TY - JOUR
T1 - Integrated data envelopment analysis
T2 - Linear vs. nonlinear model
AU - Mahdiloo, Mahdi
AU - Toloo, Mehdi
AU - Duong, Thach Thao
AU - Farzipoor Saen, Reza
AU - Tatham, Peter
N1 - Funding Information:
The authors would like to thank the editor Professor Robert G. Dyson and three anonymous reviewers for their constructive comments which significantly improved an earlier version of this paper. The second author (Mehdi Toloo) was supported by the European Social Fund ( CZ.1.07/2.3.00/20.0296 ) and the Czech Science Foundation ( GAČR 16-17810S ). All support is greatly acknowledged.
Publisher Copyright:
© 2018 Elsevier B.V.
PY - 2018/7/1
Y1 - 2018/7/1
N2 - This paper develops a relationship between two linear and nonlinear data envelopment analysis (DEA) models which have previously been developed for the joint measurement of the efficiency and effectiveness of decision making units (DMUs). It will be shown that a DMU is overall efficient by the nonlinear model if and only if it is overall efficient by the linear model. We will compare these two models and demonstrate that the linear model is an efficient alternative algorithm for the nonlinear model. We will also show that the linear model is more computationally efficient than the nonlinear model, it does not have the potential estimation error of the heuristic search procedure used in the nonlinear model, and it determines global optimum solutions rather than the local optimum. Using 11 different data sets from published papers and also 1000 simulated sets of data, we will explore and compare these two models. Using the data set that is most frequently used in the published papers, it is shown that the nonlinear model with a step size equal to 0.00001, requires running 1,955,573 linear programs (LPs) to measure the efficiency of 24 DMUs compared to only 24 LPs required for the linear model. Similarly, for a very small data set which consists of only 5 DMUs, the nonlinear model requires running 7861 LPs with step size equal to 0.0001, whereas the linear model needs just 5 LPs.
AB - This paper develops a relationship between two linear and nonlinear data envelopment analysis (DEA) models which have previously been developed for the joint measurement of the efficiency and effectiveness of decision making units (DMUs). It will be shown that a DMU is overall efficient by the nonlinear model if and only if it is overall efficient by the linear model. We will compare these two models and demonstrate that the linear model is an efficient alternative algorithm for the nonlinear model. We will also show that the linear model is more computationally efficient than the nonlinear model, it does not have the potential estimation error of the heuristic search procedure used in the nonlinear model, and it determines global optimum solutions rather than the local optimum. Using 11 different data sets from published papers and also 1000 simulated sets of data, we will explore and compare these two models. Using the data set that is most frequently used in the published papers, it is shown that the nonlinear model with a step size equal to 0.00001, requires running 1,955,573 linear programs (LPs) to measure the efficiency of 24 DMUs compared to only 24 LPs required for the linear model. Similarly, for a very small data set which consists of only 5 DMUs, the nonlinear model requires running 7861 LPs with step size equal to 0.0001, whereas the linear model needs just 5 LPs.
KW - Data envelopment analysis
KW - Effectiveness
KW - Efficiency
KW - Linear programming
KW - Nonlinear programming
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U2 - 10.1016/j.ejor.2018.01.008
DO - 10.1016/j.ejor.2018.01.008
M3 - Article
AN - SCOPUS:85041547457
SN - 0377-2217
VL - 268
SP - 255
EP - 267
JO - European Journal of Operational Research
JF - European Journal of Operational Research
IS - 1
ER -