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Journal of Econometrics
Volume 80, Issue 1, September 1997, Pages 63-84
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doi:10.1016/S0304-4076(97)00003-1 | How to Cite or Link Using DOI
Copyright © 1997 Published by Elsevier Science B.V. Cited By in Scopus (17)
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Analyzing properties of K-cones in the generalized data envelopment analysis model*1
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Quanling Weia, ** and Gang Yub, b, , **
a The Institute of Operations Research and Mathematical Economics, The People's University of China, Beijing 100872, China
b Department of MSIS, Graduate School of Business and Center for Management of Operations and Logistics, The University of Texas at Austin, Austin,TX 78712, USA
Revised 1 May 1996. Available online 10 June 1998.
Abstract
We study the properties of the K-cone in a generalized Data Envelopment Analysis (DEA) model. This model includes the following four important classes of models: Charnes et al. (1978) model, Banker et al. (1984) and Charnes et al. (1985) model, Färe and Grosskopf (1985) model, and Seiford and Thrall (1990) model as its special cases. The main contribution of this paper is to introduce to the above four models (a) the input-output preference cone W to represent the relative importance of different input/output categories viewed by the evaluator (one who evaluates the decision-making units (DMUs)); and (b) the so-called predilection cone to describe preference of the evaluator to selected DMUs. We discuss the new characterizations of DEA efficient DMUs in the case of K-cone. We also describe the use of elementary predilection operators to achieve special preference for one or more DMUs. This method can be easily applied to find all the DEA efficient DMUs that are on a common efficient face as one or more prespecified DMUs. The method provided in this paper is complete in the sense that only those DMUs that are on a common efficient face with the predileccted ones will be DEA efficient after predilection. We believe that the results of this paper will play in important role in determining the structure of efficient frontiers.
Author Keywords: Data envelopment analysis; Efficient frontier; Multiple input/output decision making; Production possibility set
JEL classification codes: C30; C67; C80
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*1 Gang Yu's research is supported in part by ONR grant N00014-91-J-1241, ONR grant N00014-92-J-1536, a URI research grant and a CBA research award from the University of Texas at Austin. This research has been partially supported by The National Natural Science Foundation of China.
** We are grateful to W.W. Cooper for insightful comments. We would like to take this opportunity to thank the two anonymous referees for their dedicated effort in reviewing this paper and for their constructive suggestions. A significant amount of revisions was based on their comments and it made the paper more readable and rigorous.
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