Multicriteria Spatial Price Networks: Statics and Dynamics

Abstract

In this paper, we develop a spatial price network equilibrium model in which consumers at the demand markets consider both the transportation cost and the transportation time associated with obtaining the particular commodity. We provide the governing equilibrium conditions for the multicriteria spatial price problem and derive the variational inequality formulation. We establish existence and uniqueness of the equilibrium commodity shipment and demand price pattern and then propose a dynamic tatonnement process whose set of stationary points coincides with the set of solutions of the variational inequality problem. An iterative scheme is described which provides a time discretization of the continuous time adjustment process and which converges to a stationary point. Numerical examples are given for illustrative purposes.