Hyperbolic Efficiency Measurement: A Conic Programming Approach

Abstract

In this article, we develop a computational procedure for the hyperbolic distance function (HDF) within the nonparametric framework of data envelopment analysis. We convert the nonlinear HDF model under variable returns to scale into an equivalent conic optimization problem with linear constraints plus a 'toppled ice cream cone' constraint that can be efficiently solved by specialized interior point methods in about the same time as a linear program. Applying the dual of an ice cream cone, we formulate a multiplier based (dual) HDF model. We elaborate on the structural details of both primal and dual HDF models through geometrical figures. We apply our method to measure the performance of a sample of US banks. This paper was invited as an innovative paper for the Brisbane conference, Annual CEPA International Workshop. It is also under review in European Journal of Operation Research special issue.