Integer solutions of multicriteria network flow problems

Integer solutions of multicriteria network flow problems

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Article ID: iaor20003690
Country: Portugal
Volume: 19
Issue: 2
Start Page Number: 229
End Page Number: 243
Publication Date: Dec 1999
Journal: Investigao Operacional
Authors:
Keywords: decision theory: multiple criteria
Abstract:

This paper is concerned with the solution of integer multicriteria network flow problems. The single criterion network flow problem and a sketch of the out-of-kilter method are presented. Important results from (linear) multicriteria optimization are stated and their importance for network flow problems discussed. The main topic of the paper is the presentation of a method to solve integer multicriteria network flow problems. The set of all efficient solutions in objective space is determined in two steps: first the set of all maximal efficient faces of the linear relaxation is determined. The second step consists in finding all integer efficient points. Finally the lexicographic max-ordering theory is proposed to choose a compromise solution. (This paper is a corrected version of the paper which was abstracted in IAOR in June 2000 (IAOR 72014).)

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