A solution proposal to the transportation problem with the linear fractional objective function

Emiroglu, Ibrahim; Güler, Coşkun; Taşçi, Fatih

doi:10.1109/icmsao.2011.5775530

Cited by 10 publications

(3 citation statements)

References 10 publications

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“…Moreover, they established sufficient conditions for the existence of a paradoxical solution and obtained a paradoxical range of flow. Sivri et al (2011) developed a new algorithm looking like the Vogel approximation method for TP to find an initial point for LFTP. Also, they constituted the optimality conditions.…”

Section: Pakistan Journal Of Statistics and Operation Researchmentioning

confidence: 99%

A novel iterative method to solve a linear fractional transportation problem

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2022

Pak.j.stat.oper.res.

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The linear fractional transportation problem (LFTP) is widely encountered as a particular type of transportation problem (TP) in real-life. In this paper, a novel algorithm, based on the traditional definition of continuity, is presented to solve the LFTP. An iterative constraint is constructed by combining the objective function of the LFTP and the supply-demand condition since the fractional objective function is continuous at every point of the feasible region. By this constraint obtained, LFTP is converted into an iterative linear programming (LP) problem to reach the optimum solution. In this study, the case of asymptotic solution for LFTP is discussed for the first time in the literature. The numerical examples are performed for the linear and asymptotic cases to illustrate the method, and the approach proposed is compared with the other existing methods to demonstrate the efficiency of the algorithm. Also, an application had environmentalist objective is solved by proposed mathematical method using the software general algebraic modeling system (GAMS) with data set of the real case. Finally, some computational results from tests performed on randomly generated large-scale transportation problems are provided.

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Section: Pakistan Journal Of Statistics and Operation Researchmentioning

confidence: 99%

A novel iterative method to solve a linear fractional transportation problem

Bas

Köçken

Özkök

2022

Pak.j.stat.oper.res.

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“…Mahmoodirad et al [25] designed a linear fractional TP under uncertain environment. In recent years, many researchers have studied on FPP/FTP by considering the parameters of FTP as either a crisp or an interval or a fuzzy value, such as Chang [8], Bhati & Singh [5], Das et al [9], Ebrahimnejad et al [11], Sivri et al [43] and Arya et al [3]. In the last few decades, many researchers have shown significant interest in uncertain environment to tackle uncertainty in FTP and FCTP.…”

Section: Literature Surveymentioning

confidence: 99%

Fuzzy multiple objective fractional optimization in rough approximation and its aptness to the fixed-charge transportation problem

2021

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This article presents a multiple objective fractional fixed-charge transportation problem (MFFTP) in a rough decision-making framework. A transformation procedure is modified to convert non-linear multi-objective transportation problem to its linear version. The parameters of the designed model are considered to be fuzzy. We employ separate kinds of fuzzy scale, i.e., possibility, credibility and necessity measures, to deal with the fuzzy parameters. Using the fuzzy chance-constrained rough approximation (FCRA) technique, we extract the more preferable optimal solution from our suggested MFFTP. The initial result is compared with that of the robust ranking (RR) technique. We also use the theory of rough sets for expanding as well as dividing the feasible domain of the MFFTP to accommodate more information by considering two approximations. Employing these approximations, we introduce two variants, namely, the lower approximation (LA) and the upper approximation (UA), of the suggested MFFTP. Finally, by using these models, we provide the optimal solutions for our proposedproblem. We also associate our MFFTP with a real-world example to showcase its applicability as well as performance. Our core concept of this article is that it tackles an MFFTP using two separate kinds of uncertainty and expands its feasible domain for optimal solutions. Optimal solutions of the designed model (obtained from FCRA technique) belong to two separate regions, namely, “surely region” and “possible region”. The optimal solution which belongs to the “surely region” is better (as these are minimum values) than the one in the “possible region” and other cases. An interpretation of our approach along with offers about the intended future research work are provided at last.

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“…Swarup [2] was the first who proposed an LFTP. The systematic development of LFTP is found in [3,4,5,6,7].…”

Section: Literature Surveymentioning

confidence: 99%

Solving Multi-Objective Linear Fractional Stochastic Transportation Problems Involving Normal Distribution using Simulation-Based Genetic Algorithm

Gessesse¹,

Mishra²,

Acharya³

2019

IJEAT

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In real-life situations, we human beings faced with multi-objective problems that are conflicting and non-commensurable with each other. Especially, when goods are transported from source to locations with a goal to keep exact relationships between a few parameters, those parameters of such problems might also arise in the form of fractions which are linear in nature such as; actual transportation fee/total transportation cost, delivery fee/desired path, total return/total investment, etc. Due to the uncertainty of nature, such a relationship is not deterministic. Mathematically such kinds of mathematical problems are characterized as a multi-objective linear fractional stochastic transportation problem. However, it is difficult to handle such types of mathematical problems. It can't be solved directly using mathematical programming approaches. In this paper, a solution procedure is proposed for the above problem using a stochastic Genetic Algorithm based simulation. The parameters in the constraint of the above problem follow a normal distribution. The probabilistic constraints are handled by stochastic simulation-based GA for the solution procedure of the proposed problem. The feasibility of probability constraints is checked by the stochastic programming through the Genetic Algorithm approach, without finding the equivalent deterministic model. The feasibility is maintained all-over the problem. The stochastic simulation-based Genetic Algorithm is considered to generate non-dominated solutions for the given problem. Then, a numerical case study is provided to illustrate the method.

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A solution proposal to the transportation problem with the linear fractional objective function

Cited by 10 publications

References 10 publications

A novel iterative method to solve a linear fractional transportation problem

A novel iterative method to solve a linear fractional transportation problem

Fuzzy multiple objective fractional optimization in rough approximation and its aptness to the fixed-charge transportation problem

Solving Multi-Objective Linear Fractional Stochastic Transportation Problems Involving Normal Distribution using Simulation-Based Genetic Algorithm

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