Handling negative data in slacks-based measure data envelopment analysis models

This paper proposes slacks-based measure (SBM) data envelopment analysis (DEA) models that handle negative data. Unlike existing negative data allowable DEA models, the proposed SBM DEA models are consistent with ordinary SBM models and units invariant, they handle various types of returns to scale, and they avoid division by zero. These new SBM DEA models transform original negative inputs and outputs into positive counterparts based on a newly defined “base point”. Hence, these models are referred to as the BP-SBM DEA models. In addition to the basic BP-SBM DEA models, this research further develops data-oriented and application-oriented BP-SBM DEA-type models for different application problems involving negative data. Numerical examples are provided to illustrate various aspects and implementation details of these models.