Fuzzy Transportation Problem Research Articles

An Average Based Method for Finding the Basic Feasible Solution for the Fuzzy Transportation Problems

Fuzzy transport problems are another special type of transport problem (TP). In a transportation problem, what is primarily considered is how to carry out the relevant process while reduce the total cost of the transporting the goods to different destinations. This objective is also valid for fuzzy TP. However, the supply quantity, demand, and unit cost values cannot be determined precisely, and those values are represented by "fuzzy number sets." There, the relevant solution value is obtained as a basic solution or an optimal solution. Thus, various researchers have proposed various algorithms to obtain an efficient initial solution or an optimal solution (OS) to fuzzy transportation problems. Accordingly, in this research article, we have presented another method to obtain an basic feasible solution (BFS) value for fuzzy transportation problems. It is prepared by creating a new value for each cell based on Yager's robust ranking method. In obtaining these values, the average of the crisp values of the columns and rows of the relevant column or row was basically considered. After that, the algorithm was used to solve mathematical problems. In here, the proposed method is primarily considered for triangular and trapezoidal fuzzy transportation problems. Also, the basic solution obtained from those solutions was that algorithm and the current approach are compared, and the efficiency and correctness of the proposed method were tested. Based on the analysis of the obtained data, the new method can be shown as an easy method to understand the efficiency that can be used to obtain the BFS to fuzzy transportation problems.

On Fuzzy Linear Fractional Programming Problems via α-Cut-Based Method with Application in Transportation Sector

The article provides an α-cut-based method that solves linear fractional programming problems with fuzzy variables and unrestricted parameters. The parameters and variables are considered as asymmetric triangular fuzzy numbers, which is a generalization of the symmetric case. The problem is solved by using α-cut of fuzzy numbers wherein the α- and r-cut are applied to the objective function and constraints, respectively. This reduces the problem into an equivalent biobjective model which leads to the upper and lower bounds of the given problem. Afterwards, the membership functions corresponding to various values of r∈(0,1] are obtained using the optimal values of the biobjective model. The proposed method is illustrated by taking an example from the literature to highlight the fallacy of an existing approach. Finally, a fuzzy linear fractional transportation problem is modelled and solved using the aforementioned technique.

A new method to determine the Fermatean fuzzy optimal solution of transportation problems

Transportation Problems (TP) have multiple applications in supply chain management to reduce costs. Efficient methods have been developed to address TP when all factors, including supply, demand, and unit transportation costs, are precisely known. However, due to uncertainty in practical applications, it is necessary to study TP in an uncertain environment. In this paper, we define the Trapezoidal Fermatean Fuzzy Number (TrFFN) and its arithmetic operations. Then we introduce a new approach to solve TP, where transportation cost, supply, and demand are treated as TrFFN, and we call it Fermatean Fuzzy TP (FFTP). We illustrate the feasibility and superiority of this method with two application examples, and compare the performance of this method with existing methods. Furthermore, the advantages of the proposed method over existing methods are described to address TP in uncertain environments.

An approach to fuzzy transportation problem using Triacontakaidigon fuzzy number with alpha cut ranking technique

One of the particular issues with linear programming is transportation. These are optimization efforts whose goal is to reduce the overall cost of moving goods or people through intricate logistical systems. To reduce the overall transit costs involved in distribution, the problem can be solved by optimizing the delivery system of the specific entity (such as any goods, a person, or a material) from sources (suppliers) to destinations (customers). When evacuating a region, transportation concerns are used to determine the best route for evacuees to take from boarding points to evacuation centers. Particular attention is paid to the travel distance and the overall cost of moving one person.Finding the right number of items to send from each warehouse to each customer while keeping costs to a minimum is the goal of this problem’s solution. In this study, a novel fuzzy number called the Triacontakaidigon Fuzzy Number and its membership function are introduced. In terms of both form and computation, the triacontakaidigon fuzzy number is more complex than the triangular and trapezoidal fuzzy numbers. A fuzzy ranking approach is an efficient tool for addressing the fuzzy transportation problem, as demonstrated by numerical examples.

Fuzzy Multi-objective Solid Transportation Problem: Genetic Algorithm Based Solution Approach

Fuzzy Multi-objective Solid Transportation Problem: Genetic Algorithm Based Solution Approach

Multi-goal Multi-product Fuzzy Solid Transportation Problem via Goal Programming Technique

Multi-goal Multi-product Fuzzy Solid Transportation Problem via Goal Programming Technique

New approach to solve fuzzy multi-objective multi-item solid transportation problem

This paper explores the study of Multi-Objective Multi-item Solid Transportation Problem (MMSTP) under the fuzzy environment. Realizing the impact of real-life situations, here we consider MMSTP with parameters, e.g., transportation cost, supply, and demand, treat as trapezoidal fuzzy numbers. Trapezoidal fuzzy numbers are then converted into nearly approximation interval numbers by using (P. Grzegorzewski, Fuzzy Sets Syst. 130 (2002) 321–330.) conversation rule, and we derive a new rule to convert trapezoidal fuzzy numbers into nearly approximation rough interval numbers. We derive different models of MMSTP using interval and a rough interval number. Fuzzy programming and interval programming are then applied to solve converted MMSTP. The expected value operator is used to solve MMSTP in the rough interval. Thereafter, two numerical experiments are incorporated to show the application of the proposed method. Finally, conclusions are provided with the lines of future study of this manuscript.

An approach for solving fully fuzzy linear fractional transportation problem with the using of splitting technique

An approach for solving fully fuzzy linear fractional transportation problem with the using of splitting technique

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

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.

Three-phase algorithms in solving full fuzzy transportation problem by using fuzzy analytical hierarchy process

Three-phase algorithms in solving full fuzzy transportation problem by using fuzzy analytical hierarchy process

Multi-objective fuzzy transportation problem with fuzzy decision variables - NSGA-II approach

Multi-objective fuzzy transportation problem with fuzzy decision variables - NSGA-II approach

Tetracontatetragonal fuzzy number with application of fuzzy transportation problem

Tetracontatetragonal fuzzy number with application of fuzzy transportation problem

Extended DEA method for solving multi-objective transportation problem with Fermatean fuzzy sets

<abstract><p>Data envelopment analysis (DEA) is a linear programming approach used to determine the relative efficiencies of multiple decision-making units (DMUs). A transportation problem (TP) is a special type of linear programming problem (LPP) which is used to minimize the total transportation cost or maximize the total transportation profit of transporting a product from multiple sources to multiple destinations. Because of the connection between the multi-objective TP (MOTP) and DEA, DEA-based techniques are more often used to handle practical TPs. The objective of this work is to investigate the TP with Fermatean fuzzy costs in the presence of numerous conflicting objectives. In particular, a Fermatean fuzzy DEA (FFDEA) method is proposed to solve the Fermatean fuzzy MOTP (FFMOTP). In this regard, every arc in FFMOTP is considered a DMU. Additionally, those objective functions that should be maximized will be used to define the outputs of DMUs, while those that should be minimized will be used to define the inputs of DMUs. As a consequence, two different Fermatean fuzzy effciency scores (FFESs) will be obtained for every arc by solving the FFDEA models. Therefore, unique FFESs will be obtained for every arc by finding the mean of these FFESs. Finally, the FFMOTP will be transformed into a single objective Fermatean fuzzy TP (FFTP) that can be solved by applying standard algorithms. A numerical example is illustrated to support the proposed method, and the results obtained by using the proposed method are compared to those of existing techniques. Moreover, the advantages of the proposed method are also discussed.</p></abstract>

PENERAPAN METODE IMPROVED EXPONENTIAL APPROACH DALAM MENYELESAIKAN MASALAH TRANSPORTASI FUZZY DI PERUM BULOG SUB.DIVRE MEDAN

Transportation is an activities that affect the smooth wheels of the economy. The core problem of transportation is to minimize distribution costs. Matters that affect distribution costs are in the form of demand quantities, supply quantities, and transportation costs. In 2021, the rice distribution costs of Perum Bulog Sub Divre Medan was very high accompanied by uncertain demand and supply so it is expressed in fuzzy numbers. It is necessary to use a method that can solve this transportation problem optimally. In this study, the improved exponential approach method was used to find the optimal solution in rice distribution and combined with fuzzy integer transportation to find the integer value of the parameters with fuzzy values. The improved exponential approach method is a method of solving balanced and unbalanced transportation problems directly. The results showed that the improved exponential approach method can be applied to solve the fuzzy transportation problem. The cost of distributing rice in 2021 using the improved exponential approach method has decreased by IDR 41,155,480 from the actual distribution cost. Through these results, it can be concluded that the improved exponential approach method can optimally solve the fuzzy transportation problem in 2021 at Bulog Sub-Divre Perum Medan

Minimum demand supply based stepping stone approach to solve a special trapezoidal fuzzy transportation problem

ABSTRACT In literature, a variety of fuzzy transportation problems are discussed and solved by defuzzification of the fuzzy input values to the crisp values. This crisp-valued conversion, in the beginning, limits the features of fuzziness as it does not take into account the uncertainties occurring in the course of intermediate calculations. The present study is a successful effort to overcome this limitation by proposing a minimum demand supply-based methodology to obtain a fuzzy initial basic feasible solution (FIBFS) of the problem. A unique ordering of trapezoidal fuzzy numbers is proposed to make the demand and supply allocation in a fuzzy form. The proposed method has been applied to a special class of fuzzy transportation problems, having all the inputs viz. demand, supply, and cost as trapezoidal fuzzy numbers. Further, the incenter fuzzy ranking process is used to convert FIBFS in a crisp initial basic feasible solution (IBFS). The optimality of the IBFS thus obtained is tested through the stepping stone method. The results obtained by the proposed approach are compared with the fuzzy Hungarian-MODI approach and the presence of inherent uncertainties in FIBFS makes the former approach superior to the latter.

Response to a Note on “A New Ranking Approach for Solving Fully Fuzzy Transportation Problem in Intuitionistic Fuzzy Environment”

Response to a Note on “A New Ranking Approach for Solving Fully Fuzzy Transportation Problem in Intuitionistic Fuzzy Environment”

A Note on “A New Ranking Approach for Solving Fully Fuzzy Transportation Problem in Intuitionistic Fuzzy Environment”

A Note on “A New Ranking Approach for Solving Fully Fuzzy Transportation Problem in Intuitionistic Fuzzy Environment”

An approach to solve interval valued intuitionistic fuzzy transportation problem of Type-2

An approach to solve interval valued intuitionistic fuzzy transportation problem of Type-2

A New Approach to Solve Fully Fuzzy Multi-Objective Transportation Problem

The transportation problem is the problem of transferring goods from several sources or producers to multiple destinations or consumers in a cost-effective way, which is one of the most important problems in the supply chain management problems. The application of this problem in addition to the distribution of goods in the location and production planning problems is also important. Many real-life transportation problems encounter multiple, conflicting, and incommensurable objective functions. In addition, in real applications, due to lack of information, it is not possible to accurately estimate the parameters of this problem. Therefore, the main goal of this paper is to find the Pareto optimal solutions of fully fuzzy multi-objective transportation problem under the conditions of uncertainty. In accordingly, a new approach based on nearest interval approximation is proposed to solve the problem. Numerical examples are provided to illustrate the proposed approach and results.

Improved Segregated Advancement (I-SA): a new method for solving full triangular fuzzy transportation problems

ABSTRACT In this paper, triangular fuzzy numbers (TFN) are used to represent the uncertainty of data in the transportation problems (TP), which are referred to as fuzzy transportation problems (FTP). The main issues in the FTP are the lack of information, error of the basic trading rules, incomplete fuzzy data, and the limitations of the existing fuzzy-ranking functions which is failed to compare two TFN. Segregated advancement (SA) is a separation approach where the TFN represented by low, middle, and upper are solved part by part. The flaw of SA is that it uses the classical algorithms which are NWC, LCM, and VAM. Therefore, we proposed the improvement based on the combination of total ratio cost matrix and total difference method by column without using classical ranking functions. The first and second examples illustrate the existing methods without using the SA approach. The results show that the proposed method obtained the optimal solution of FTP, whereas the existing methods produced infeasible solution. The third example presents the limitation of existing methods along with the SA approach. The results show that the proposed method is capable in solving the third example whereas the existing approach failed to solve the said example.