On Solving Linear Fractional Programming Problems

Pandian, P.; Mohan, Jayalakshmi

doi:10.5539/mas.v7n6p90

Cited by 10 publications

(5 citation statements)

References 26 publications

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“…Finally, using the optimal solution in Table 3, which represents the optimal values of the numerator and denominator respectively, we obtain the optimal solution for the linear fractional model. Now, we compare our results of the presented example with the Charnes and Cooper method [26], denominator objective restriction method [27], and development complementary [28] method, which are well-known methods for solving linear fractional models in Table 4 as follows:…”

Section: Discussion Of the Results Of Solving Decision-making Problems With Stochastic Linear Fractional Modelsmentioning

confidence: 99%

A novel approach for solving decision-making problems with stochastic linear-fractional models

Laith

Al-Salih

Habeeb

2021

EEJET

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Stochastic chance-constrained optimization has a wide range of real-world applications. In some real-world applications, the decision-maker has to formulate the problem as a fractional model where some or all of the coefficients are random variables with joint probability distribution. Therefore, these types of problems can deal with bi-objective problems and reflect system efficiency. In this paper, we present a novel approach to formulate and solve stochastic chance-constrained linear fractional programming models. This approach is an extension of the deterministic fractional model. The proposed approach, for solving these types of stochastic decision-making problems with the fractional objective function, is constructed using the following two-step procedure. In the first stage, we transform the stochastic linear fractional model into two stochastic linear models using the goal programming approach, where the first goal represents the numerator and the second goal represents the denominator for the stochastic fractional model. The resulting stochastic goal programming problem is formulated. The second stage implies solving stochastic goal programming problem, by replacing the stochastic parameters of the model with their expectations. The resulting deterministic goal programming problem is built and solved using Win QSB solver. Then, using the optimal value for the first and second goals, the optimal solution for the fractional model is obtained. An example is presented to illustrate our approach, where we assume the stochastic parameters have a uniform distribution. Hence, the proposed approach for solving the stochastic linear fractional model is efficient and easy to implement. The advantage of the proposed approach is the ability to use it for formulating and solving any decision-making problems with the stochastic linear fractional model based on transforming the stochastic linear model to a deterministic linear model, by replacing the stochastic parameters with their corresponding expectations and transforming the deterministic linear fractional model to a deterministic linear model using the goal programming approach

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Section: Discussion Of the Results Of Solving Decision-making Problems With Stochastic Linear Fractional Modelsmentioning

confidence: 99%

A novel approach for solving decision-making problems with stochastic linear-fractional models

Laith

Al-Salih

Habeeb

2021

EEJET

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“…The problem LFRP D is still a nonlinear programming problem, but it is a quasi-convex problem, so any KKT point is its global optimal solution. Moreover, the problem LFRP D is also a LFP problem, which can be solved by the methods in [6,27,28,39]. However, we present a method similar to that in [35] for solving problem LFRP D .…”

Section: Linear Fractional Relaxation Problemmentioning

confidence: 99%

A New Global Optimization Algorithm for Mixed-Integer Quadratically Constrained Quadratic Fractional Programming Problem

Zhang¹,

Gao²,

Huang³

2024

JCM

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The mixed-integer quadratically constrained quadratic fractional programming (MIQC-QFP) problem often appears in various fields such as engineering practice, management science and network communication. However, most of the solutions to such problems are often designed for their unique circumstances. This paper puts forward a new global optimization algorithm for solving the problem MIQCQFP. We first convert the MIQC-QFP into an equivalent generalized bilinear fractional programming (EIGBFP) problem with integer variables. Secondly, we linearly underestimate and linearly overestimate the quadratic functions in the numerator and the denominator respectively, and then give a linear fractional relaxation technique for EIGBFP on the basis of non-negative numerator. After that, combining rectangular adjustment-segmentation technique and midpointsampling strategy with the branch-and-bound procedure, an efficient algorithm for solving MIQCQFP globally is proposed. Finally, a series of test problems are given to illustrate the effectiveness, feasibility and other performance of this algorithm.

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“…Kornbluth and Steuer [12] presented a simplex-based method for the solution of multi-objective fractional mathematical programming problem. Latter Ponnaiah and Mohan [16] proposed a simplex method to find the solution of linear fractional mathematical programming problems by restricting the denominator of objective function. A fortran computer programme is developed by Saha et al [20] to find the solution of LFP by transforming to a linear programming problem where the constant term of the denominator and numerator are negative.…”

Section: Literature Surveymentioning

confidence: 99%

Multi-Objective Probabilistic Fractional Programming Problem Involving Two Parameters Cauchy Distribution

Acharya

Belay

Mishra

2019

Mathematical Modelling and Analysis

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The paper presents the solution methodology of a multi-objective probabilistic fractional programming problem, where the parameters of the right hand side constraints follow Cauchy distribution. The proposed mathematical model can not be solved directly. The solution procedure is completed in three steps. In ﬁrst step, multi-objective probabilistic fractional programming problem is converted to deterministic multi-objective fractional mathematical programming problem. In the second step, it is converted to its equivalent multi-objective mathematical programming problem. Finally, ε -constraint method is applied to ﬁnd the best compromise solution. A numerical example and application are presented to demonstrate the procedure of proposed mathematical model.

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On Solving Linear Fractional Programming Problems

Cited by 10 publications

References 26 publications

A novel approach for solving decision-making problems with stochastic linear-fractional models

A novel approach for solving decision-making problems with stochastic linear-fractional models

A New Global Optimization Algorithm for Mixed-Integer Quadratically Constrained Quadratic Fractional Programming Problem

Multi-Objective Probabilistic Fractional Programming Problem Involving Two Parameters Cauchy Distribution

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