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.

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

2018 ◽  
pp. 791-821
Author(s):  
Animesh Biswas ◽  
Nilkanta Modak
Keyword(s):  
Goal Programming ◽  
Fuzzy Numbers ◽  
Programming Model ◽  
Optimal Solution ◽  
Fuzzy Goal Programming ◽  
Transportation Problems ◽  
Fuzzy Goal ◽  
Constrained Programming ◽  
The Individual ◽  
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.

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 Study Of Fuzzy Goal Programming Model To Production Planning Problems Approach

2021 ◽  
Vol 13 (2) ◽  
pp. 75-81
Author(s):  
Desi Vinsensia ◽  
Yulia Utami
Keyword(s):  
Production Planning ◽  
Goal Programming ◽  
Programming Model ◽  
Raw Materials ◽  
Labor Cost ◽  
Fuzzy Goal Programming ◽  
Planning System ◽  
Programming Approach ◽  
Goal Programming Model ◽  
Fuzzy Goal

The production planning system can provide satisfaction to the manufacture with the desire target and also with the available raw materials. In achieving the target of goals also face a situation of uncertainty (fuzzy). The aims of this study is proposed the model of fuzzy goal programming approach to optimize production planning system. In this model obtaining maximizing profit and revenue with consider minimize costs of labor cost, raw materials cost, time machine production, and also inventory cost. The numerical example is illustrate that the fuzzy goal programming model can optimize optimize production and profit according desired of decision maker.

scholarly journals Hybrid Uncertainty-Goal Programming Model with Scaled Index for Production Planning Assessment

FinTech ◽  
2021 ◽  
Vol 1 (1) ◽  
pp. 1-24
Author(s):  
Junzo Watada ◽  
Nureize Binti Arbaiy ◽  
Qiuhong Chen
Keyword(s):  
Production Planning ◽  
Goal Programming ◽  
Optimization Problems ◽  
Programming Model ◽  
Business Goals ◽  
Target Values ◽  
Goal Programming Model ◽  
Quantitative Results ◽  
Hybrid Uncertainty ◽  
Fuzzy Random

Goal programming (GP) can be thought of as an extension or generalization of linear programming to handle multiple, normally conflicting objective measures. Each of these measures is given a goal or target value to be achieved. Unwanted deviations from this set of target values are then minimized in an achievement function. Production planning is an important process that aims to leverage the resources available in industry to achieve one or more business goals. However, the production planning that typically uses mathematical models has its own challenges where parameter models are sometimes difficult to find easily and accurately. Data collected with various data collection methods and human experts’ judgments are often prone to uncertainties that can affect the information presented by quantitative results. This study focuses on resolving data uncertainties as well as multi-objective optimization using fuzzy random methods and GP in production planning problems. GP was enhanced with fuzzy random features. Scalable approaches and maximum minimum operators were then used to solve multi-object optimization problems. Scaled indices were also introduced to resolve fuzzy symbols containing unspecified relationships. The application results indicate that the proposed approach can mitigate the characteristics of uncertainty in the analysis and achieve a satisfactory optimized solution.

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