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Models with Restricted Multipliers

In: Data Envelopment Analysis

Author

Listed:
  • William W. Cooper

    (University of Texas)

  • Lawrence M. Seiford

    (University of Michigan)

  • Kaoru Tone

    (National Graduate Institute for Policy Studies)

Abstract

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
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