Geodesic
A new geometric approach to multiobjective linear programming problems
Mathematica Applicanda, Tome 51 (2023) no. 1, pp. 3-12.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

In this paper, we present a novel method for solving multiobjective linear programming problems (MOLPP) that overcomes the need to calculate the optimal value of each objective function. This method is a follow-up to our previous work on sensitivity analysis, where we developed a new geometric approach. The first step of our approach is to divide the space of linear forms into a finite number of sets based on a fixed convex polygonal subset of R^2. This is done using an equivalence relationship, which ensures that all the elements from a given equivalence class have the same optimal solution. We then characterize the equivalence classes of the quotient set using a geometric approach to sensitivity analysis. This step is crucial in identifying the ideal solution to the MOLPP. By using this approach, we can determine whether a given MOLPP has an ideal solution without the need to calculate the optimal value of each objective function. This is a significant improvement over existing methods, as it significantly reduces the computational complexity and time required to solve MOLPP. To illustrate our method, we provide a numerical example that demonstrates its effectiveness. Our method is simple, yet powerful, and can be easily applied to a wide range of MOLPP. This paper contributes to the field of optimization by presenting a new approach to solving MOLPP that is efficient, effective, and easy to implement.
DOI : 10.14708/ma.v51i1.7166
Classification : 49K40, 90C05
Mots-clés : Linear programming, sensitivity analysis, affine geometry, multiobjective programming. 
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Mustapha Kaci; Sonia Radjef. A new geometric approach to multiobjective linear programming problems. Mathematica Applicanda, Tome 51 (2023) no. 1, pp.  3-12. doi : 10.14708/ma.v51i1.7166. http://geodesic.mathdoc.fr/articles/10.14708/ma.v51i1.7166/

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