Using Fuzzy Goal Programming Technique to Solve Multiobjective Chance Constrained Programming Problems in a Fuzzy Environment

2012 ◽  
Vol 2 (1) ◽  
pp. 71-80 ◽  
Author(s):  
Animesh Biswas ◽  
Nilkanta Modak
Keyword(s):  
Decision Making ◽  
Programming Problem ◽  
Goal Programming ◽  
Fuzzy Goal Programming ◽  
Chance Constrained Programming ◽  
Membership Functions ◽  
Programming Technique ◽  
Goal Programming Model ◽  
Fuzzy Goal ◽  
Constrained Programming

In this paper a fuzzy goal programming technique is presented to solve multiobjective decision making problems in a probabilistic decision making environment where the right sided parameters associated with the system constraints are exponentially distributed fuzzy random variables. In model formulation of the problem, the fuzzy chance constrained programming problem is converted into a fuzzy programming problem by using general chance constrained methodology. Then by realizing the fuzzy nature of the parameters associated with the system constraints, the problem is decomposed by considering the tolerance ranges of the parameters. The tolerance membership functions of each of the individual objectives are defined in isolation to measure the degree of achievements of the goal levels of the objectives. Then a fuzzy goal programming model is developed to achieve the highest degree of each of the defined membership functions to the extent possible. In the solution process the minsum fuzzy goal programming technique is used to find the most satisfactory decision in the decision making environment. An example is solved to illustrate the proposed methodology and the achieved solution is compared with the solution of another existing technique.

On Solving Multiobjective Transportation Problems with Fuzzy Random Supply and Demand Using Fuzzy Goal Programming

2017 ◽  
Vol 8 (3) ◽  
pp. 54-81 ◽  
Author(s):  
Animesh Biswas ◽  
Nilkanta Modak
Keyword(s):  
Goal Programming ◽  
Fuzzy Numbers ◽  
Optimal Allocation ◽  
Programming Model ◽  
Fuzzy Goal Programming ◽  
Chance Constrained Programming ◽  
Transportation Problems ◽  
Goal Programming Model ◽  
Fuzzy Goal ◽  
Fuzzy Random

In this article a fuzzy goal programming model is developed to solve multiobjective unbalanced transportation problems with fuzzy random parameters. In model formulation process the cost coefficients of the objectives are considered as fuzzy numbers and the supplies and demands are considered as fuzzy random variables with known fuzzy probability distribution from the view point of probabilistic as well as possibilistic uncertainties involved with the model. A fuzzy programming model is first constructed by applying chance constrained programming methodology in fuzzy environment. Then, the model is decomposed on the basis of the tolerance ranges of the fuzzy numbers associated with it. The individual optimal solution of each decomposed objectives is found in isolation to construct the membership goals of the objectives. Finally, priority based fuzzy goal programming technique is used to achieve the highest degree of each of the defined membership goals to the extent possible by minimizing the under deviational variables and thereby obtaining optimal allocation of products by using distance function in a cost minimizing decision making environment. An illustrative example is solved and compared with existing technique to explore the potentiality of the proposed methodology.

scholarly journals Fuzzy Goal Programming Procedure to Bilevel Multiobjective Linear Fractional Programming Problems

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Mahmoud A. Abo-Sinna ◽  
Ibrahim A. Baky
Keyword(s):  
Goal Programming ◽  
Fractional Programming ◽  
Programming Model ◽  
Fuzzy Goal Programming ◽  
Decision Makers ◽  
Membership Functions ◽  
Linear Fractional Programming ◽  
Goal Programming Model ◽  
Fuzzy Goals ◽  
Fuzzy Goal

This paper presents a fuzzy goal programming (FGP) procedure for solving bilevel multiobjective linear fractional programming (BL-MOLFP) problems. It makes an extension work of Moitra and Pal (2002) and Pal et al. (2003). In the proposed procedure, the membership functions for the defined fuzzy goals of the decision makers (DMs) objective functions at both levels as well as the membership functions for vector of fuzzy goals of the decision variables controlled by first-level decision maker are developed first in the model formulation of the problem. Then a fuzzy goal programming model to minimize the group regret of degree of satisfactions of both the decision makers is developed to achieve the highest degree (unity) of each of the defined membership function goals to the extent possible by minimizing their deviational variables and thereby obtaining the most satisfactory solution for both decision makers. The method of variable change on the under- and over-deviational variables of the membership goals associated with the fuzzy goals of the model is introduced to solve the problem efficiently by using linear goal programming (LGP) methodology. Illustrative numerical example is given to demonstrate the procedure.

On Development of a Fuzzy Stochastic Programming Model with Its Application to Business Management

2017 ◽  
pp. 353-378
Author(s):  
Animesh Biswas ◽  
Arnab Kumar De
Keyword(s):  
Production Planning ◽  
Goal Programming ◽  
Fuzzy Numbers ◽  
Programming Model ◽  
Random Variables ◽  
Fuzzy Goal Programming ◽  
Fuzzy Random Variables ◽  
Fuzzy Goal ◽  
Constrained Programming ◽  
Fuzzy Random

This chapter expresses efficiency of fuzzy goal programming for multiobjective aggregate production planning in fuzzy stochastic environment. The parameters of the objectives are taken as normally distributed fuzzy random variables and the chance constraints involve joint Cauchy distributed fuzzy random variables. In model formulation process the fuzzy chance constrained programming model is converted into its equivalent fuzzy programming using probabilistic technique, a-cut of fuzzy numbers and taking expectation of parameters of the objectives. Defuzzification technique of fuzzy numbers is used to find multiobjective linear programming model. Membership function of each objective is constructed depending on their optimal values. Afterwards a weighted fuzzy goal programming model is developed to achieve the highest degree of each of the membership goals to the extent possible by minimizing group regrets in a multiobjective decision making context. To explore the potentiality of the proposed approach, production planning of a health drinks manufacturing company has been considered.

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