Discrete infinite transportation problems

The finite classical transportation problem is extended to an infinite one having a countable number of origins and destinations. The approach taken is essentially discrete and requires no compactness, measure theoretic, or metric properties of any of its constructions. Duality results are presented for the infinite transportation problem extension and its dual, as well as for two of the relaxations. A constructive approximation procedure is given for obtaining program values arbitrarily close to the infinite program values of the extension.