<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper, we propose an algorithm which is based on many things: the notions well-known of the simplex network method, Ford Fulkerson’s algorithm and our new idea, which is &lt;&lt; the gain cycles >>, applied on a bi-objective minimum cost flow problem. This algorithm permits us to have a good order of many criteria in a rapid and an efficient way; because this classification permits us to structure the optimal area, in which we can choose the best action among the others which exist in the objective space. From this one, we distinguish, that the resolution of this problem comes to find an under set of good actions, among which the decider can select an action of best compromise, or make a decision, in the case where reference indications of the deciders may change. A didactic example is done to illustrate our algorithm.</p>
</abstract>

In this paper, we propose an algorithm which is based on many things: the notions well-known of the simplex network method, Ford Fulkerson’s algorithm and our new idea, which is << the gain cycles >>, applied on a bi-objective minimum cost flow problem. This algorithm permits us to have a good order of many criteria in a rapid and an efficient way; because this classification permits us to structure the optimal area, in which we can choose the best action among the others which exist in the objective space. From this one, we distinguish, that the resolution of this problem comes to find an under set of good actions, among which the decider can select an action of best compromise, or make a decision, in the case where reference indications of the deciders may change. A didactic example is done to illustrate our algorithm.

An Algorithm for Choosing, Ordering a New Criteria of a Bi-Objective Flow Problem

Département de Recherche Opérationnelle, Faculté de Mathématiques

Université des Sciences et de la Technologie Houari Boumedienne

Foundations of Computing and Decision Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

In this paper, we propose an algorithm which is based on many things: the notions well-known of the simplex network method, Ford Fulkerson’s algorithm and our new idea, which is >, applied on a bi-objective minimum cost flow problem. This algorithm permits us to have a good order of many criteria in a rapid and an efficient way; because this classification permits us to structure the optimal area, in which we can choose the best action among the others which exist in the objective space. From this one, we distinguish, that the resolution of this problem comes to find an under set of good actions, among which the decider can select an action of best compromise, or make a decision, in the case where reference indications of the deciders may change. A didactic example is done to illustrate our algorithm.

In this paper, we propose an algorithm which is based on many things: the notions well-known of the simplex network method, Ford Fulkerson’s algorithm and our...

An Algorithm for Choosing, Ordering a New Criteria of a Bi-Objective Flow Problem

Published Online: Mar 01, 2021

Page range: 11 - 26

Received: Feb 28, 2020

Accepted: Sep 30, 2020

DOI: https://doi.org/10.2478/fcds-2021-0002

Keywords
Bi-objective minimum cost flow problem, Network flows, Network mathematical programming, Efficient extreme point

© 2021 Salima Nait Belkacem, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

An Algorithm for Choosing, Ordering a New Criteria of a Bi-Objective Flow Problem

Published Online: Mar 01, 2021

Page range: 11 - 26

Received: Feb 28, 2020

Accepted: Sep 30, 2020

DOI: https://doi.org/10.2478/fcds-2021-0002

KeywordsBi-objective minimum cost flow problem, Network flows, Network mathematical programming, Efficient extreme point

© 2021 Salima Nait Belkacem, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Bi-objective minimum cost flow problem, Network flows, Network mathematical programming, Efficient extreme point