Optimal Decision Making for Fractional Multi-commodity Network Flow Problem in a Multi-choice Fuzzy Stochastic Hybrid Environment (original) (raw)
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Fuzzy Information and Engineering
In this paper, due to increasing competition in the business world, which makes decision makers dealing with multiple options/ information for optimal decisions on a single task, we will look at multi-choice programming in hybrid fuzzy random environment. Alternative choices multi-choice parameters are considered as fuzzy random variables. By using polynomials interpolation for each multichoice parameter, the model is transformed into a fuzzy random programming problem. Then, to convert this model to its deterministic form, we use the concept of the mean value of fuzzy random variables. Finally, to validate the proposed mathematical operations, we solve a multi-commodity transportation problem with fuzzy random multi-choice parameters.
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T he fractional programming is a generalization of linear programming where the objective function is a ratio of two linear functions. Similarly, in fractional transportation problem the objective is to optimize the ratio of two cost functions or damage functions or demand functions. As the ratio of two functions is considered, the fractional programming models become more suitable for real life problems. Keeping in view the complexities associated with real life transportation problem like vagueness and uncertainty involved with the parameters. The implementation of fuzzy techniques can be very useful. Therefore, in this article a Fully Fuzzy Multi-objective Fractional Transportation Problem (FFMOFTP) is considered. All the coefficients of the parameters, demands and supplies are considered as fuzzy numbers. The purpose of using fuzzy numbers is to deal with the uncertainties and vagueness associated with the parameters. Two cases are considered, one with triangular and other with ...
International Journal of System Assurance Engineering and Management, 2019
In real life situations, it is difficult to handle multi-objective linear fractional stochastic transportation problem. It can't be solved directly using mathematical programming approaches. In this paper, a solution procedure is proposed for the above problem using a genetic algorithm based fuzzy programming method. The supply and demand parameters of the said problem follow fourparameters Burr distribution. The proposed approach omits the derivation of deterministic equivalent form as required in case of classical approach. In the given methodology, initially the probabilistic constraints present in the problem are tackled using stochastic programming combining the strategy adopted in genetic algorithm. Throughout the problem, feasibility criteria is maintained. Then after, the non-dominated solution are obtained using genetic algorithm based fuzzy programming approach. In the proposed approach, the concept of fuzzy programming approach is inserted in the genetic algorithm cycle. The proposed algorithm has been compared with fuzzy programming approach and implemented on two examples. The result shows the efficacy of the proposed algorithm over fuzzy programming approach.
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International Journal of Fuzzy Systems, 2017
A new version of fractional minimal cost flow problem with fuzzy arc costs is focused in this study. The fuzzy arc costs are applied as in most of the real-world applications, the parameters have high degree of uncertainty. The goal of this problem is to determine the minimum fuzzy fractional cost of sending and passing a specified flow value into and from a network. A decomposition-based solution methodology is introduced to tackle this problem. The methodology applies Zadeh's extension principle to decompose the problem to two upper bound and lower bound problems. These problems are capable of being solved for different a-cut values to construct the fuzzy fractional minimal cost flow value as the objective function value. The efficiency of the proposed solution methodology is studied over some well-known examples of fractional minimal cost flow problem. The obtained results show the superiority of the proposed approach comparing to the methods of the literature.
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A Model for Uncertain Multi-objective Transportation Problem with Fractional Objectives
International Journal of Operations Research, 2017
Fractional programming problems take into account the situations where the decision maker is interested to maximize or minimize the ratios of some functions rather than a simple function. Fractional programming modeling approach has a lot of scope in dealing with the transportation planning decision problems. This paper presents a model for transportation problem with multiple fractional objectives involving uncertain parameters. In order to make the model more realistic, we have considered the case when there exists more than one fractional objective. All the parameters involved in the proposed model viz. objective function coefficients, availabilities and demands are assumed to be uncertain. Moreover, an equivalent deterministic model is also presented. Fuzzy goal programming approach is discussed as the solution approach for reaching the compromise solution. A numerical example is also given to illustrate the model more clearly.
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