A New Approach for Solving Linear Fractional Programming Problems with Duality Concept

Simi, Farhana Ahmed; Talukder, Md. Shahjalal

doi:10.4236/ojop.2017.61001

Cited by 4 publications

(1 citation statement)

References 10 publications

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“…Tantawy [17] presented a concept of duality for the LFP problem in which the objective function is a linear fractional function and the constraint functions are in the form of linear inequalities. Using the concept of duality, Simi and Talukder [18] presented a new approach for solving LFP problem.…”

Section: Introductionmentioning

confidence: 99%

An exact iterative algorithm to solve a linear fractional programming problem

Köçken¹,

Özkök²,

Ahlatçıoğlu³

2022

Scientia Iranica

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The Linear Fractional Programming (LFP) problem that optimizes the ratio of two linear objective functions under linear constraints has a wide range of application areas. Based on the traditional definition of continuity, we developed an exact iterative algorithm that does not depend on big-M coefficients.Removing the nonlinearity in the fractional objective function by converting the objective function into a linear form, an equivalent linear-iterative problem is obtained and a computationally efficient algorithm is proposed. We also analyze the unbounded and asymptotic solution case of the LFP. To demonstrate the efficiency of the proposed method, illustrative numerical examples are provided for all solution cases. Also, we analyze the validity of our algorithm and compare our results with the existing algorithm from the literature by generating random large-scale test problems.

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Section: Introductionmentioning

confidence: 99%

An exact iterative algorithm to solve a linear fractional programming problem

Köçken¹,

Özkök²,

Ahlatçıoğlu³

2022

Scientia Iranica

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Discrete mission planning algorithm for air-sea integrated search model

2021

Sci Rep

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The selection of optimal search effort for air-sea integrated search has become the most concerned issue for maritime search and rescue (MSAR) departments. Helicopters play an important role in maritime search because of their strong maneuverability and hovering ability. In this work, the requirements of maritime search were analyzed, from which a global optimization model with quantitative constraints for vessels and aircraft was developed by setting the least search time as single-objective optimization problem; then the improved Dinkelbach algorithm was used to solve the continuous programming problem, and the discrete mission planning algorithm was used to improve the calculation accuracy of search time and area. A case study shows that the errors in calculating search time and area decrease from 12–18 min to 36 s and from 76.5 to 0.45 n mile2, respectively. The results obtained from the discrete mission planning algorithm can provide better guidance for MASR departments in selecting optimal search scheme.

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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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A New Approach for Solving Linear Fractional Programming Problems with Duality Concept

Cited by 4 publications

References 10 publications

An exact iterative algorithm to solve a linear fractional programming problem

An exact iterative algorithm to solve a linear fractional programming problem

Discrete mission planning algorithm for air-sea integrated search model

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

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