A New Approach of Solving Linear  Fractional Programming Problem  (LFP) by Using Computer  Algorithm

Saha, Sumon Kumar; Hossain, Md. Rezwan; Uddin, Md. Kutub; Mondal, Rabindra Nath

doi:10.4236/ojop.2015.43010

Cited by 13 publications

(5 citation statements)

References 10 publications

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“…problem [38], [39]. This type of special fractional programming problem is the so-called fractional knapsack problem (FKP) and can be solved by the Dinkelbach algorithm in polynomial time [40].…”

Section: B Model-solving Methods Analysismentioning

confidence: 99%

Optimal Search Facilities Selection Model for Joint Aeronautical and Maritime Search

Xing

2021

IEEE Access

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Joint aeronautical and maritime search and rescue is the most effective way of performing rescues at sea. The value and effectiveness of a search and rescue (SAR) are far greater when using a coordinated air-maritime search than when using only vessels or aircraft. However, the harmonization of aeronautical and maritime SAR is complex and potentially life-threatening. When the location of the target in distress is unknown, the search process must be carried out. As the sole way to locate and rescue survivors, the search process is the most costly, hazardous, and complicated part of the whole SAR operation. This paper focuses on the key problem of the optimal selection of search facilities, that is often encountered in largearea maritime search practice and urgently needs to be solved in joint aeronautical and maritime search operations. The problem may be abstracted into an optimization model with vessel and aircraft quantitative constraints that fully considers the area of the sea region to be searched, maximum speeds, search capabilities, initial distances of vessels and aircraft from the search area, and maximum endurance of aircraft. By introducing 0-1 decision variables, the search facility selection can be judged and optimized directly and effectively. By analyzing the results with different vessel and aircraft quantities, and taking the relationship between search coverage time and the number of search facilities (cost) into account, the optimal (most economic and feasible) search facility selection scheme can be produced. INDEX TERMS Joint aeronautical and maritime search, marine safety, search facility, optimal model.

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Section: B Model-solving Methods Analysismentioning

confidence: 99%

Optimal Search Facilities Selection Model for Joint Aeronautical and Maritime Search

Xing

2021

IEEE Access

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“…Latter Ponnaiah and Mohan [16] proposed a simplex method to find the solution of linear fractional mathematical programming problems by restricting the denominator of objective function. A fortran computer programme is developed by Saha et al [20] to find the solution of LFP by transforming to a linear programming problem where the constant term of the denominator and numerator are negative. Odior [15] adopted a solution method for linear fractional mathematical programming problems using the concept of duality and partial fractions.…”

Section: Literature Surveymentioning

confidence: 99%

Multi-Objective Probabilistic Fractional Programming Problem Involving Two Parameters Cauchy Distribution

Acharya

Belay

Mishra

2019

Mathematical Modelling and Analysis

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The paper presents the solution methodology of a multi-objective probabilistic fractional programming problem, where the parameters of the right hand side constraints follow Cauchy distribution. The proposed mathematical model can not be solved directly. The solution procedure is completed in three steps. In ﬁrst step, multi-objective probabilistic fractional programming problem is converted to deterministic multi-objective fractional mathematical programming problem. In the second step, it is converted to its equivalent multi-objective mathematical programming problem. Finally, ε -constraint method is applied to ﬁnd the best compromise solution. A numerical example and application are presented to demonstrate the procedure of proposed mathematical model.

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“…1.1, describes how the objective functions are optimized. We have to solve by modified simplex method (equation (1.9)) [11] which implies Table I c B c j Basis …”

Section: Flow Chart For New Arithmetic and Geometric Average Techniquementioning

confidence: 99%

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

Nahar¹,

Alim²

2017

IOSR JM

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A New Approach of Solving Linear Fractional Programming Problem (LFP) by Using Computer Algorithm

Cited by 13 publications

References 10 publications

Optimal Search Facilities Selection Model for Joint Aeronautical and Maritime Search

Optimal Search Facilities Selection Model for Joint Aeronautical and Maritime Search

Multi-Objective Probabilistic Fractional Programming Problem Involving Two Parameters Cauchy Distribution

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

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