A primal-dual simplex method for linear programs

Curet, Norman D.

doi:10.1016/0167-6377(93)90045-i

Cited by 15 publications

(10 citation statements)

References 8 publications

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“…Since 1951 when the first programmed solution code based on Dantzig’s simplex method was developed, a series of papers have discussed the different aspects related to linear programming and simplex method such as: computational aspects [ 1 , 2 ], adapting the simplex approach to bilevel linear programming [ 3 , 4 ], applying simplex method for singularly perturbed linear programs [ 5 ], determining the conditions for reachability on a simplex algorithm [ 6 ], and computing experimental designs using simplex method [ 7 ].…”

Section: State-of-the-artmentioning

confidence: 99%

Linear Programming and Fuzzy Optimization to Substantiate Investment Decisions in Tangible Assets

Boloș

Bradea

Delcea

2020

Entropy

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This paper studies the problem of tangible assets acquisition within the company by proposing a new hybrid model that uses linear programming and fuzzy numbers. Regarding linear programming, two methods were implemented in the model, namely: the graphical method and the primal simplex algorithm. This hybrid model is proposed for solving investment decision problems, based on decision variables, objective function coefficients, and a matrix of constraints, all of them presented in the form of triangular fuzzy numbers. Solving the primal simplex algorithm using fuzzy numbers and coefficients, allowed the results of the linear programming problem to also be in the form of fuzzy variables. The fuzzy variables compared to the crisp variables allow the determination of optimal intervals for which the objective function has values depending on the fuzzy variables. The major advantage of this model is that the results are presented as value ranges that intervene in the decision-making process. Thus, the company’s decision makers can select any of the result values as they satisfy two basic requirements namely: minimizing/maximizing the objective function and satisfying the basic requirements regarding the constraints resulting from the company’s activity. The paper is accompanied by a practical example.

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Section: State-of-the-artmentioning

confidence: 99%

Linear Programming and Fuzzy Optimization to Substantiate Investment Decisions in Tangible Assets

Boloș

Bradea

Delcea

2020

Entropy

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“…Active-set approaches have been studied in the past, including those by Stone [5], Thompson et al [6], Adler et al [7], Zeleny [8], Myers and Shih [9], and Curet [10], with the term "constraint selection technique" used in Myers and Shih [9]. Adler et al [7] added constraints randomly, without any selection criteria.…”

Section: Background and Literature Reviewmentioning

confidence: 99%

Constraint Optimal Selection Techniques (COSTs) for Linear Programming

Saito¹,

Corley²,

Rosenberger³

2013

AJOR

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We describe a new active-set, cutting-plane Constraint Optimal Selection Technique (COST) for solving general linear programming problems. We describe strategies to bound the initial problem and simultaneously add multiple constraints. We give an interpretation of the new COST’s selection rule, which considers both the depth of constraints as well as their angles from the objective function. We provide computational comparisons of the COST with existing linear programming algorithms, including other COSTs in the literature, for some large-scale problems. Finally, we discuss conclusions and future research.

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“…Active-set methods have been studied by Stone [5], Thompson et al [6], Adler et al [7], Zeleny [8], Myers and Shih [9], Curet [10], and Bixby et al [11], among others. The term ''constraint selection technique'' was introduced in [9], while the approaches of [7] and [8] illustrate two distinct classes of active-set methods.…”

Section: Introductionmentioning

confidence: 99%

Posterior Constraint Selection for Nonnegative Linear Programming

Corley¹,

Noroziroshan²,

Rosenberger³

2017

AJOR

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Posterior constraint optimal selection techniques (COSTs) are developed for nonnegative linear programming problems (NNLPs), and a geometric interpretation is provided. The posterior approach is used in both a dynamic and non-dynamic active-set framework. The computational performance of these methods is compared with the CPLEX standard linear programming algorithms, with two most-violated constraint approaches, and with previously developed COST algorithms for large-scale problems.

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A primal-dual simplex method for linear programs

Cited by 15 publications

References 8 publications

Linear Programming and Fuzzy Optimization to Substantiate Investment Decisions in Tangible Assets

Linear Programming and Fuzzy Optimization to Substantiate Investment Decisions in Tangible Assets

Constraint Optimal Selection Techniques (COSTs) for Linear Programming

Posterior Constraint Selection for Nonnegative Linear Programming

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