An Integer Generalized Transportation Model for Optimal Job Assignment in Computer Networks

Balachandran, V.

doi:10.1287/opre.24.4.742

Cited by 67 publications

(28 citation statements)

References 15 publications

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“…For given locations of the concentrators, the problem of assigning terminals to concentrators can be formulated as a GAP (see e. g. Mirzaian (1985) and Chardaire (1999)). Other applications of the GAP in the area of telecommunication and Computer networks concern e. g. the assignment of tasks in a network of functionally similar Computers (Balachandran (1976)) or the assignment of user nodes to processing sites with the objective of minimising telecommunication costs subject to capacity constraints on processors (Pirkul (1986)). …”

Section: Generalised Assignment Problemmentioning

confidence: 99%

Combinatorial Optimisation Problems of the Assignment Type and a Partitioning Approach

Klose

Drexl

2002

Lecture Notes in Economics and Mathematical Systems

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract Assignment type problems consist in optimally assigning or allocating a given set of "activities" to a given set of "resources". Optimisation problems of the assignment type have numerous applications in production planning and logistics. A populär approach to solve such problems or to compute lower b ounds on the optimal Solution value (in case of a minimisation problem) is to employ column generation. By means of co nsidering subsets of "activities" which can feasibly be assigned to a Single resource, the problem is reformulated as some kind of set-partitioning problem. Column generation is then used in order to solve the linear relaxation of the reformulation. The lower bound obtainable from this approach may, however, be improved by partitioning the set of resources into subsets and by considering subsets of activities which can feasibly be assigned to subsets of resources. This paper outlines the application of this partitioning method to a number of important combinatorial optimisation problems of the assignment type. Terms of use: Documents in EconStor may

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Section: Generalised Assignment Problemmentioning

confidence: 99%

Combinatorial Optimisation Problems of the Assignment Type and a Partitioning Approach

Klose

Drexl

2002

Lecture Notes in Economics and Mathematical Systems

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“…Code development has been reported by Eisemann [14], Maurras [40], Glover, Klingman, and Stutz [25], Bhaumik and Jensen [8], Langley [38], and Balachandran [2], among others. Most of these papers report findings for only certain classes of GN problems and all of them are limited in the scope of the computational analysis.…”

Section: Motivations For Using Gn Modelsmentioning

confidence: 99%

Generalized Networks: A Fundamental Computer-Based Planning Tool

Glover

Hultz²,

Klingman³

et al. 1978

Management Science

106

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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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“…Bradley, Brown and Graves (1977) trace the historical developments leading to contemporary primal simplex pure network algorithms, their supporting data structures, and efficient implementations such as GNET. For other subclasses of generalized networks, algorithms have been reported by Jewell (1962), Eisemann (1964, Maurras (1972), Glover, Hultz, Klingman and Stutz (1977, 1978, Balachandran (1976), and Jensen and Bhaumik (1977). An efficient algorithm for large generalized network problems has been developed by Glover, Klingman, Hultz, Stutz, Karney and Elam (1979, 1977, 1978, 1973, 1973.…”

Section: Introductionmentioning

confidence: 99%

Solving Generalized Networks

Brown

McBride

1984

Management Science

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A complete, unified 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 generalized transshipment problems solved includes the capacitated and uncapacitated generalized transportation problems and the continuous generalized assignment problem, as well as the pure network flow models which are specializations of these problems. These formulations are used for a large number of diverse applications to determine how (or at what rate) flows through the arcs of a network can minimize total shipment costs. A generalized network problem can also be viewed as a linear program with at most two nonzero entries in each column of the constraint matrix; this property is exploited in the mathematical presentation with special emphasis on data structures for basis representation, basis manipulation, and pricing mechanisms. A literature review accompanies computational testing of promising ideas, and extensive experimentation is reported which has produced GENNET, an extremely efficient family of generalized network systems.networks/graphs: flow algorithms, networks/graphs: generalized

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An Integer Generalized Transportation Model for Optimal Job Assignment in Computer Networks

Cited by 67 publications

References 15 publications

Combinatorial Optimisation Problems of the Assignment Type and a Partitioning Approach

Combinatorial Optimisation Problems of the Assignment Type and a Partitioning Approach

Generalized Networks: A Fundamental Computer-Based Planning Tool

Solving Generalized Networks

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