A primal algorithm for solving a capacitated network flow problem with additional linear constraints

Chen, S.; Saigal, Romesh

doi:10.1002/net.3230070105

Cited by 55 publications

(21 citation statements)

References 9 publications

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“…The s k 's and are side variables because they do not appear as variables in an NP model. Therefore, the AWTNP in (12)-(16) can be solved with the special simplex method for network problems with side constraints (Chen and Saigal 1977, Kennington and Helgason 1980, Murty 1992). …”

Section: The Multiple-objectivementioning

confidence: 98%

“…Because of the side constraints, the computationally efficient network simplex algorithms cannot be directly applied to AWTNPs. Options of solving AWTNPs include the direct use of the simplex method for linear-programming problems, or the direct use of the special simplex method for network problems with side constraints (Chen and Saigal 1977, Kennington and Helgason 1980, Murty 1992. Barr et al (1986), Glover et al (1978), and Klingman (1981, 1985) proposed different specialized approaches to implement this special simplex method.…”

Section: The Multiple-objectivementioning

confidence: 99%

“…Once an initial basic feasible solution is found, the special simplex method for network problems with side constraints (Chen and Saigal 1977, Kennington and Helgason 1980, Murty 1992 can be used to solve the AWTNP. All routines use the same strategy of constructing an initial basic feasible solution for an AWTNP from an optimal solution of another by reducing the number of basic flow variables or by increasing the number of basic nonflow variables.…”

Section: Introductionmentioning

confidence: 99%

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Warm-Start Routines for Solving Augmented Weighted Tchebycheff Network Programs in Multiple-Objective Network Programming

Sun

2005

INFORMS Journal on Computing

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T hree warm-start routines are developed to find initial basic feasible solutions for augmented weighted Tchebycheff network programs, subproblems derived from multiple-objective network-programming problems. In an interactive solution procedure, a series of augmented weighted Tchebycheff network programs need to be solved sequentially to find representative nondominated solutions. To speed up the solution process using the network structure of the problem, these warm-start routines start the solution process of one augmented weighted Tchebycheff network program from the optimal solution of the previous one. All three warm-start routines use the same strategy but different ways of reducing the number of basic flow variables, or equivalently increasing the number of basic nonflow variables to construct a basic solution. These warm-start routines can be used by any interactive procedures to facilitate the solution process of multiple-objective network-programming problems. A detailed example is presented. A computational experiment is conducted to compare the performance of these warm-start routines. A cold-start routine and NETSIDE, specialized software for solving network problems with side constraints, are also used as references in the experiment. These warm-start routines can save substantial computation time.

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Section: The Multiple-objectivementioning

confidence: 98%

Section: The Multiple-objectivementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Warm-Start Routines for Solving Augmented Weighted Tchebycheff Network Programs in Multiple-Objective Network Programming

Sun

2005

INFORMS Journal on Computing

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“…The network simplex method with side constraints proposed by Chen and Saigal [CS77] is capable of solving the occuring MCFs with side constraints. Three strategies are proposed to produce good starting solutions for this special network simplex algorithm:…”

Section: Mustafa and Gohmentioning

confidence: 99%

Multiple objective minimum cost flow problems: A review

Hamacher

Pedersen

Ruzika

2007

European Journal of Operational Research

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In this paper, theory and algorithms for solving the multiple objective minimum cost flow problem are reviewed. For both the continuous and integer case exact and approximation algorithms are presented. In addition, a section on compromise solutions summarizes corresponding results. The reference list consists of all papers known to the authors which deal with the multiple objective minimum cost flow problem.

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“…It was one of the ÿrst time-sharing analysis tools developed for use by nonengineers in the OTCs. On a professional level, the work on DSAP by McCallum and Chen was recognized in the mid-1970s by The Institute of Management Sciences (TIMS), whose College on the Practice of Management Science cited the work as an outstanding example of the application of OR concepts (Chen and McCallum 1977).…”

Section: Inventory Management For Stationmentioning

confidence: 99%

Operations Research at Bell Laboratories through the 1970s: Part II

Dawson¹,

McCallum²,

Murphy³

et al. 2000

Operations Research

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This historical account of operations research at Bell Laboratories was drafted in the late 1970s when the authors were part of the Operations Research Center within Bell Laboratories at AT&T; it has not previously appeared in the open literature. We have added a few references to later publications that describe particular aspects of the period covered. Discussions of technological practices and organizational arrangements expressed in the present tense represent a viewpoint of about 1980, before “divestiture” split up the Bell System. A comprehensive table of contents for parts I, II, and III can be found in the Online Collection of the Operations Research Home Page, at www.informs.org/pubs . We describe the work done in the Bell System up to about 1980, mainly at Bell Labs, both in developing the techniques of operations research and in applying them to the telecommunications business. This account does not include military OR or direct support of other federal government activities. Part II covers capacity expansion and operations analysis.

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A primal algorithm for solving a capacitated network flow problem with additional linear constraints

Cited by 55 publications

References 9 publications

Warm-Start Routines for Solving Augmented Weighted Tchebycheff Network Programs in Multiple-Objective Network Programming

Warm-Start Routines for Solving Augmented Weighted Tchebycheff Network Programs in Multiple-Objective Network Programming

Multiple objective minimum cost flow problems: A review

Operations Research at Bell Laboratories through the 1970s: Part II

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