scholarly journals On tropical fractional linear programming

2014 ◽  
Vol 459 ◽  
pp. 384-396 ◽  
Author(s):  
Vinicius Mariano Gonçalves ◽  
Carlos Andrey Maia ◽  
Laurent Hardouin
Keyword(s):  
Linear Programming ◽  
Fractional Linear Programming

A PENALTY METHOD FOR SOLVING BILEVEL LINEAR FRACTIONAL/LINEAR PROGRAMMING PROBLEMS

2004 ◽  
Vol 21 (02) ◽  
pp. 207-224 ◽  
Author(s):  
HERMINIA I. CALVETE ◽  
CARMEN GALÉ
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimization Approach ◽  
Fractional Linear Programming ◽  
Linear Programming Problems ◽  
Level Problem ◽  
The Relationship ◽  
Planning Problems

Bilevel programming involves two optimization problems where the constraint region of the first-level problem is implicitly determined by another optimization problem. This model has been applied to decentralized planning problems involving a decision process with a hierarchical structure. In this paper, we consider the bilevel linear fractional/linear programming problem, in which the objective function of the first-level is linear fractional, the objective function of the second level is linear, and the common constraint region is a polyhedron. For this problem, taking into account the relationship between the optimization problem of the second level and its dual, a global optimization approach is proposed that uses an exact penalty function based on the duality gap of the second-level problem.

scholarly journals Determination of optimal values for the technical characteristics of construction machinery unit with application of fractional linear programming

2021 ◽  
Vol 263 ◽  
pp. 04034
Author(s):  
Victoria Fomicheva ◽  
Anna Zanina ◽  
Anton Radaev
Keyword(s):  
Linear Programming ◽  
Linear Form ◽  
Optimization Model ◽  
Simplex Method ◽  
Efficient Solution ◽  
Practical Case ◽  
Construction Machinery ◽  
Fractional Linear Programming ◽  
Optimal Values

Paper covers issues connected to the determination of the technical characteristics of construction machinery unit performing a certain category of work. On the basis of the results of the review and analysis of scientific works concerning the problem under consideration the key disadvantages have been identified for the existing techniques. Optimization model for determination of the technical characteristics of construction machinery unit has been created. Initial form of the model is not linear toward unknown variables but it can be transformed to the linear form that allows application of simplex method for efficient solution of the problem. The created model has been implemented on a practical case – the obtained results indicated the adequacy of the developed tool.

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