Statistical Averaging Method and New Statistical Averaging Method for Solving Extreme Point Multi–Objective Linear Programming Problem

Nahar, Samsun

doi:10.11648/j.ml.20180403.12

Cited by 3 publications

(4 citation statements)

References 5 publications

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“…For MOLFPP, a new geometric average technique was proposed by Nahar and Alim [9]. Veeramani and Sumathi [10] solved fuzzy linear fractional programming problem (FLFPP) where the cost, resources and technological coefficients of the objective function were triangular fuzzy numbers. In the solution procedure, they converted the FLFPP into a multi-objective linear fractional programming problem.…”

Section: Introductionmentioning

confidence: 99%

Solving Fuzzy Multi-Objective Linear Programming Problem by Applying Statistical Method

Nahar¹,

Akter²,

Alim³

2022

AJOR

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In this paper, the statistical averaging method and the new statistical averaging methods have been used to solve the fuzzy multi-objective linear programming problems. These methods have been applied to form a single objective function from the fuzzy multi-objective linear programming problems. At first, a numerical example of solving fuzzy multi-objective linear programming problem has been provided to validate the maximum risk reduction by the proposed method. The proposed method has been applied to assess the risk of damage due to natural calamities like flood, cyclone, sidor, and storms at the coastal areas in Bangladesh. The proposed method of solving the fuzzy multi-objective linear programming problems by the statistical method has been compared with the Chandra Sen's method. The numerical results show that the proposed method maximizes the risk reduction capacity better than Chandra Sen's method.

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Section: Introductionmentioning

confidence: 99%

Solving Fuzzy Multi-Objective Linear Programming Problem by Applying Statistical Method

Nahar¹,

Akter²,

Alim³

2022

AJOR

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“…Nahar, S. and Alim, M. A. [6] proposed a new statistical averaging method to solve MOLPP. Different elimination techniques for linear programming problems have been studied earlier by Kohler [7], Williams [8], Kanniappan et al [9], Sharma et al [10].…”

Section: Introductionmentioning

confidence: 99%

“…Jain et al [19] commented on the result obtained by Nahar, S. and Alim, M. A. [6] in the case of new harmonic average technique.…”

Section: Introductionmentioning

confidence: 99%

Modeling of Gauss Elimination Technique and AHA Simplex Algorithm for Multi-objective Linear Programming Problems

Jain

Mangal

2020

AJPAS

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In this research paper, an effort has been made to solve each linear objective function involved in the Multi-objective Linear Programming Problem (MOLPP) under consideration by AHA simplex algorithm and then the MOLPP is converted into a single LPP by using various techniques and then the solution of LPP thus formed is recovered by Gauss elimination technique. MOLPP is concerned with the linear programming problems of maximizing or minimizing, the linear objective function having more than one objective along with subject to a set of constraints having linear inequalities in nature. Modeling of Gauss elimination technique of inequalities is derived for numerical solution of linear programming problem by using concept of bounds. The method is quite useful because the calculations involved are simple as compared to other existing methods and takes least time. The same has been illustrated by a numerical example for each technique discussed here.

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“…Weighted sum techniques are more popular [1] in solving MOO problems. Several MOO averaging techniques [2][3][4][5][6] have been developed during the recent past. Most of these techniques have been tested with non conflicting objectives that were not appropriate.…”

Section: Introductionmentioning

confidence: 99%

Improved averaging techniques for solving multi-objective optimization (MOO) problems

Sen

2020

SN Appl. Sci.

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This study evaluates the existing averaging techniques used for solving multi-objective optimization (MOO) problems. The problems are solved using mean, geometric and harmonic mean averaging techniques. The solutions obtained using the existing averaging techniques were not appropriate. Improved averaging techniques using mean, geometric and harmonic mean are proposed in this study. These techniques have been tested with the suitable examples and found superior to existing MOO averaging techniques.

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Statistical Averaging Method and New Statistical Averaging Method for Solving Extreme Point Multi–Objective Linear Programming Problem

Cited by 3 publications

References 5 publications

Solving Fuzzy Multi-Objective Linear Programming Problem by Applying Statistical Method

Solving Fuzzy Multi-Objective Linear Programming Problem by Applying Statistical Method

Modeling of Gauss Elimination Technique and AHA Simplex Algorithm for Multi-objective Linear Programming Problems

Improved averaging techniques for solving multi-objective optimization (MOO) problems

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