Equilibrium in a vector supply–demand network with capacity constraints
Dinh The Luc, Mateo Rocca, Melanie Papalia · Applicable Analysis · 2010
In this article, we study a multi-class, multi-criteria supply–demand network with elasticity demand and capacity constraints. We introduce a concept of elementary flows and construct a vector variational inequality problem which is equivalent to the vector network problem. Then we present a general scheme for scalarizing vector networks which allows us to obtain and strengthen a number of existing results on weakly vector equilibrium. A particular scalarization by augmented smallest monotone functions leads to a complete characterization of vector equilibrium. Necessary and sufficient conditions of vector equilibrium in terms of solutions to scalarized variational inequalities and efficient solutions to vector optimization problems are also established.