Integer solutions of multicriteria network flow problems

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 step 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.