Stability of lexicographical multicommodity flow problem

Conference · Sat Dec 31 04:00:00 EST 1994

OSTI ID:35933

Davidson, M

We consider the following lexicographical multicommodity network flow problem which generalizes the feasibility problem. Let {theta}{sub 1} = max (x, z) E X(d) {theta} z{sub i} {>=} {theta}f{sub i}, i = 1, ..., M where X(d) is the set of all admissible multicommodity flows x; z E R{sub +}{sup M} is the vector of flow values; parameters d and f are the vectors of edge capacities and flow requirements, respectively. Assuming that the problem is solved and letting z{sub i} = {theta}f{sub i} for all i such that there is no optimal solution (x*, z*) with z* > {theta}{sub 1}f{sub i} (denote the set of all such i by M{sub i}), we come to the next problem {theta}{sub 2} = max (x, z) E X(d) {theta} z{sub i} = {theta}{sub 1}f{sub i}, i E M{sub 1}, z{sub i}, {>=} {theta}f{sub i}, i M{sub 1}. Let us continue solving the sequence of such problems until {union}M{sub i} = M, thus obtaining the Pareto-optimal vector z{sup 0} closest to the vector f. We prove that the procedure and the Pareto-optimal solution z{sup 0} are stable with respectable to perturbations in d and f.

• OSTI ID: 35933
• Report Number(s): CONF-9408161--
• Country of Publication: United States
• Language: English

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