Measuring Efficiency in Data Envelopment Analysis Under Conditional Convexity

Data Envelopment Analysis (DEA) assesses relative efficiency of decision-making units (DMUs) considering a production possibility set that is built from the observations maintaining some assumptions, like convexity, constant or variable returns to scale and free disposability. Alternative approaches have been developed assuming only some of those postulates or relaxing them. In particular, Kuosmanen (EJOR, 132:326–342, 2001) proposes the so-called conditional convexity (CC), which relaxes the convexity to allow only for convex combinations of DMUs that do not dominate efficient units. The aim is to preserve the efficiency classification. Despite its potential advantages, CC has hardly attracted the attention of users and researchers, perhaps because of difficulties in computation. The implementation of CC requires solving a series of linear programming (LP) problems with disjunctive constraints, which is often computationally expensive. In this paper, we develop a single LP model that allows to measuring efficiency under CC, which results from the reformulation of a bi-level linear programming problem. Once the computational difficulties have been sorted out, we are able to use in practice this approach for the evaluation of performance of organizations, and explore enhancements of CC over DEA and Free Disposal Hull together with its possible extensions.