IDEAS home Printed from
   My bibliography  Save this book chapter

Models with Restricted Multipliers

In: Data Envelopment Analysis


  • William W. Cooper

    (University of Texas)

  • Lawrence M. Seiford

    (University of Michigan)

  • Kaoru Tone

    (National Graduate Institute for Policy Studies)


In this chapter, we introduced the assurance region and cone-ratio methods for combining subjective and expert evaluations with the more objective methods of DEA. 1. Usually expressed in the form of lower and upper bounds, the assurance region method puts constraints on the ratio of input (output) weights or multiplier values. This helps to get rid of zero weights which frequently appear in solution to DEA models. The thus evaluated efficiency score generally drops from its initial (unconstrained) value. Careful choice of the lower and upper bounds is recommended. 2. Not covered in this chapter is the topic of “linked constraints” in which conditions on input and output multipliers are linked. See Problem 6.3. 3. The cone-ratio method confines the feasible region of virtual multipliers v, u, to a convex cone generated by admissible directions. Formulated as a “cone ratio envelopment” this method can be regarded as a generalization of the assurance region approach. 4. Example applications were used to illustrate uses of both of the “assurance region” and “cone ratio envelopment” approaches.

Suggested Citation

  • William W. Cooper & Lawrence M. Seiford & Kaoru Tone, 2007. "Models with Restricted Multipliers," Springer Books, in: Data Envelopment Analysis, edition 0, chapter 6, pages 177-213, Springer.
  • Handle: RePEc:spr:sprchp:978-0-387-45283-8_6
    DOI: 10.1007/978-0-387-45283-8_6

    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.


    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:sprchp:978-0-387-45283-8_6. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: .

    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: .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.