Vector network equilibrium problems with uncertain demands and capacity constraints of arcs

Abstract

In this paper, a vector network equilibrium problem with uncertain demands and capacity constraints of arcs is investigated, where the demands belong to a closed interval. By considering two kinds of vector cost functions, i.e., the costs of each path depend on the whole path flow and the path flow itself, the corresponding (weak) vector equilibrium principles are proposed. For the former, some existence results of (weak) vector equilibrium flows are derived based on the vector variational inequalities and the Fan–Browder’s fixed point theorem. For the latter, we introduce the vector minimum cost flow problem with uncertain demands and capacity constraints of arcs. Meanwhile, the relations between the (weak) vector minimum cost flows and the (weak) vector equilibrium flows are revealed. Finally, several numerical examples are given to show the effectiveness of the derived theoretical results.