The NETFORM concept

Abstract

Recent years have seen many important advances in the solution of network problems. New solution algorithms and implementation techniques have dramatically reduced the cost of solving linear and convex network flow problems. For example, the cost of solving network problems with 2400 equations and 500,000 arcs on an IBM 360/65 has been reduced from d30,000 in 1968 to d300 in 1976 by these advances. In addition, these advances have stimulated the development of new nonlinear modeling techniques for handling a multitude of problems that arise in applications of scheduling, routing, resource allocation, production, inventory management, facilities location and other areas.This paper presents modeling techniques which are mathematically and symbolically linked to network and augmented network structures. These modeling techniques are called the NETFORM (network formulation) concept or approach. The pictorial aspect of this approach has proven to be extremely valuable in both communicating and refining nonlinear and combinatorial relationships. Additionally, the NETFORM concept often yields a formulation that enables the problem to be solved as a sequence of linear network problems with dramatic gains in efficiency over alternative approaches. The paper illustrates these attributes by providing a concrete example of a NETFORM model construction. Three real world applications are then described which have profited by the use of NETFORM techniques.