Integrated data envelopment analysis: Linear vs. nonlinear model

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 mosel with a step size equal to 0.00001 reauires running 1,955,573 linear problems (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.