Some Limitations of Two DEA Models

Rolf Färe, Shawna Grosskopf and Dimitris Margaritis

Chapter 6 in Advances in Data Envelopment Analysis, 2015, pp 87-91 from World Scientific Publishing Co. Pte. Ltd.

Abstract: In this chapter we consider two DEA models, the first is the DEA specification with a non-Archimedean infinitesimal and the second is the ‘super-efficiency’ model. The first of these was introduced to address Charnes, Cooper and Rhodes' (1978) concern that the piecewise linear construction of technology in DEA may yield vertical and horizontal extensions, and the secondwas introduced byAndersen and Petersen (1993) to provide a means to ‘break ties’, i.e., to allow for ranking the DMU:s in a sample which are technically efficient.For these two problems we provide an example which demonstrates the limitations of these 'fixes.' In the case of the non-Archimedian, we show that a slight change in the choice of the approximation for the non-Archimedean can result in changes in the rankings of DMUs. For the superefficiency model we provide an example showing that this approach may fail to break ties.

Keywords: Optimization Techniques; Multifactor Productivity; Intertemporal Firm Choice; Technological Change: Choices and Consequences; Diffusion Processes; Data Envelopment Analysis; Operations Research (search for similar items in EconPapers)
Date: 2015
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