The necessary and sufficient conditions for returns to scale properties in generalized data envelopment analysis model

We give definitions on increasing, constant and decreasing returns to scale under the generalized data envelopment analysis (GDEA) model. The GDEA model possesses cone structures for describing evaluators' preferences toward different decision making units (DMU) and toward different input/output categories. The GDEA model contains many important DEA models as its subclasses. Based upon the definition, we discuss and rigorously prove the necessary and sufficient conditions for a DMU to have increasing, constant and decreasing returns to scale under a GDEA model, and discuss and clarify the differences and relationships of these conditions under different subclasses of the GDEA model. Furthermore, we describe a method based on a two-stage linear program to test returns to scale properties.