Exceptional Paper—Design and Implementation of Large Scale Primal Transshipment Algorithms

Abstract

A complete description is given of the design, implementation and use of a family of very fast and efficient large scale minimum cost (primal simplex) network programs. The class of capacitated transshipment problems solved is the most general of the minimum cost network flow models which include the capacitated and uncapacitated transportation problems and the classical assignment problem; these formulations are used for a large number of diverse applications to determine how (or at what rate) a good should flow through the arcs of a network to minimize total shipment costs. The presentation tailors the unified mathematical framework of linear programming to networks with special emphasis on data structures which are not only useful for basis representation, basis manipulation, and pricing mechanisms, but which also seem to be fundamental in general mathematical programming. A review of pertinent optimization literature accompanies computational testing of the most promising ideas. Tuning experiments for the network system, GNET, are reported along with important extensions such as exploitation of special problem structure, element generation techniques, postoptimality analysis, operation with problem generators and external problem files, and a simple noncycling pivot selection procedure which guarantees finiteness for the algorithm.