scholarly journals Solving the Fuzzy BiLevel Linear Programming with Multiple Followers through Structured Element Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Shengyue Deng ◽  
Liqian Zhou ◽  
Xinfan Wang
Keyword(s):  
Linear Programming ◽  
Optimal Solution ◽  
Bilevel Linear Programming ◽  
Numerical Example ◽  
Fuzzy Structured Element ◽  
Multiple Followers ◽  
Element Theory ◽  
Element Method

The optimal solution of fuzzy bilevel linear programming with multiple followers (MFFBLP) model is shown to be equivalent to the optimal solution of the bilevel linear programming with multiple followers by using fuzzy structured element theory. The optimal solution to this model is found out by adopting the Kuhn-Tucker approach. Finally, an illustrative numerical example for this model is also provided to demonstrate the feasibility and efficiency of the proposed method.

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.

The Improvement of Optimality Test over Possible Reaction Set in Bilevel Linear Optimization with Ambiguous Objective Function of the Follower

2015 ◽  
Vol 19 (5) ◽  
pp. 645-654 ◽  
Author(s):  
Puchit Sariddichainunta ◽  
◽  
Masahiro Inuiguchi
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Linear Optimization ◽  
Convex Polytope ◽  
Optimal Solution ◽  
Global Optimality ◽  
Basic Solution ◽  
Bilevel Linear Programming ◽  
Coefficient Vector ◽  
Optimality Test

Verifying a rational response is the most crucial step in searching for an optimal solution in bilevel linear programming. Such verification is even difficult in a model with ambiguous objective function of the follower who reacts rationally to a leader’s decision. In our model, we assume that the ambiguous coefficient vector of follower lies in a convex polytope and we formulate bilevel linear programming with the ambiguous objective function of the follower as a special three-level programming problem. We use thek-th best method that sequentially enumerates a solution and examine whether it is the best of all possible reactions. The optimality test process over possible reactions in lower-level problems usually encounters degenerate bases that become obstacles to verifying the optimality of an enumerated solution efficiently. To accelerate optimality verification, we propose search strategies and the evaluation of basic possible reactions adjacent to a degenerate basic solution. We introduce these methods in both local and global optimality testing, confirming the effectiveness of our proposed methods in numerical experiments.

scholarly journals Data-based polyhedron model for optimization of engineering structures involving uncertainties

2021 ◽  
Vol 2 ◽  
Author(s):  
Zhiping Qiu ◽  
Han Wu ◽  
Isaac Elishakoff ◽  
Dongliang Liu
Keyword(s):  
Linear Programming ◽  
Convex Polyhedron ◽  
Linear Optimization ◽  
Optimal Solution ◽  
Composite Plates ◽  
Convex Polyhedra ◽  
Chebyshev Inequality ◽  
Engineering Structures ◽  
Load Bearing ◽  
Polyhedron Model

Abstract This paper studies the data-based polyhedron model and its application in uncertain linear optimization of engineering structures, especially in the absence of information either on probabilistic properties or about membership functions in the fussy sets-based approach, in which situation it is more appropriate to quantify the uncertainties by convex polyhedra. Firstly, we introduce the uncertainty quantification method of the convex polyhedron approach and the model modification method by Chebyshev inequality. Secondly, the characteristics of the optimal solution of convex polyhedron linear programming are investigated. Then the vertex solution of convex polyhedron linear programming is presented and proven. Next, the application of convex polyhedron linear programming in the static load-bearing capacity problem is introduced. Finally, the effectiveness of the vertex solution is verified by an example of the plane truss bearing problem, and the efficiency is verified by a load-bearing problem of stiffened composite plates.

scholarly journals Linear programming measures for solving the problem of a linear division of convex multiplayers.

2018 ◽  
Vol 10 (2) ◽  
Author(s):  
Sarmad H. Ali ◽  
Osamah A. Ali ◽  
Samir C. Ajmi
Keyword(s):  
Machine Learning ◽  
Linear Programming ◽  
Optimal Solution ◽  
Optimal Method ◽  
Linear Separation ◽  
Different Types ◽  
Simplex Methods

In this research, we are trying to solve Simplex methods which are used for successively improving solution and finding the optimal solution, by using different types of methods Linear, the concept of linear separation is widely used in the study of machine learning, through this study we will find the optimal method to solve by comparing the time consumed by both Quadric and Fisher methods.

scholarly journals Applying Simulation Modelling in Quantifying Optimization Results

2021 ◽  
Vol 15 (4) ◽  
pp. 518-523
Author(s):  
Ratko Stanković ◽  
Diana Božić
Keyword(s):  
Linear Programming ◽  
Simulation Model ◽  
Input Data ◽  
Optimization Problems ◽  
Programming Model ◽  
Optimal Solution ◽  
Simulation Modelling ◽  
Simulation Software ◽  
Programming Models ◽  
Freight Forwarding

Improvements achieved by applying linear programming models in solving optimization problems in logistics cannot always be expressed by physically measurable values (dimensions), but in non-dimensional values. Therefore, it may be difficult to present the actual benefits of the improvements to the stake holders of the system being optimized. In this article, a possibility of applying simulation modelling in quantifying results of optimizing cross dock terminal gates allocation is outlined. Optimal solution is obtained on the linear programming model by using MS Excel spreadsheet optimizer, while the results are quantified on the simulation model, by using Rockwell Automation simulation software. Input data are collected from a freight forwarding company in Zagreb, specialized in groupage transport (Less Than Truckload - LTL).

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.

scholarly journals THE OPTIMAL PRINCIPLE OF BELLMAN IN THE PROBLEM OF OPTIMAL MEANS DISTRIBUTION BETWEEN ENTERPRISES FOR THE EXPANSION OF PRODUCTION

2019 ◽  
pp. 132-138 ◽  
Author(s):  
A. Tarasenko ◽  
I. Egorova
Keyword(s):  
Dynamic Programming ◽  
Nonlinear Programming ◽  
Optimal Solution ◽  
Optimal Distribution ◽  
Optimality Principle ◽  
Numerical Example ◽  
Maximum Profit ◽  
Cost Forecasting ◽  
Method Of Dynamic Programming ◽  
Minimum Costs

The method of dynamic programming has been considered, which is used in solving multiple problems in economics, on the example of using Bellman’s optimality principle for solving nonlinear programming problems. On a specific numerical example, the features of the solution have been shown in detail with all the calculations. The problem of optimal distribution of funds among enterprises for the expansion of production has been formulated, which would give the maximum total increase in output. The solution of the task has been presented in the case, when the number of enterprises is 3. It has been shown, that the Bellman optimality principle allows you solve applied problems of cost forecasting with obtaining the optimal solution-maximum profit at minimum costs.

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