Fuzzy fractional stochastic transportation problem involving exponential distribution

Agrawal, Prachi; Ganesh, Talari

doi:10.1007/s12597-020-00458-5

Cited by 4 publications

(4 citation statements)

References 21 publications

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“…Ma et al [12] developed a chance-constraint programming model under a fuzzy environment, where waste generation amount are supposed to be type-2 fuzzy variable and treated capacities of facilities are assumed to be type-1 fuzzy variables. Agrawal and Ganesh [13] developed developed a method to solve fuzzy fractional transportation problem in which the parameters of the transportation problem, supply, and demand, are stochastic in nature and considered as a fuzzy random variable that follows the exponential distribution with fuzzy mean and fuzzy variance. Suo et al [14] developed a type-2 fuzzy chance-constraint programming method for supporting energy systems planning under uncertainty.…”

Section: Introductionmentioning

confidence: 99%

“…Dan et al [21] investigated the notion of a minimum spanning tree (MST) of an undirected type-2 fuzzy weighted connected graph (UT2FWCG), where the edge weights are represented as discrete type-2 fuzzy variables. Also, from the literature survey, we two studies [5,13]. In [5], the authors considered multi-objective STP, where parameters are independent normally distributed fuzzy random variables.…”

Section: Introductionmentioning

confidence: 99%

“…In [5], the authors considered multi-objective STP, where parameters are independent normally distributed fuzzy random variables. Agrawal and Ganesh [13] developed a method to solve the fuzzy fractional transportation problem in which the parameters of the transportation problem, supply, and demand, are stochastic in nature and considered as a fuzzy random variable that follows the exponential distribution with fuzzy mean and fuzzy variance. In this paper, a novel strategy is developed for STP involving fuzzy gamma distribution.…”

Section: Introductionmentioning

confidence: 99%

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Type-2 Fuzzy Stochastic Transportation Problem with Gamma Distribution

Chaini

Ranarahu

2023

IJFIS

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The transportation problem in real-life is an uncertain problem. Particularly when goods are transported from the source to destinations with the best transportation setup that satisfies the decision maker's preferences by taking into account the competing objectives/criteria such as maintaining exact relationships between a few linear parameters, 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. In this stochastic transportation problem supplies are considered as fuzzy random variables, which follow fuzzy gamma distribution, with shape parameter α and scale parameter β. Here β is a perfectly normal interval type-2 fuzzy random variable. This paper proposes a solution methodology for solving the fuzzy stochastic transportation problem, where fuzziness and randomness occur under one roof. Therefore, we converted it to an equivalent deterministic mathematical programming problem by applying the following two steps. In the first step of the solution procedure, fuzziness is removed by using alpha-cut technique to obtain stochastic transportation problem. In the second step, the stochastic transportation problem is converted to an equivalent crisp transportation problem using the chance constrained technique. This mathematical model is solved by existing methodology or software. In order to illustrate the methodology a case study is provided.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Type-2 Fuzzy Stochastic Transportation Problem with Gamma Distribution

Chaini

Ranarahu

2023

IJFIS

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“…To convert stochastic transportation problems into deterministic problems, a strategy that includes conventional randomness is applied. Agrawal and Ganesh [20] dealt with the solution of the fuzzy fractional transportation problem in which the parameters of the transportation problem, supply and demand, are stochastic in nature and considered as fuzzy random variables that follow exponential distributions with fuzzy means and fuzzy variances. Mahapatra et al [21] utilize fuzzy programming to turn a multiobjective function into a single-objective function.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Transportation Problem with Multichoice Random Parameter

Ganesh,

Paidipati,

Chesneau

2023

Computational and Mathematical Methods

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This paper deals with the situation of multiple random choices along with multiple objective functions of the transportation problem. Due to the uncertainty in the environment, the choices of the cost coefficients are considered multichoice random parameters. The other parameters (supply and demand) are replaced by random variables with Gaussian distributions, and each multichoice parameter alternative is treated as a random variable. In this paper, the Newton divided difference interpolation technique is used to convert the multichoice parameter into a single choice in the objective function. Then, the chance-constrained method is applied to transform the probabilistic constraints into deterministic constraints. Due to the consideration of multichoices in the objective function, the expectation minimization model is used to get the deterministic form. Moreover, the fuzzy programming approach with the membership function is utilized to convert the multiobjective function into a single-objective function. A case study is also illustrated for a better understanding of the methodology.

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