Possibilistic Linear Programming Problems involving Normal Random Variables

2016 ◽  
Vol 5 (3) ◽  
pp. 1-13 ◽  
Author(s):  
Suresh Kumar Barik ◽  
M. P. Biswal
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Random Variables ◽  
Fuzzy Programming ◽  
Solution Procedure ◽  
Mathematical Programming Problem ◽  
Possibility Distribution ◽  
Linear Programming Problems ◽  
The Right ◽  
Possibilistic Linear Programming

A new solution procedure of possibilistic linear programming problem is developed involving the right hand side parameters of the constraints as normal random variables with known means and variances and the objective function coefficients are considered as triangular possibility distribution. In order to solve the proposed problem, convert the problem into a crisp equivalent deterministic multi-objective mathematical programming problem and then solved by using fuzzy programming method. A numerical example is presented to illustrate the solution procedure and developed methodology.

Multiobjective Random Fuzzy Linear Programming Problems Based on the Possibility Maximization Model

2009 ◽  
Vol 13 (4) ◽  
pp. 373-379 ◽  
Author(s):  
Takashi Hasuike ◽  
◽  
Hideki Katagiri ◽  
Hiroaki Ishii ◽  
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Fuzzy Programming ◽  
Fuzzy Linear Programming ◽  
Maximization Problem ◽  
Deterministic Equivalent ◽  
Linear Programming Problems ◽  
Previous Solution ◽  
Fuzzy Goal ◽  
Equivalent Problems

Two multiobjective random fuzzy programming problems considered based on the possibility maximization model using possibilistic and stochastic programming are not initially well defined due to the random variables and fuzzy numbers included. To solve them analytically, probability criteria are set for objective functions and chance constraints are introduced. Taking into account the decision maker’s subjectivity and the original plan’s flexibility, a fuzzy goal is introduced for each objective function. The original problems are then changed into deterministic equivalent problems to make the possibility fractile optimization problem equivalent to a linear programming problem. The possibility maximization problem for probability is changed into a nonlinear programming problem, and an analytical solution is constructed extending previous solution approaches.

MULTI-OBJECTIVE FULLY FUZZIFIED LINEAR PROGAMMING

2001 ◽  
Vol 09 (05) ◽  
pp. 605-621 ◽  
Author(s):  
JAMES J. BUCKLEY ◽  
THOMAS FEURING ◽  
YOICHI HAYASHI
Keyword(s):  
Linear Programming ◽  
Evolutionary Algorithm ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Solution Procedure ◽  
Fuzzy Linear Programming ◽  
Multi Objective ◽  
Linear Programming Problems ◽  
Single Objective

In this paper we wish to solve multi-objective fully fuzzified linear programming problems which are multi-objective linear programming problems where all the parameters and variables are fuzzy numbers. We change this problem into a single objective fuzzy linear programming problem and then show that our solution procedure can be used to explore the whole undominated set. An evolutionary algorithm is then designed to generate undominated solutions. An example is presented showing our evolutionary algorithm solution.

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.

A dual simplex method for grey linear programming problems based on duality results

2020 ◽  
Vol 10 (2) ◽  
pp. 145-157
Author(s):  
Davood Darvishi Salookolaei ◽  
Seyed Hadi Nasseri
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Simplex Method ◽  
Dual Problem ◽  
Complementary Slackness ◽  
Dual Simplex Method ◽  
Content Type ◽  
Dual Simplex ◽  
Linear Programming Problems

PurposeFor extending the common definitions and concepts of grey system theory to the optimization subject, a dual problem is proposed for the primal grey linear programming problem.Design/methodology/approachThe authors discuss the solution concepts of primal and dual of grey linear programming problems without converting them to classical linear programming problems. A numerical example is provided to illustrate the theory developed.FindingsBy using arithmetic operations between interval grey numbers, the authors prove the complementary slackness theorem for grey linear programming problem and the associated dual problem.Originality/valueComplementary slackness theorem for grey linear programming is first presented and proven. After that, a dual simplex method in grey environment is introduced and then some useful concepts are presented.

Sign in / Sign up

Export Citation Format

Share Document