An Outer Approximation Algorithm for Generating All Efficient Extreme Points in the Outcome Set of a Multiple Objective Linear Programming Problem
 Harold P. Benson
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Various difficulties have been encountered in using decision setbased vector maximization methods to solve a multiple objective linear programming problem (MOLP). Motivated by these difficulties, some researchers in recent years have suggested that outcome setbased approaches should instead be developed and used to solve problem (MOLP). In this article, we present a finite algorithm, called the Outer Approximation Algorithm, for generating the set of all efficient extreme points in the outcome set of problem (MOLP). To our knowledge, the Outer Approximation Algorithm is the first algorithm capable of generating this set. As a byproduct, the algorithm also generates the weakly efficient outcome set of problem (MOLP). Because it works in the outcome set rather than in the decision set of problem (MOLP), the Outer Approximation Algorithm has several advantages over decision setbased algorithms. It is also relatively easy to implement. Preliminary computational results for a set of randomlygenerated problems are reported. These results tangibly demonstrate the usefulness of using the outcome set approach of the Outer Approximation Algorithm instead of a decision setbased approach.
 Title
 An Outer Approximation Algorithm for Generating All Efficient Extreme Points in the Outcome Set of a Multiple Objective Linear Programming Problem
 Journal

Journal of Global Optimization
Volume 13, Issue 1 , pp 124
 Cover Date
 199801
 DOI
 10.1023/A:1008215702611
 Print ISSN
 09255001
 Online ISSN
 15732916
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Efficient set
 Global optimization
 Multiple objective linear programming
 Outer approximation
 Vector maximization
 Industry Sectors
 Authors

 Harold P. Benson ^{(1)}
 Author Affiliations

 1. College of Business Administration, Department of Decision and Imformation Sciences, University of Florida, P.O. Box 117169, Gainesville, FL, 32611–7169, USA Email