
Y1 - 2014/7/1
N2 - Data envelopment analysis (DEA), considering the best condition for each decision making unit (DMU), assesses the relative efficiency and partitions DMUs into two sets: efficient and inefficient. Practically, in traditional DEA models more than one efficient DMU are recognized and these models cannot rank efficient DMUs. Some studies have been carried out aiming at ranking efficient DMUs, although in some cases only discrimination of the most efficient unit is desirable. Furthermore, several investigations have been done for finding the most CCR-efficient DMU. The basic idea of the majority of them is to introduce an integrated model which achieves an optimal common set of weights (CSW). These weights help us identify the most efficient unit in an identical condition.Recently, Toloo (2012) [13] proposed a new mixed integer programming (MIP) model to find the most BCC-efficient unit. Based on this study, we propose a new basic integrated linear programming (LP) model to identify candidate DMUs for being the most efficient unit; next a new MIP integrated DEA model is introduced for determining the most efficient DMU. Moreover, these models exclude the non-Archimedean epsilon and consequently the optimal solution of these models can be obtained, straightforwardly. We claim that the most efficient unit, which could be obtained from all other integrated models, has to be one of the achieved candidates from the basic integrated LP model. Two numerical examples are illustrated to show the variant use of these models in different important cases.
AB - Data envelopment analysis (DEA), considering the best condition for each decision making unit (DMU), assesses the relative efficiency and partitions DMUs into two sets: efficient and inefficient. Practically, in traditional DEA models more than one efficient DMU are recognized and these models cannot rank efficient DMUs. Some studies have been carried out aiming at ranking efficient DMUs, although in some cases only discrimination of the most efficient unit is desirable. Furthermore, several investigations have been done for finding the most CCR-efficient DMU. The basic idea of the majority of them is to introduce an integrated model which achieves an optimal common set of weights (CSW). These weights help us identify the most efficient unit in an identical condition.Recently, Toloo (2012) [13] proposed a new mixed integer programming (MIP) model to find the most BCC-efficient unit. Based on this study, we propose a new basic integrated linear programming (LP) model to identify candidate DMUs for being the most efficient unit; next a new MIP integrated DEA model is introduced for determining the most efficient DMU. Moreover, these models exclude the non-Archimedean epsilon and consequently the optimal solution of these models can be obtained, straightforwardly. We claim that the most efficient unit, which could be obtained from all other integrated models, has to be one of the achieved candidates from the basic integrated LP model. Two numerical examples are illustrated to show the variant use of these models in different important cases.
KW - Common set of weights
KW - Data envelopment analysis
KW - Epsilon-free approach
KW - Facility layout design
KW - Mixed integer programming model
KW - The most efficient unit
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U2 - 10.1016/j.apm.2013.11.028
DO - 10.1016/j.apm.2013.11.028
M3 - Article
AN - SCOPUS:84900850264
SN - 0307-904X
VL - 38
SP - 3182
EP - 3192
JO - Applied Mathematical Modelling
JF - Applied Mathematical Modelling
IS - 13
ER -