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Hyperbolic efficiency measurement: A conic programming approach

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  • Hasannasab, Maryam
  • Margaritis, Dimitris
  • Roshdi, Israfil
  • Rouse, Paul

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.

Suggested Citation

  • Hasannasab, Maryam & Margaritis, Dimitris & Roshdi, Israfil & Rouse, Paul, 2019. "Hyperbolic efficiency measurement: A conic programming approach," European Journal of Operational Research, Elsevier, vol. 278(2), pages 401-409.
    • Handle: RePEc:eee:ejores:v:278:y:2019:i:2:p:401-409
    DOI: 10.1016/j.ejor.2018.12.005
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    3. Halická, Margaréta & Trnovská, Mária & Černý, Aleš, 2024. "A unified approach to radial, hyperbolic, and directional efficiency measurement in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 312(1), pages 298-314.
    4. Alcaraz, Javier & Anton-Sanchez, Laura & Aparicio, Juan & Monge, Juan F. & Ramón, Nuria, 2021. "Russell Graph efficiency measures in Data Envelopment Analysis: The multiplicative approach," European Journal of Operational Research, Elsevier, vol. 292(2), pages 663-674.
    5. Roshdi, Israfil & Mahdiloo, Mahdi & Arjomandi, Amir & Margaritis, Dimitris, 2023. "On second order cone programming approach to two-stage network data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 309(2), pages 953-956.
    6. Alcaraz, Javier & Aparicio, Juan & Monge, Juan Fco & Ramón, Nuria, 2022. "Weight profiles in cross-efficiency evaluation based on hypervolume maximization," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    7. Aparicio, Juan & Monge, Juan F. & Ramón, Nuria, 2021. "A new measure of technical efficiency in data envelopment analysis based on the maximization of hypervolumes: Benchmarking, properties and computational aspects," European Journal of Operational Research, Elsevier, vol. 293(1), pages 263-275.
    8. Aparicio, Juan & Monge, Juan F., 2022. "The generalized range adjusted measure in data envelopment analysis: Properties, computational aspects and duality," European Journal of Operational Research, Elsevier, vol. 302(2), pages 621-632.

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