Translation Invariance in Data Envelopment Analysis

In this chapter we present an overview of the different approaches that have considered translation invariant Data Envelopment Analysis (DEA) models. Translation invariance is a relevant property for dealing with non-positive input and/or non-positive output values. We start by considering the classical approach and continue revising recent contributions. We also consider non-translation invariant DEA models that are able to deal with negative data at the expense of modifying the model itself. Finally, we propose to study translation invariance in a general framework through a recently introduced distance function: the linear loss distance function.