scholarly journals Scheme of a multidimensional nomographic model for the selection of the optimal solution of a general linear programming problem

1973 ◽  
Vol 18 (3) ◽  
pp. 188-203
Author(s):  
I. A. Vil'ner ◽  
Pavel Galajda
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Optimal Solution ◽  
General Linear ◽  
Selection Of

scholarly journals Ranking Function Application for Optimal Solution of Fractional programming problem

2020 ◽  
Vol 25 (1) ◽  
Author(s):  
Rasha Jalal
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Fractional Programming ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Ranking Function ◽  
Linear Fractional Programming ◽  
Fractional Programming Problem ◽  
Linear Programming Problems

The aim of this paper is to suggest a solution procedure to fractional programming problem based on new ranking function (RF) with triangular fuzzy number (TFN) based on alpha cuts sets of fuzzy numbers. In the present procedure the linear fractional programming (LFP) problems is converted into linear programming problems. We concentrate on linear programming problem problems in which the coefficients of objective function are fuzzy numbers, the right- hand side are fuzzy numbers too, then solving these linear programming problems by using a new ranking function. The obtained linear programming problem can be solved using win QSB program (simplex method) which yields an optimal solution of the linear fractional programming problem. Illustrated examples and comparisons with previous approaches are included to evince the feasibility of the proposed approach.

Construction Method of Constraint Matrices Corresponded by an Optimal Solution

2014 ◽  
Vol 513-517 ◽  
pp. 1617-1620
Author(s):  
Xiao Liu ◽  
Wei Li ◽  
Peng Zhen Liu
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Linear Equations ◽  
Optimal Solution ◽  
Construction Method ◽  
Interval Linear Programming ◽  
Interval Linear

Through deep analysis of the solvability, which is based on interval linear equations and inequalities systems, for a given optimal solution to interval linear programming problem, we propose the construction method of constraint matrices corresponded by the optimal solution in this paper.

scholarly journals Solving the Fully Fuzzy Bilevel Linear Programming Problem through Deviation Degree Measures and a Ranking Function Method

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Aihong Ren
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Function Method ◽  
Optimal Solution ◽  
Ranking Function ◽  
Objective Functions ◽  
Bilevel Linear Programming ◽  
Fuzzy Optimal Solution ◽  
Deviation Degree

This paper is concerned with a class of fully fuzzy bilevel linear programming problems where all the coefficients and decision variables of both objective functions and the constraints are fuzzy numbers. A new approach based on deviation degree measures and a ranking function method is proposed to solve these problems. We first introduce concepts of the feasible region and the fuzzy optimal solution of a fully fuzzy bilevel linear programming problem. In order to obtain a fuzzy optimal solution of the problem, we apply deviation degree measures to deal with the fuzzy constraints and use a ranking function method of fuzzy numbers to rank the upper and lower level fuzzy objective functions. Then the fully fuzzy bilevel linear programming problem can be transformed into a deterministic bilevel programming problem. Considering the overall balance between improving objective function values and decreasing allowed deviation degrees, the computational procedure for finding a fuzzy optimal solution is proposed. Finally, a numerical example is provided to illustrate the proposed approach. The results indicate that the proposed approach gives a better optimal solution in comparison with the existing method.

scholarly journals Mathematical modeling in economics for selection of optimum investment solution

2021 ◽  
Vol 273 ◽  
pp. 08003
Author(s):  
Arthur Alukhanyan ◽  
Olga Panfilova
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Linear Programming ◽  
Mathematical Models ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Target Function ◽  
Investment Portfolio ◽  
Monetary Relations ◽  
Selection Of

This work is devoted to development of economic and mathematical models for selection of the optimum investment solution. Moreover, it states the basis for development of model examples and correction of the model considering the results obtained in the examples. In the work the problem is set for selection of the investment sources and objects, which is limited to the linear programming problem. The controlled variable and basic limitations simulating real credit and monetary relations are distinguished in the provided model. The discounted profit obtained from implementation of the optimum investment portfolio is considered as a target function. The economic and mathematical model presented in the article allows finding the optimum investment solution within the limits of the credit and monetary relations taking place both at the micro- and macroeconomic level.

scholarly journals A New Approach to Find an Optimal Solution of a Fuzzy Linear Programming Problem by Fuzzy Dynamic Programming

2018 ◽  
Vol 7 (4.10) ◽  
pp. 360
Author(s):  
T. Nagalakshmi ◽  
G. Uthra
Keyword(s):  
Dynamic Programming ◽  
Linear Programming ◽  
Objective Function ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
New Approach ◽  
The Cost ◽  
Recursive Equations

This paper mainly focuses on a new approach to find an optimal solution of a fuzzy linear programming problem with the help of Fuzzy Dynamic Programming. Linear programming deals with the optimization of a function of variables called an objective function, subject to a set of linear inequalities called constraints. The objective function may be maximizing the profit or minimizing the cost or any other measure of effectiveness subject to constraints imposed by supply, demand, storage capacity, etc., Moreover, it is known that fuzziness prevails in all fields. Hence, a general linear programming problem with fuzzy parameters is considered where the variables are taken as Triangular Fuzzy Numbers. The solution is obtained by the method of FDP by framing fuzzy forward and fuzzy backward recursive equations. It is observed that the solutions obtained by both the equations are the same. This approach is illustrated with a numerical example. This feature of the proposed approach eliminates the imprecision and fuzziness in LPP models. The application of Fuzzy set theory in the field of dynamic Programming is called Fuzzy Dynamic Programming. 

scholarly journals Fundamentals of Transportation Problem

2021 ◽  
Vol 10 (5) ◽  
pp. 90-103
Author(s):  
Bhabani Mallia ◽  
Manjula Das ◽  
C. Das
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Transportation Problem ◽  
Feasible Solution ◽  
Optimal Solution ◽  
Optimal Solutions ◽  
Basic Feasible Solution ◽  
Distribution Method

Transportation Problem is a linear programming problem. Like LPP, transportation problem has basic feasible solution (BFS) and then from it we obtain the optimal solution. Among these BFS the optimal solution is developed by constructing dual of the TP. By using complimentary slackness conditions the optimal solutions is obtained by the same iterative principle. The method is known as MODI (Modified Distribution) method. In this paper we have discussed all the aspect of transportation problem.

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