Equilibrium in a vector supply–demand network with capacity constraints

Abstract

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.

Keywords:

• multi-class supply–demand network
• scalarization
• vector equilibrium
• variational inequalities
• Pareto-efficiency

AMS Subject Classifications::

• 90B10
• 90B50
• 90C29