Duality Principles and the Algebraic Transportation Problem

In this paper we consider a primal Solution method for the algebraic transportation problem (ATP). The ATP covers besides the classical Hitchcock and the bottleneck or time transportation problem several other types of transportation problems of practical relevance. The algebraic structure of the problem is described in terms of an ordered commutative semimodule over real numbers. The Solution method is based on duality principles which yield similar optimality criteria as known for the classical Hitchcock transportation problem.