Chapter 2 A generalized data envelopment analysis model: A unification and extension of existing methods for efficiency analysis of decision making units

Abstract

In this paper, we introduce a generalized Data Envelopment Analysis (DEA) model which unifies and extends most of the well-known DEA models developed over the past fifteen years and points the way to new models. By setting three binary parameters of this model to different values, we obtain subclasses of the DEA models with generalK cone andW cone descriptions to represent the evaluator's preferences for the Decision Making Units (DMU) and the input/output categories. We also show relationships among the various different subclasses of the generalized DEA model and give special attention to efficiency definitions and solutions. Furthermore, we state and rigorously prove the equivalence between DEA efficiency and the nondominated solutions of a corresponding multi-objective program. This latter result is especially important for understanding and interpreting the concept of efficiency. Detailed examples are also presented to demonstrate the functions ofK cone andW cone, as well as their characteristics.