Hyperbolic Efficiency Measurement: A Conic Programming Approach

European Journal of Operational Research, 278(2), 401-409. https://doi.org/10.1016/j.ejor.2018.12.005

The University of Auckland Business School Research Paper Series

Posted: 28 Jan 2022

See all articles by Maryam Hasannasab

Maryam Hasannasab

University of Auckland Business School

Dimitris Margaritis

University of Auckland Business School

Israfil Roshdi

Islamic Azad University (IAU) - Damghan Branch

Paul Rouse

University of Auckland Business School

Date Written: 2019

Abstract

In this paper, 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. Full paper available at https://doi.org/10.1016/j.ejor.2018.12.005

Keywords: Data envelopment analysis, Hyperbolic distance function, Conic optimization, Duality, Shadow prices

Suggested Citation

Hasannasab, Maryam and Margaritis, Dimitris and Roshdi, Israfil and Rouse, Paul, Hyperbolic Efficiency Measurement: A Conic Programming Approach (2019). European Journal of Operational Research, 278(2), 401-409. https://doi.org/10.1016/j.ejor.2018.12.005, The University of Auckland Business School Research Paper Series, Available at SSRN: https://ssrn.com/abstract=4018630

Maryam Hasannasab

University of Auckland Business School ( email )

12 Grafton Rd
Private Bag 92019
Auckland, 1010
New Zealand

Dimitris Margaritis

University of Auckland Business School ( email )

12 Grafton Rd
Private Bag 92019
Auckland, 1010
New Zealand

Israfil Roshdi (Contact Author)

Islamic Azad University (IAU) - Damghan Branch ( email )

Semnan
Iran

Paul Rouse

University of Auckland Business School ( email )

Private Bag 92019
Auckland
New Zealand
+64 9 373 7599 (Phone)
+64 9 373 7406 (Fax)

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