On characterizing the production possibility set for the CCR ratio model in DEA

Abstract

This work makes two contributions. The first is to establish the relation between the production possibility set in the CCR ratio model and a polyhedral cone. The relation is based on a one-to-one correspondence between elements from a well-defined subset of the generators which are extreme rays of the cone and the extreme-efficient DMUs of the production possibility set. The second contribution is to demonstrate that the reduced set of extreme-efficient DMUs is sufficient to perform DEA analysis on a complete data set. Therefore, the polyhedral cone proposed here may be used to obtain the extreme-efficient DMUs a priori in a CCR ratio problem and using this set all other DMUs can be subsequently scored. This two-stage approach to DEA offers several potential advantages. One is that a body of work on finding extreme rays of finitely generated cones becomes directly relevant to DEA analysis. Other advantages include working with smaller linear programs, not having to check for 'weak* efficiency from among the extreme-efficient DMUs, and occurrence of induced degeneracy