A method of transferring cones of intersection form to cones of sum form and its applications in data envelopment analysis models

Abstract

This paper develops an algebra-based method for transferring polyhedral cones of intersection form to the cones of sum form. The method recursively identifies all the extreme rays of the cone of intersection form without adding any pre-assumption on it, which allows us to represent the cone with a finitely generated form (sum form). Our method takes m recursions dealing with each of the m homogeneous linear inequalities in each recursion. The implementation is efficient in terms of both computational time and storage space. Illustrative examples are provided. We also show how the procedure can be applied to generalized cone ratio data envelopment analysis models.