A New Geometric Average Technique to Solve Multi-Objective Linear Fractional Programming Problem and Comparison with New Arithmetic Average Technique

Nahar, Samsun; Alim, Md. Abdul

doi:10.9790/5728-1303013952

Cited by 11 publications

(14 citation statements)

References 5 publications

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“…New average techniques (geometric and arithmetic) had been proposed by Refs. [9,10], which suggested harmonic average and advanced harmonic average techniques to solve multiobjective linear fractional programming problems. Advanced transformation and new statistical averaging techniques have been applied to solve a multiobjective linear programming problem [11][12][13].…”

Section: Review Of the Literaturementioning

confidence: 99%

New Mean and Median Techniques to Solve Multiobjective Linear Fractional Programming Problem and Comparison with Other Techniques

Fentaw,

Akate

2024

Journal of Optimization

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In the field of operation research, both linear and fractional programming problems have been more encountered in recent years because they are more realistic in expressing real-life problems. Fractional programming problem is used when several rates need to be optimized simultaneously such as resource allocation planning, financial and corporate planning, healthcare, and hospital planning. There are several techniques to solve the multiobjective linear fractional programming problem. However, because of the use of scalarization, these techniques have some limitations. This paper proposed two new mean and median techniques to solve the multiobjective linear fractional programming problem by overcoming the limitations. After utilizing mean and median techniques, the problem is converted into an equivalent linear fractional programming problem; then, the linear fractional programming problem is transformed into linear programming problem and solved by the conventional simplex method or mathematical software. Some numerical examples have been illustrated to show the efficiency of the proposed techniques and algorithm. The performance of these solutions was evaluated by comparing their results with other existing methods. The numerical results have shown that the proposed techniques are better than other techniques. Furthermore, the proposed techniques solve a pure multiobjective maximization problem, which is even impossible with some existing techniques. The present investigation can be improved further, which is left for future research.

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Section: Review Of the Literaturementioning

confidence: 99%

New Mean and Median Techniques to Solve Multiobjective Linear Fractional Programming Problem and Comparison with Other Techniques

Fentaw,

Akate

2024

Journal of Optimization

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“…In this paper, we solve MOLPP by using fuzzy programming method. For making single objective from multi-objective, we apply Chandra Sen's method and statistical averaging method by Nahar and Alim [9]. It can be seen that when we use fuzzy programming method, we get better result rather than solving ordinary simplex method.…”

Section: Introductionmentioning

confidence: 99%

Solving Multi-Objective Linear Programming Problem by Statistical Averaging Method with the Help of Fuzzy Programming Method

Nahar¹,

Akter²,

Alim³

2023

AJOR

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A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming problem can be converted into the single objective function by various methods as Chandra Sen's method, weighted sum method, ranking function method, statistical averaging method. In this paper, Chandra Sen's method and statistical averaging method both are used here for making single objective function from multi-objective function. Two multi-objective programming problems are solved to verify the result. One is numerical example and the other is real life example. Then the problems are solved by ordinary simplex method and fuzzy programming method. It can be seen that fuzzy programming method gives better optimal values than the ordinary simplex method.

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“…Nahar and Alim [8] discussed Chandra Sen's approach, statistical averaging method and new statistical averaging method to solve MOLPP. 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.…”

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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A New Geometric Average Technique to Solve Multi-Objective Linear Fractional Programming Problem and Comparison with New Arithmetic Average Technique

Cited by 11 publications

References 5 publications

New Mean and Median Techniques to Solve Multiobjective Linear Fractional Programming Problem and Comparison with Other Techniques

New Mean and Median Techniques to Solve Multiobjective Linear Fractional Programming Problem and Comparison with Other Techniques

Solving Multi-Objective Linear Programming Problem by Statistical Averaging Method with the Help of Fuzzy Programming Method

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

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