Integrated data envelopment analysis: Linear vs. nonlinear model

Mahdiloo, Mahdi and Toloo, Mehdi and Duong, Thach-Thao ORCID: https://orcid.org/0000-0003-2294-3619 and 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. ISSN 0377-2217


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.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Faculty/School / Institute/Centre: No Faculty
Faculty/School / Institute/Centre: No Faculty
Date Deposited: 30 Mar 2022 03:31
Last Modified: 28 Apr 2022 04:03
Uncontrolled Keywords: Data envelopment analysis; Effectiveness; Efficiency; Linear programming; Nonlinear programming
Fields of Research (2020): 46 INFORMATION AND COMPUTING SCIENCES > 4699 Other information and computing sciences > 469999 Other information and computing sciences not elsewhere classified
Identification Number or DOI: https://doi.org/10.1016/j.ejor.2018.01.008
URI: http://eprints.usq.edu.au/id/eprint/46975

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