Generalized Networks: A Fundamental Computer-Based Planning Tool

Abstract

This paper documents the recent emergence of generalized networks as a fundamental computer-based planning tool and demonstrates the power of the associated modeling and solution techniques when used together to solve real-world problems.The first sections of the paper give a non-technical account of how generalized networks are used to model a diversity of significant practical problems. To begin, we discuss the model structure of a generalized network (GN) and provide a brief survey of applications which have been modeled as GN problems. Next we explain a somewhat newer modeling technique in which generalized networks form a major, but not the only, component of the model.The later sections give a technical exposition of the design and analysis of computer solution techniques for large-scale GN problems. They contain a study of GN solution strategies within the framework of specializations of the primal simplex method. We identify an efficient solution procedure derived from an integrated system of start, pivot, and degeneracy rules. The resulting computer code is shown, on large problems, to be at least 50 times more efficient than the LP system, APEX III. (NETWORKS; FLOWS; PROGRAMMING COMPUTERS) IntroductionA generalized network (GN) problem is simply a type of LP problem and can thus be solved using any standard LP solution technique. However, none of the current LP systems is capable of fully exploiting the structure of generalized network problems. With the recent development of GN computer codes, Bradley's 1975 prediction that GN problems "in the near future . .. could come to be regarded as a fundamental model" [10] is coming true. Modelers have begun to devote attention to deterrnining if an LP model is a GN problem and, more importantly, to devising formulations in which generalized networks play the role of critical components.There are two powerful incentives for adopting a GN formulation whenever possible. The major advantage is the ability to solve GN problems-and by extension a variety of problems with GN components-with a remarkable degree of efficiency. The second motivation for using GN models is that they can be conceptualized graphically as well as algebraically. The pictorial presentation of a generalized network is a useful device for communicating mathematical models to nonscientific users and for teaching others how to formulate problems.The purpose of this paper is to document the recent emergence of generalized networks as a fundamental computer-based planning tool and to demonstrate the power of the associated modeling and solution technologies when used in concert to solve real-world applications. The paper contains a nontechnical account of how generalized networks are used to model a diversity of significant practical problems. Using a graphical representation, we first define the model structure of a generalized network. Next we provide a brief survey of applications which have been modeled as GN problems. We then explain somewhat newer modeling techniques in which generalized net...

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