Multiobjective Capacitated Fractional Transportation Problem with Mixed Constraints

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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“…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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“…Some cases of objectives for transportation problems belonging to the fractional programming category may include the minimization of total actual cost/standard cost, actual time/ standard time, actual deterioration/standard deterioration, and risk assets/capital [24]. Sadia et al [25] proposed a compromise solution to a MOFTP with mixed constraints by using fuzzy programming and lexicographic GP with minimum distance methods. Costa [26] proposed a new method for optimizing a weighted sum of linear fractional objective functions.…”

Section: Introductionmentioning

confidence: 99%

Solving the Multiobjective Fractional Transportation Problem through the Neutrosophic Goal Programming Approach

Veeramani

Edalatpanah

Sharanya

2021

Discrete Dynamics in Nature and Society

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Nowadays, the transportation problem is a multiobjective decision-making problem. It involves deciding to determine the ideal transportation setup that matches the decision maker’s preferences while taking into account competing objectives/criteria such as transportation cost, transportation time, and environmental and social concerns. This study presents a general framework of the multiobjective fractional transportation problem (MOFTP) to deal with such complex scenarios. This paper’s major goal is to propose a solution methodology to solve the MOFTP based on a neutrosophic goal programming (NGP) approach. By obtaining the optimal compromise solution using three memberships, namely, truth membership, indeterminacy membership, and falsity membership, the suggested technique gives a novel insight into solving the MOFTP. A real-world problem such as selling wind turbine blades’ problem and a numerical example are used to demonstrate the efficacy and superiority of the proposed method.

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“…Dangwal et al [27] gave a goal programming approach to find the suitable ideal solution of the multi-objective linear fractional problem in a vague environment. Sadia et al [28,29] worked on multi-objective fractional problems by taking the capacitated transportation problem with mixed and uncertain constraints, i.e., in a fuzzy environment. Maruti [30] provided a solution procedure for solving MOFTP.…”

Section: Introductionmentioning

confidence: 99%

A Fuzzy Optimization Technique for Multi-Objective Aspirational Level Fractional Transportation Problem

et al. 2021

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In this research work, a soft computing optimization operating approach is developed for a multi-objective aspirational level fractional transportation problem. In the proposed technique, a mathematical model is formulated for the multi-objective aspirational level fractional transportation problem (MOFTP) based on the highest value of one and all objectives of the model. We also used the symmetry concept over our model to identify the best optimum solution based on symmetrical data. We constructed the membership grades for the set of fetched parameters having symmetry. In this work, we also used the concept of ranking function in our mathematical model to obtain the optimum solution of the fuzzy multi-objective fractional transportation. In this proposed algorithm, the aspiration levels are also associated with the objective function of MOFTP. We are also proposing a new approach for the optimization of fractional problems in which the objectives are being optimized by using the numerator function and denominator function simultaneously. Further, a methodology is also developed to find the average cost for each fractional objective of the model. After that, we will find the ranking function for each parameter by using the defuzzification method. By this methodology, we will be able to convert the MOFTP into a bi-objective transportation problem. The provided technique is elaborated with the help of numerical computations to prove the beauty and power of the proposed technique.

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Multiobjective Capacitated Fractional Transportation Problem with Mixed Constraints

Cited by 16 publications

References 0 publications

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

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

Solving the Multiobjective Fractional Transportation Problem through the Neutrosophic Goal Programming Approach

A Fuzzy Optimization Technique for Multi-Objective Aspirational Level Fractional Transportation Problem

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