Computing Equilibrium Single Commodity Trade Flows Using Successive Overrelaxation

We consider a market economy that is composed of separate regions, each endowed with linear supply and demand curves and represented as a point on a transportation network. The problem addressed is to determine an equilibrium price in each region so that regional price differences do not exceed unit transportation costs, and when trade takes place between two regions, prices differ by the associated transportation cost.

The problem has several quadratic programming formulations. We adopt an approach based on a net import relation. Properties are then given which lead to reductions in the quadratic program. A successive overrelaxation algorithm is proposed that is particularly well-suited to the task of solving the inherent large-scale instances of the problem, while at the same time is simple to implement.