Integrated data envelopment analysis: Linear vs. nonlinear model

Article


Mahdiloo, Mahdi, Toloo, Mehdi, Duong, Thach-Thao, Saen, Reza Farzipoor and Tatham, Peter. 2018. "Integrated data envelopment analysis: Linear vs. nonlinear model." European Journal of Operational Research. 268 (1), pp. 255-267. https://doi.org/10.1016/j.ejor.2018.01.008
Article Title

Integrated data envelopment analysis: Linear vs. nonlinear model

ERA Journal ID148
Article CategoryArticle
AuthorsMahdiloo, Mahdi (Author), Toloo, Mehdi (Author), Duong, Thach-Thao (Author), Saen, Reza Farzipoor (Author) and Tatham, Peter (Author)
Journal TitleEuropean Journal of Operational Research
Journal Citation268 (1), pp. 255-267
Number of Pages13
Year2018
Place of PublicationNetherlands
ISSN0377-2217
1872-6860
Digital Object Identifier (DOI)https://doi.org/10.1016/j.ejor.2018.01.008
Web Address (URL)https://www.sciencedirect.com/science/article/pii/S0377221718300080
Abstract

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.

KeywordsData envelopment analysis; Effectiveness; Efficiency; Linear programming; Nonlinear programming
ANZSRC Field of Research 2020469999. Other information and computing sciences not elsewhere classified
Byline AffiliationsDeakin University
Technical University of Ostrava, Czech Republic
Griffith University
Islamic Azad University, Iran
Institution of OriginUniversity of Southern Queensland
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