Combinatoric classes of the transportation problem and their properties

This paper considers the partitioning of all transportation problem instances into a finite number of equivalent classes. Combinatoric properties of each class, in both primal and dual spaces, are investigated. The problem instances are partitioned into convex regions by degeneracy hyperplanes. Properties of adjacent regions are fully developed. It turns out that adjacency relations are much more complex in the primal space than in the dual space. Finally, algorithms based on the simplex method are classified according to how they behave in each class.