Application of Classical Transportation Methods to Find the Fuzzy Optimal Solution of Fuzzy Transportation Problems

Kumar, Amit; Kaur, Amarpreet

doi:10.1007/s12543-011-0068-7

Cited by 30 publications

(11 citation statements)

References 20 publications

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“…The use of the ranking function in the solving of FTP has a very significant impact on the resulting fuzzy optimal solution. As the results of [13] which produce a negative fuzzy optimal solution, this is contrary to the constraints that must be non-negative in the FTP model. In addition, the ranking process takes a long time to compute so that it will affect the computational performance that is not good.…”

Section: Introductionmentioning

confidence: 82%

Three stages algorithm for finding optimal solution of balanced triangular fuzzy transportation problems

Sam'an¹

2021

joscex

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In the literature, the fuzzy optimal solution of balanced triangular fuzzy transportation problem is negative fuzzy number. This is contrary to the constraints that must be non-negative. Therefore, the three stages algorithm is proposed to overcome this problem. The proposed algorithm consists of segregated method with segregating triangular fuzzy parameters into three crisp parameters. This method avoids the ranking technique. Next, total difference method is used to get the initial basic feasible solution (IBFS) value based on segregating triangular fuzzy parameters. While modified distribution algorithm is used to determine optimal solution based on IBFS value. In order to illustrate the proposed algorithm is given the numerical example and based on the result comparison, the proposed algorithm equality to the two existing algorithms and better than the one existing algorithm. The proposed algorithm can solve the fuzzy decision-making problems and can also be extended to an unbalanced fuzzy transportation problem.

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Section: Introductionmentioning

confidence: 82%

Three stages algorithm for finding optimal solution of balanced triangular fuzzy transportation problems

Sam'an¹

2021

joscex

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“…So, these methods can also be used for solving such single-objective solid transportation problems as well as same type of single and multi-objective transportation problems. However, the existing methods (Gen et al 1995;Ojha et al 2009;Liu & Kao 2004) can not be used to find the fuzzy optimal solution of such existing single and multi-objective transportation problems (Kumar & Kaur 2011;Gupta et al 2011;Liu & Kao 2004) and such single-objective solid transportation problems (Liu 2006) in which all the parameters are represented by fuzzy numbers. (ii) Since, the existing method (Yang & Liu 2007) is proposed to solve such single-objective fixed charge solid transportation problems in which all the parameters except the quantity of the product that should be transported from source to destinations are represented by fuzzy numbers.…”

Section: Limitations Of Existing Methodsmentioning

confidence: 99%

“…So, it can also be used to solve same type of fuzzy solid transportation problems and fuzzy transportation problems. However, the existing method (Yang & Liu 2007) can not be used to find the fuzzy optimal solution of such existing single objective transportation problems (Kumar & Kaur 2011;Liu & Kao 2004) and single-objective solid transportation problems (Liu 2006) in which all the parameters are represented by fuzzy numbers. (iii) Since, the existing methods (Jimenez & Verdegay 1997, 1998 are proposed to solve such solid transportation problems in which all the parameters except cost parameters are represented by fuzzy numbers.…”

Section: Limitations Of Existing Methodsmentioning

confidence: 99%

“…So, these methods can also be used to find the fuzzy optimal solution of same type of single-objective transportation problems. However, the existing methods (Jimenez & Verdegay 1997, 1998 can not used to find the fuzzy optimal solution of such existing single-objective transportation problems (Kumar & Kaur 2011;Liu & Kao 2004) and single-objective solid transportation problems (Liu 2006) in which all the parameters are represented by fuzzy numbers.…”

Section: Limitations Of Existing Methodsmentioning

confidence: 99%

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Optimal way of selecting cities and conveyances for supplying coal in uncertain environment

Kumar

Kaur

2014

Sadhana

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In this paper, the limitations and shortcomings of the existing methods for solving fuzzy solid transportation problem are pointed out and to overcome these shortcomings, a new method is proposed for solving fuzzy solid transportation problem. The advantages of the proposed method over the existing methods are discussed. To illustrate the proposed method, an existing fuzzy solid transportation problem is solved. Also, to show the application of the proposed method in real life problems an existing real life fuzzy solid transportation problem is solved by the proposed method. Keywords. Fuzzy solid transportation problem; ranking function;LR flat fuzzy number.Fuzzy solid transportation problem 167 If m = n then A = (m, n, α, β) LR will be converted into A = (m, α, β) LR and is said to be LR fuzzy number. L and R are called reference functions, which are continuous, non-increasing functions that defines the left and right shapes of μ A (x), respectively and L(0) = R(0) = 1.If L(x) = R(x) = maximum {0, 1 − x} then an LR flat fuzzy number (m, n, α, β) LR and an LR fuzzy number (m, α, β) LR are said to be trapezoidal and triangular fuzzy numbers and denoted by (m, n, α, β) and (m, α, β), respectively. A = (m, n, α, β) LR be an LR flat fuzzy number and λ be a real number in the interval [0, 1] then the crisp set Definition 2 (Dubois & Prade 1980). LetDefinition 3 (Dubois & Prade 1980). An LR flat fuzzy numberÃ = (m, n, α, β) LR is said to be zero LR flat fuzzy number if and only if m = 0, n = 0, α = 0, β = 0.Definition 4 (Dubois & Prade 1980). Two LR flat fuzzy numbersÃ 1 = (m 1 , n 1 , α 1 , β 1 ) LR and A 2 = (m 2 , n 2 , α 2 , β 2 ) LR are said to be equal i.e.,Ã 1 =Ã 2 if and only if m 1 = m 2 , n 1 = n 2 , α 1 = α 2 , β 1 = β 2 .Definition 5 (Dehghan et al 2006). An LR flat fuzzy numberÃ = (m, n, α, β) LR is said to be non-negative LR flat fuzzy number if m − α ≥ 0.Remark 1. If m = n then an LR flat fuzzy number (m, n, α, β) LR is said to be an LR fuzzy number and is denoted as (m, m, α, β) LR or (n, n, α, β) LR or (m, α, β) LR or (n, α, β) LR .

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“…Furthermore multi-objective transportation problem and MOTP with interval cost, source and destination parameters derived by [7,8]. Amit Kumar presented application of classical transportation methods to find the fuzzy optimal solution of fuzzy transportation problem and also find the optimal solution of transshipment [14,15]. Lee and Li proposed an idea for optimizing transportation problem with multiple objectives, and fuzzy approach to the MOTP [17,18].…”

Section: Literature Reviewmentioning

confidence: 99%

Goal programming approach for solving transportation problem with interval cost

Narayanamoorthy

Anukokila

2014

Journal of Intelligent &Amp; Fuzzy Systems

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This paper presents a fuzzy goal programming approach for solving multi-objective transportation problem with interval cost. The fuzzy goal programming approach is used for achieving highest degree of each of the membership goals by minimizing negative deviational variables. Also a special type of hyperbolic membership function to each objective function describe fuzzy goal. A numerical example is given to illustrate the potential use of the proposed approach.

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Application of Classical Transportation Methods to Find the Fuzzy Optimal Solution of Fuzzy Transportation Problems

Cited by 30 publications

References 20 publications

Three stages algorithm for finding optimal solution of balanced triangular fuzzy transportation problems

Three stages algorithm for finding optimal solution of balanced triangular fuzzy transportation problems

Optimal way of selecting cities and conveyances for supplying coal in uncertain environment

Goal programming approach for solving transportation problem with interval cost

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