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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 607829, 7 pages
Research Article

A New Representation of Efficient Point Sets and Its Applications in DEA

Department of Mathematics, Taizhou University, Linhai, Zhejiang 317000, China

Received 18 January 2013; Accepted 25 February 2013

Academic Editor: Zhuming Bi

Copyright © 2013 Maoqin Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


, the set of Pareto efficient (weak efficient) points of a set with respect to a cone in , is expressed as a differencebetweentwo sets and ( and ). Using the new representation, the properties of are proved more easily than before. When or is in the form of union, intersection, sum, or difference of two sets or two cones, respectively, the properties of are considered. Most of the properties are proved by the binary operations of sets, which is a new method in the multiobjective optimization. Then these properties are used to solve some types of multiobjective linear programming problems corresponding to Data Envelopment Analysis (DEA) models. The structures of the DEA efficient solution sets of four most representative DEA models are developed. Further more, the relationships between efficiencies of the four DEA models are deduced.