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: | Ehrgott Matthias |
Keywords: | decision theory: multiple criteria |
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).)