solving linear fractional programming problems with interval coefficients in the objective function. a new approach (original) (raw)
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In this paper, two approaches were introduced to obtain Stackelberg solutions for two-level linear fractional programming problems with interval coefficients in the objective functions. The approaches were based on the Kth best method and the method for solving linear fractional programming problems with interval coefficients in the objective function. In the first approach, linear fractional programming with interval coefficients in the objective function and linear programming were utilized to obtain Stackelberg solution, but in the second approach only linear programming is used. Since a linear fractional programming with interval coefficients can be equivalently transformed into a linear programming, therefore both of approaches have same results. Numerical examples demonstrate the feasibility and effectiveness of the methods. aBSTraK Dalam kajian ini, dua kaedah diperkenalkan untuk mendapatkan penyelesaian Stackelberg bagi masalah pengaturcaraan pecahan linear dua-aras dengan pekali selang dalam fungsi objektif. Kaedah yang digunakan adalah berdasarkan kaedah terbaik peringkat-K dan kaedah penyelesaian masalah pengaturcaraan pecahan linear dengan pekali selang dalam fungsi objektif. Dalam kaedah pertama, pengaturcaraan pecahan linear dengan pekali selang dalam fungsi objektif dan pengaturcaraan linear digunakan untuk mendapatkan penyelesaian Stackelberg, tetapi dalam kaedah kedua hanya pengaturcaraan linear digunakan. Oleh sebab suatu pengaturcaraan pecahan linear dengan pekali selang boleh dijelmakan secara setara kepada pengaturcaraan linear, kedua-dua kaedah menghasilkan keputusan yang sama. Beberapa contoh berangka menunjukkan kesauran dan keberkesanan kaedah-kaedah ini. Kata kunci: Pekali selang; pengaturcaraan dua-aras; pengaturcaraan pecahan linear; penyelesaian Stackelberg
A MOLFP Method for Solving Linear Fractional Programming under Fuzzy Environment
A B S T R A C T In this paper, a solution procedure is proposed to solve Fully Fuzzy Linear Fractional Programming (FFLFP) problem where all the variables and parameters are triangular fuzzy numbers. Here, FFLFP problem transformed into an equivalent Multi-Objective Linear Fractional Programming (MOLFP) problem. Then MOLFP converted into an equivalent multi objective linear programming problem by using Mathematical programming approach. The proposed solution illustrated through numerical examples and compared with existing methods.
In this paper, an interval-valued inventory optimization model is proposed. The model involves the price-dependent demand and no shortages. The input data for this model are not fixed, but vary in some real bounded intervals. The aim is to determine the optimal order quantity, maximizing the total profit and minimizing the holding cost subjecting to three constraints: budget constraint, space constraint, and budgetary constraint on ordering cost of each item. We apply the linear fractional programming approach based on interval numbers. To apply this approach, a linear fractional programming problem is modeled with interval type uncertainty. This problem is further converted to an optimization problem with interval-valued objective function having its bounds as linear fractional functions. Two numerical examples in crisp case and interval-valued case are solved to illustrate the proposed approach.
In this paper, an interval-valued inventory optimization model is proposed. The model involves the price dependent demand and no shortages. The input data for this model are not fixed, but vary in some real bounded intervals. The aim is to determine the optimal order quantity, maximizing the total profit and minimizing the holding cost subjecting to three constraints: budget constraint, space constraint, and budgetary constraint on ordering cost of each item. We apply the linear fractional programming approach based on interval numbers. To apply this approach, a linear fractional programming problem is modeled with interval type uncertainty. This problem is further converted to an optimization problem with intervalvalued objective function having its bounds as linear fractional functions. Two numerical examples in crisp case and interval-valued case are solved to illustrate the proposed approach.
The paper is developed to study interval-valued inventory optimization problem. We consider a constant demand inventory model without shortages the input data of which are not fixed, but vary in some real bounded intervals. The aim of this paper is to determine the optimal order quantity, maximizing the total profit and minimizing the holding cost subjecting to three constraints: budget constraint, space constraint, and budgetary constraint on ordering cost of each item. We apply interval-valued linear fractional programming (IVLFP) approach to solve the model. In this respect, we convert the IVLFP problem to an optimization problem with interval-valued objective function having its bounds as linear fractional functions. We solved three numerical examples to illustrate the proposed model in crisp case and interval-valued case.
Convexity in Linear Fractional Programming Problem.
International Journal of Engineering Sciences & Research Technology, 2013
Linear programming is a mathematical programming technique to optimize performance under a set of resource constraints as specified by organization. Linear fractional programming is a generalization of linear programming. The objective functions in linear programs are linear functions while the objective function in a linear fractional program is a ratio of two linear functions. In his paper an attempt is made to solve the convexity in linear fractional programming problem by taking CCR model, which states that the collection of all feasible solution to CCR model constitutes a convex set whose extreme points correspond to the basic feasible solutions.
International Journal of Engineering Sciences & Research Technology, 2013
Linear programming is a mathematical programming technique to optimize performance under a set of resource constraints as specified by organization. Linear fractional programming is a generalization of linear programming. The objective functions in linear programs are linear functions while the objective function in a linear fractional program is a ratio of two linear functions. In his paper an attempt is made to solve the convexity in linear fractional programming problem by taking CCR model, which states that the collection of all feasible solution to CCR model constitutes a convex set whose extreme points correspond to the basic feasible solutions.