IDEAS home Printed from https://ideas.repec.org/h/spr/isochp/978-1-4899-7553-9_1.html
   My bibliography  Save this book chapter

Distance Functions in Primal and Dual Spaces

In: Data Envelopment Analysis

Author

Listed:
  • Rolf Färe

    (Oregon State University)

  • Shawna Grosskopf

    (Department of Economics and CERE)

  • Dimitri Margaritis

    (University of Auckland)

Abstract

This chapter provides an overview of the dual measurement of efficiency by means of distance functions and their value duals, the profit, revenue and cost functions. We start by showing how the Shephard (input) distance function in quantity space is a cost function in price space and how the cost function in quantity space is a distance function in price space. We then proceed to formulate a more unifying structure that allows for the simultaneous adjustment of inputs and outputs via establishing duality between the profit function and the directional (technology) distance function which also enables us to derive duality results for the revenue and cost functions as special cases. We complete our exposition by explaining how we can implement empirically dual forms of these efficiency measures either via activity analysis accounting for environmental technologies, slack-based measures and endogenous directional vectors or via parametric methods.

Suggested Citation

  • Rolf Färe & Shawna Grosskopf & Dimitri Margaritis, 2015. "Distance Functions in Primal and Dual Spaces," International Series in Operations Research & Management Science, in: Joe Zhu (ed.), Data Envelopment Analysis, edition 127, chapter 1, pages 1-21, Springer.
    • Handle: RePEc:spr:isochp:978-1-4899-7553-9_1
    DOI: 10.1007/978-1-4899-7553-9_1
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Malin Song & Jianlin Wang & Jiajia Zhao & Tomas Baležentis & Zhiyang Shen, 2020. "Production and safety efficiency evaluation in Chinese coal mines: accident deaths as undesirable output," Annals of Operations Research, Springer, vol. 291(1), pages 827-845, August.
    2. Shulei Cheng & Wei Fan & Jianlin Wang, 2022. "Investigating the humanitarian labor efficiency of China: a factor-specific model," Annals of Operations Research, Springer, vol. 319(1), pages 439-461, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:isochp:978-1-4899-7553-9_1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.