Fractional programming approach to a cost minimization problem in electricity market (original) (raw)

A Case Study on Solutions of Linear Fractional Programming Problems

International Journal of Mechanical and Industrial Engineering, 2022

In some decision making problems, objective function can be defined as the ratio of two linear functional subjects to given constraints. These types of problems are known as linear fractional programming problems. The importance of linear fractional programming problems comes from the fact that many real life problems can be expressed as the ratio of physical or economical values represented by linear functions, for example traffic planning, game theory and production planning etc. In this article, correspond to a production planning problem the mathematical model developed, is a linear fractional programming and in order to solve it, various fractional programming techniques has been used. Finally result is compared with the solution obtained by graphical method. To illustrate the efficiency of stated method a numerical example has given.

A global optimization algorithm for linear fractional programming

Applied Mathematics and Computation, 2008

In this paper, we present an efficient branch and bound method for general linear fractional problem (GFP). First, by using a transformation technique, an equivalent problem (EP) of GFP is derived, then by exploiting structure of EP, a linear relaxation programming (LRP) of EP is obtained. To implement the algorithm, the main computation involve solving a sequence of linear programming problem, which can be solved efficiently. The proposed algorithm is convergent to the global maximum through the successive refinement of the solutions of a series of linear programming problems. Numerical experiments are reported to show the feasibility of our algorithm.

On Solving Linear Fractional Programming Problems

Modern Applied Science, 2013

A new method namely, denominator objective restriction method based on simplex method is proposed for solving linear fractional programming problems. Further, another method namely, decomposition-restriction method based on decomposition principle and the denominator objective restriction method is proposed for obtaining an optimal fuzzy solution to the fully fuzzy linear fractional programming problem. The procedures for the proposed methods are illustrated with the numerical examples.

A single stage single constraints linear fractional programming problem: An approach

In the present paper we present a new method for solving a class of single stage single constraints linear fractional programming (LFP) problem. The proposed method is based on transformation the objective value and the constraints also. After reducing the fractional program in to equivalent linear program with the help of transformation technique, after that we apply Simplex method to find objective value. Numerical examples are constructed to show the applicability of the above technique

Method of Centers for Generalized Fractional Programming

Journal of Optimization Theory and Applications, 2000

We propose an algorithm to solve generalized fractional programming problems. The proposed algorithm combines the parametric approach and the Huard method of centers. A minimum of the problem is obtained by solving a sequence of unconstrained optimization problems.

SOLVING GENERALIZED FRACTIONAL PROGRAMMING PROBLEMS WITH APPROXIMATION

ABSTRACT. The present paper proposes a new approach to solve generalized fractional programming problems with approximation. Capitalizing on two alternatives, we review the Dinkelbach-type methods and set forth the main difficulty in applying these methods. In order to cope with this difficulty, we propose an approximation approach that can be controlled by a predetermined parameter. The proposed approach is promising particularly when it is acceptable to find an effective, but nearoptimal value in an efficient manner.

A Single Stage Single Constraints Linear Fractional Programming Problem

A new algorithm for generalized fractional programs

Mathematical Programming, 1996

A new dual problem for convex generalized fractional programs with no duality gap is presented and it is shown how this dual problem can be efficiently solved using a parametric approach. The resulting algorithm can be seen as “dual” to the Dinkelbach-type algorithm for generalized fractional programs since it approximates the optimal objective value of the dual (primal) problem from below. Convergence results for this algorithm are derived and an easy condition to achieve superlinear convergence is also established. Moreover, under some additional assumptions the algorithm also recovers at the same time an optimal solution of the primal problem. We also consider a variant of this new algorithm, based on scaling the “dual” parametric function. The numerical results, in case of quadratic-linear ratios and linear constraints, show that the performance of the new algorithm and its scaled version is superior to that of the Dinkelbach-type algorithms. From the computational results it also appears that contrary to the primal approach, the “dual” approach is less influenced by scaling.

A Proposed Method for Solving a Special Case of Multi-Objective Fractional Programming Problem

CERN European Organization for Nuclear Research - Zenodo, 2022

This paper presents a special case of multi-objective linear fractional programming (MOLFP) problem as a new assumption to transform MOLFP to the multi-objective linear programming (MOLP) problem. The new assumption is, the denominators of the fractional objective functions in the MOLFP problem are the same. In the beginning, we introduced the linear fractional programming (LFP) problem with the solution method to illustrate the proposed method. Our proposed is based on Charnes and Cooper transformation, which is transforming the fractional objective functions to MOLP problem. The Weighted sum method is considered in this paper to solve the MOLP problem after Charnes and Cooper transformation. To illustrate the proposed method, a numerical example is presented.

Fractional programming approach to a cost minimization problem in electricity market (original) (raw)

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