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Duality and profit efficiency for the hyperbolic measure model

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  • Halická, Margaréta
  • Trnovská, Mária

Abstract

The hyperbolic measure (HM) model is a radial, non-oriented model that is often used in Data Envelopment Analysis (DEA). It is formulated as a non-linear programming problem and hence the conventional linear programming methods, customarily used in DEA, cannot be applied to it in general. In this paper, we reformulate the hyperbolic measure model in a semidefinite programming framework which opens the way to solving the HM model by reliable and efficient interior point algorithms and allows us to benefit from simple primal-dual correspondence in semidefinite programming. We derive the dual of the HM model and so, for the first time, establish its multiplier form. We also offer an economic interpretation of the dual HM model via a comparison with the multiplier form of the directional distance model and relate the HM score to the so-called Nerlovian profit efficiency.

Suggested Citation

  • Halická, Margaréta & Trnovská, Mária, 2019. "Duality and profit efficiency for the hyperbolic measure model," European Journal of Operational Research, Elsevier, vol. 278(2), pages 410-421.
    • Handle: RePEc:eee:ejores:v:278:y:2019:i:2:p:410-421
    DOI: 10.1016/j.ejor.2018.12.001
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