A two-phase modified slack-based measure approach for efficiency measurement and target setting in data envelopment analysis with negative data

Abstract

Conventional data envelopment analysis models have been introduced for technologies only with nonnegative inputs and outputs. But in real-world applications, we have some outputs and/or inputs which can take negative values. Especially, in some cases both positive and negative data appear simultaneously in output/input data. In this paper, we review and compare the most recent approaches introduced in the literature. Then, with recourse to some numerical examples, we show that present approaches may fail under two main categories in performance analysis: (a) in introducing non-negative efficient targets in the Pareto sense and (b) in introducing a complete efficiency score for the units. Subsequently, we propose a two-phase slack-based measure model which tackles both problems in an aggregated model. An empirical application in banking is used to illustrate the approach.