An Optimal Algorithm for a Fuzzy Transportation Problem

Mitlif, Rasha Jalal; Rasheed, Mohammed; Shihab, Suha

doi:10.35741/issn.0258-2724.55.3.7

Cited by 16 publications

(6 citation statements)

References 9 publications

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“…Furthermore, another example is taken from [98]. DM-TP1 found the same result as Vogel's approximation method and the generated result are represented in Figure 14.…”

Section: Examplementioning

confidence: 77%

Decision support system using Dhouib-Matrix-TP1 heuristic for pentagonal fuzzy transportation problem

Dhouib,

Kharrat,

Dhouib

et al. 2024

IJEECS

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In this paper, a decision support system (DSS) is provided to assist the decision-maker in obtaining the best solution for the transportation problem under uncertainty. Fuzzy parameters of the transportation problem are presented by pentagonal fuzzy numbers. The centroid ranking function transforms these pentagonal fuzzy numbers into crisp ones. Then, a novel, improved greedy method named Dhouib-Matrix-TP1 (DM-TP1) is used in order to help the decision-maker promptly find a suitable solution. Specifically, this DSS is composed of three components: the data base component considers a pentagonal fuzzy number; the Model Base component thinks through the original heuristic DM-TP1; and the User Interface component deliberates the convivial graphical output of the generated transportation plan solution using the Python programming language. Experiments in the literature on fuzzy transportation problems show that the novel proposed heuristic, DM-TP1, is easy to understand and allows the decision-maker to handle transportation problems under pentagonal fuzzy numbers. Also, the DM-TP1 is robust and can be applied to find a feasible initial solution in less time.

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“…Furthermore, another example is taken from [98]. DM-TP1 found the same result as Vogel's approximation method and the generated result are represented in Figure 14.…”

Section: Examplementioning

confidence: 77%

Decision support system using Dhouib-Matrix-TP1 heuristic for pentagonal fuzzy transportation problem

Dhouib,

Kharrat,

Dhouib

et al. 2024

IJEECS

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show abstract

“…A balanced fuzzy transportation problem which is given in Table 2 is discussed by Rasha Jalal Miltif [25] in which fuzzy demand, fuzzy availability, and fuzzy cost are pentagonal fuzzy numbers.…”

Section: Numerical Examplementioning

confidence: 99%

“…For the same problem, Rasha Jalal Mitlif [25] obtained only the crisp transportation cost of 149. Also, compared to existing techniques, we determine the optimal solution without affecting the fuzzy nature, and also it has lower spreads as shown in Figure 3 which benefits the decision-maker more.…”

mentioning

confidence: 99%

A New Ranking Approach for Solving Fuzzy Transportation Problem with Pentagonal Fuzzy Number

Vidhya¹,

Ganesan²

2022

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In any decision-making process, imprecision is a significant issue. To deal with the ambiguous environment of collective decision-making, various tools and approaches have been created. Fuzzy set theory is one of the most recent approaches for coping with imprecision. The Fuzzy Transportation Problem (FTP) is a well-known network planned linear programming problem which exists in a variety of situations and has received a lot of attention recently. Many authors defined and solved the fuzzy transportation problem with frequently utilized fuzzy numbers such as triangular fuzzy numbers or trapezoidal fuzzy numbers. On the other hand, real-world problems usually involve more than four variables. To tackle these concerns, the pentagonal fuzzy number is applied to the problems. This article proposes an approach to solving transportation problems whose parameters are pentagonal fuzzy numbers without requiring an initial feasible solution. An algorithm based on the core and spread method and an extended MODI method is developed to determine the optimal solution to the problem. The proposed process is based on the approximation method and gives a more efficient result. An illustrated example is used to validate the model. As a result, the proposed methodology is both simpler and more computationally efficient than the existing approaches.

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“…Mathur et al [27] converted the fuzzy parameters to crisp form using ranking function and further applied minimum demand-supply followed by MODI method to attain optimal solution of trapezoidal FTP. Mitlif et al [28] converted the problem to crisp form using proposed novel ranking function and then applied VAM followed by MODI method to obtain optimal solution. Bisht and Dangwal [29] proposed ranking function for octagonal fuzzy numbers and applied it to find optimal transportation cost for FTP.…”

Section: Introductionmentioning

confidence: 99%

Optimal solution of pentagonal fuzzy transportation problem using a new ranking technique

2023

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In this article, we propose a method based on a new ranking technique to find optimal solution for a pentagonal fuzzy transportation problem. Firstly, the proposed ranking method which is based on the centroid concept is applied. This transforms the pentagonal fuzzy transportation problem to crisp transportation problem and then the proposed algorithm is applied to find optimal solution of the problem in crisp form. Also, a new method to find initial basic feasible solution (IBFS) of crisp valued transportation problems is introduced in the paper. Further, we give two numerical illustrations for the newly proposed algorithm and compare the solution obtained with the solutions of existing methods. The proposed method can easily be understood and applied to real life transportation problems. Moreover, the proposed ranking method can be used to solve various other fuzzy problems of operations research.

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An Optimal Algorithm for a Fuzzy Transportation Problem

Cited by 16 publications

References 9 publications

Decision support system using Dhouib-Matrix-TP1 heuristic for pentagonal fuzzy transportation problem

Decision support system using Dhouib-Matrix-TP1 heuristic for pentagonal fuzzy transportation problem

A New Ranking Approach for Solving Fuzzy Transportation Problem with Pentagonal Fuzzy Number

Optimal solution of pentagonal fuzzy transportation problem using a new ranking technique

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