Integrated data envelopment analysis: Linear vs. nonlinear model

Mahdi Mahdiloo, Mehdi Toloo, Thach Thao Duong, Reza Farzipoor Saen, Peter Tatham

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)255-267
Number of pages13
JournalEuropean Journal of Operational Research
Issue number1
Early online date12 Jan 2018
Publication statusPublished - 1 Jul 2018
Externally publishedYes


  • Data envelopment analysis
  • Effectiveness
  • Efficiency
  • Linear programming
  • Nonlinear programming


Dive into the research topics of 'Integrated data envelopment analysis: Linear vs. nonlinear model'. Together they form a unique fingerprint.

Cite this