An Algorithm of a Minimum Cost Flow Problem With Time-Varying and Time-Windows

El-Sherbeny, Nasser A.

doi:10.18642/jmsaa_7100121950

Cited by 2 publications

(2 citation statements)

References 4 publications

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“…Currently, an efficient polynomial time algorithm for the MCF problem was proposed by Orlin [12] and Vygen [13]. Some theoretical results and algorithms are given in [14][15][16][17][18] for solving the MCF problem or its variants.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Algorithm for Solving Minimum Cost Flow Problem with Complementarity Slack Conditions

Zhao

Liu

et al. 2020

Mathematical Problems in Engineering

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This paper presents an algorithm for solving a minimum cost flow (MCF) problem with a dual approach. The algorithm holds the complementary slackness at each iteration and finds an augmenting path by updating node potential iteratively. Then, flow can be augmented at the original network. In contrast to other popular algorithms, the presented algorithm does not find a residual network, nor find a shortest path. Furthermore, our algorithm holds information of node potential at each iteration, and we update node potential within finite iterations for expanding the admissible network. The validity of our algorithm is given. Numerical experiments show that our algorithm is an efficient algorithm for the MCF problem, especially for the network with a small interval of cost of per unit flow.

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Section: Introductionmentioning

confidence: 99%

An Efficient Algorithm for Solving Minimum Cost Flow Problem with Complementarity Slack Conditions

Zhao

Liu

et al. 2020

Mathematical Problems in Engineering

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“…Tanaka and Asai [16] formulated general multiobjective nonlinear programming problems with fuzzy parameters. El-Sherbeny [17] formulated multiobjective linear programming problems with fuzzy parameters. Ghatee and Hashemi [18] developed a new algorithm of the fuzzy minimum cost flow problem with fuzzy time windows (FMCFPFTW) with an efficient polynomial-time algorithm based basically on Dijkstra's algorithm.…”

Section: Introductionmentioning

confidence: 99%

An Interactive Approach for Solving the Multiobjective Minimum Cost Flow Problem in the Fuzzy Environment

Alharbi

Khalifa

Ammar

2020

Journal of Mathematics

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This paper deals with the multiobjective minimum cost flow (F-MOMCF) with fuzzy penalty characterized by trapezoidal fuzzy numbers. Through the use of α-cut, the F-MOMCF problem is transformed into the α-MOMCF problem. The α-MOMCF problem can be solved using an interactive approach combined with the weighting Tchebycheff problem. The advantages of this method are that it elicits information from the decision maker (DM) to modify the given constraint set, it gives the optimum penalty, and the effort required for obtaining the solution is reduced. The stability set of the first kind related to the α-best compromise solution is determined. A numerical example is given for illustration and to check the validity of the approach.

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An Algorithm of a Minimum Cost Flow Problem With Time-Varying and Time-Windows

Cited by 2 publications

References 4 publications

An Efficient Algorithm for Solving Minimum Cost Flow Problem with Complementarity Slack Conditions

An Efficient Algorithm for Solving Minimum Cost Flow Problem with Complementarity Slack Conditions

An Interactive Approach for Solving the Multiobjective Minimum Cost Flow Problem in the Fuzzy Environment

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