Sensitivity of DEA models to measurement errors

Abstract

One of the weak points of DEA (Data Envelopment Analysis) models indicated in literature[1,2] is their sensitivity to variable measurement errors. The occurrence of data interference, whichis the basis of the productivity analysis, may distort the classification of the units and may causemisjudgement of their effectiveness.In the article the results of simulation concerning the DEA models sensitivity to occurrence andfeatures of random element in the monitored variables describing the model are presented.The set of thirty DMU (Decision Making Units) described by the means of three inputvariables, two output variables and one environmental variable was analysed. On the basis of thedetermined initial value of all the kinds of variables for each DMU, their relative effectiveness andtheir ranking were determined. Then, the value of each variable was interfered randomly with thenoise with normal distribution N(m,σ) and once again relative effectiveness and ranking of DMUwere determined. The calculation was done repeatedly, taking into account different levels ofvariance. The simulation carried out in the described manner was the basis for the assessment ofthe stability of the classification with the occurrence of measurement errors.On the basis of the research, the limits of DEA models resistance to the occurrence of errors inthe data that are used for productivity analysis were determined.In the authors’ opinion, the proposals in the article may be recognised as a vital input for thedevelopment of the methodology of comparative productivity analysis by the means of DEAmodels.