Darwin Klingman

On the Equivalence of Some Generalized Network Problems to Pure Network Problems

The purpose of this paper is to show that any generalized network problem whose matrix does not have full row rank can be transformed into an equivalent pure network problem and to give a constructive method for doing this.

Network Models in Optimization and their Applications in Practice: Glover/Network

From the Publisher: nUnique in that it focuses on formulation and case studies rather than solutions procedures covering applications for pure, generalized and integer networks, equivalent formulations plus successful techniques of network models. Every chapter contains a simple model which is expanded to handle more complicated developments, a synopsis of existing applications, one or more case studies, at least 20 exercises and invaluable references.

The NETFORM concept: A more effective model form and solution procedure for large scale nonlinear problems

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

A note on computational studies for solving transportation problems

30,000 in 1968 to

MODELING COMBINATORIAL MATHEMATICAL PROGRAMMING PROBLEMS BY NETFORMS: AN ILLUSTRATIVE APPLICATION

300 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.n 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.

Extensions of the Augmented Predecessor Index Method to Generalized Network Problems

This note provides a mathematical explanation for the superiority of certain pivot criterion heuristics when using the Row-Column Sum Method to solve transportation problems. In addition, new pivot criteria are developed using this mathematical explanation which are shown to be computationally superior to the previously best pivot criteria.

Implementation and computational study of a generalized network code

ABSTRACT Combinatorial mathematical programming problems have for years been cast in mixed integer programming formulations. Many of these formulations have been extremely difficult to solve. New advances in network solution methods have now been extended to network-related problems involving combinatorial structures, making it attractive to model combinatorial problems by means of netforms (network-related formulations). The use of netforms has resulted in one to two orders of magnitude improvement in the efficiency of solving a number of problems in production, scheduling and distribution. This paper identifies new model techniques for converting combinatorial mathematical programming relationships into netforms in the setting of a practical application.