Balanced Transportation Problem Research Articles

Applying a Fuzzy Ordering Approach in Transportation Problems with Decagonal Intuitionistic Fuzzy Numbers

In this study, the paper delves into precision challenges within traditional transportation problem solutions, which rigidly define cost, supply, and demand. Acknowledging the inherent vagueness in real world contexts, the research explores the efficacy of intuitive fuzzy sets as a potent tool. Organized into four distinct sections, this work utilizes decagonal intuitionistic fuzzy numbers for managing supply and demand, while upholding conventional approaches for cost considerations. Employing a fuzzy ordering method, optimal solutions are derived by adjusting the configuration of decagonal intuitive fuzzy numbers across each segment. Through a comparative analysis, the Study identifies the most effective solution, with initial sections addressing balanced geometric intuitionistic fuzzy transportation problems and the final part focusing on unbalanced scenarios, specifically emphasizing supply and demand complexities.

Improved fuzzy multi-objective transportation problem with Triangular fuzzy numbers

The present study investigates a Multi-Objective Transportation Problem within a fuzzy environment. The cost of transportation, supply, and demand data are assumed to be inaccurate due to market variations. As a result, the parameters are imprecise or fuzzy data. We offer a multi-objective, balanced transportation problem during this work, where all the parameters are fuzzy numbers. Following a mathematical formulation, fuzzy arithmetic will be used to divide the Fuzzy MOTP into three levels MOTP (lower, medium, upper). After reducing the problem to a crisp MOTP and applying a harmonic mean to each objective function, a suggested solution procedure is presented. Determining the optimal solutions for the FMOTP under unknown situations is, thus, the most important objective of this research.

Modified method for finding the solution of balanced transportation problems: a power rank method

The transportation problem is categorised an essential optimization problem in which a route is determined to transport a specific amount of quantity from an origin to a destinations with minimum total cost. In this paper, the authors introduce a novel method to find quick initial basic feasible solution for a balanced transportation problem. The new technique returns either the optimal solution or the solution closest to the optimal one. The proposed method is explained using a numerical problem and the results are compared with some existing methods. Задача транспортировки классифицируется как важная задача оптимизации, в которой определяется маршрут для перевозки определенного количества товара от пункта отправления до пункта назначения с минимальными общими затратами. В этой статье авторы представляют новый метод быстрого нахождения начальных базовых возможностей для решения сбалансированной транспортной задачи. Новый метод возвращает либо оптимальное решение, либо ближайшее к оптимальному решение. Предложенный метод иллюстрируется на примере численного решения, а полученные результаты сравниваются с некоторыми существующими методами.

Graph Colouring to Solve Both Balanced and Unbalanced Transportation Problems

Graph Colouring to Solve Both Balanced and Unbalanced Transportation Problems

Leaders and Followers Algorithm for Balanced Transportation Problem

Leaders and Followers algorithm is a metaheuristic algorithm which uses two sets of solutions and avoid comparison between random exploratory sample solutions and the best solutions. In this paper, it is used to solve the balanced transportation problem. There are some modifications in the proposed algorithm in order to fit the algorithm to the problem. The proposed algorithm is evaluated using 138 problems. The results are better than the results obtained by other algorithm from previous studies. Overall, Leaders and Followers algorithm has no difficulty in finding optimal solution, even in problems that have large dimension, number of supply and number of demands.

The solution to the Profit maximization transportation problem using new transportation algorithm

Any engineering system requires engineers to make numerous managerial and technological decisions during the design, building, and maintenance phases. All such decisions aim to either maximize the desired benefit or minimize the amount of effort needed. There is no solitary approach that can effectively address all optimization problems. As a result, number of optimization techniques have been created to address various optimization problems. Transportation problem (TP) formulation is the most significant programing applications in optimization which is attached to everyday life and used in industries under logistics. This study proposed a new algorithm to obtain a basic feasible solution (BFS) for the maximization TP. The approach outlined in this study yields an initial solution that is close to or optimal in most scenarios. A variety of numerical examples are used to demonstrate the new technique. The proposed technique is effective for analyzing balanced or unbalanced transportation problems with maximization objective function.

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

Balanced Transportation Problems with an Alternative Methodology for the Allocation Table Method

This research proposes an alternative approach to the allocation table method (AATM) to identify initial basic-feasible solutions (IBFS) for the balanced transportation problems (BTP). The proposed AATM has fewer steps and produces faster results than the ATM. Furthermore, the efficiency of the proposed technique has been examined by performing a variety of cost-minimizing transportation problems (TP). Therefore, it has been found that the proposed method estimates the optimal result as an efficient computed tool in comparison to conventional NWCM, LCM, VAM, and ATM methods.

Modified Hungarian Method for Solving Balanced Fuzzy Transportation Problems

This paper discusses how to solve balanced transportation problems, with transportation costs in the form of trapezoidal fuzzy numbers. Fuzzy costs are transformed into crisp costs using the Robust’s method as a ranking function. A new approach of modified Hungarian method has been applied to solve the problem of fuzzy transportation. This approach solves the fuzzy transportation problem in one stage of optimization and yields the same results as other methods that solve the problem in two stages.

A Supply Selection Method for better Feasible Solution of balanced transportation problem

Transportation Problem (TP) is correlated with product distribution between supply locations and demand locations. TP aims to minimize the total transportation cost, and TP is one of the most important challenges in optimization. To solve the TP, Initial Basic Feasible Solution (IBFS) is a crucial step to determine the Optimal Solution. However, some developed methods of IBFS do not always produce a good initial solution. This study uses a new method called Supply Selection Method (SSM), which is proposed to the get better initial solution for balanced TP. It was compared with other IBFS methods, including Vogel’s Approximation Method (VAM), Juman Hoque Method (JHM), Total Opportunity Cost Matrix – Minimal Total (TOCM-MT), and Bilqis Chastine Erma method (BCE) to evaluate the performance. The new method was examined with 45 total cases consisting of 31 cases from some journals, 4 cases generated randomly, and 10 samples of real data from XYZ company. The study results show that SSM provided a better initial basic solution than other methods, with 41 of 45 cases reached the Optimal Solution. The evaluation shows that SSM provided more outcomes with lower total minimal cost than LCM, VAM, JHM, TOCM-MT, and BCE.

Analysis on ASM Method Perfomance in Solving Fuzzy Transportation Problems

This study aims to show the performance of the ASM method on transportation problem. The transportation problem relates to the distribution of a product from several sources, with limited supply, to several destinations, with a certain demand, in order to obtain the minimum transportation costs. However, the amount of supply and demand cannot always be known with certainty and may change from time to time. In this paper, the coefficient of supply and demand uses fuzzy numbers and uses the ASM method to determine the optimal solution both to minimize costs and maximize profits. The result is that with the ASM method, the balanced transportation problem is always optimal, while the unbalanced transportation problem is not always optimal.

Comparison of Transportation Problem in Operation Research

Abstract: In Operations Research, the transportation problem is one of the predominant area and it is widely used as a decision making tool in many fields. We report the basic feasible solution and hence the methods to attain the optimal solution of the balanced transportation problem. Keywords: Transportation Problem, North-West Corner Method, Least Cost Method, Vogel’s Approximation Method.

PENGGUNAAN JUMAN & HOQUE METHOD (JHM) PADA PENENTUAN SOLUSI AWAL MASALAH TRANSPORTASI

Transportation problems are related to the efficient process of distributing goods by a company or industry. The purpose of solving transportation problems is to minimize the costs incurred in the process of distributing goods from several sources (supply) to several destinations (demand). One way to solve transportation problems is to find an initial feasible solution, continued by finding the optimal solution. This research was done by finding an initial feasible solution using the JHM (Juman & Hoque Method) for both the case of solving balanced transportation problems and unbalanced transportation problems. The method has the characteristic in the initial allocation process starting at the cell with the smallest cost in each column as much as the quantity of each demand. In addition, identification of whether the row if occupied or not was done based on the allocation for each row to the quantity of each inventory. This research aimed to explain about solving transportation problems by determining the initial feasible solution using JHM and performing optimality test using potential method. The methods of this research was to identify categories of transportation problems, determine the initial solution using JHM, and test the optimality using potential method. Based on the results of this research, JHM model may be used to solve transportation problems. In the steps of JHM there are explanations of some theorem regarding the selection of the column and row which will be the first to be processed to determine the value of intial solution of transportation problems. The initial solution by using JHM tends to approach the value of optimal solution after test of optimality was done by using the potential method.

Modified Dynamically-updated Weighted Opportunity Cost Based Algorithm for Unbalanced Transportation Problem

Recently, Weighted Opportunity Cost (WOC) based algorithms are developed for solving balanced Transportation Problems (TPs). The exceptionality of the WOC based approaches is to introduce supply and demand as weight factor to cost entries for the control of flow of allocations. But in the unbalanced TP, there exist a pitfall whenever balancing the TP with zero dummy transportation cost as done in existing classical approaches, so that the total cost is unaffected due to dummy transportations. A modified dynamically-updated weighted opportunity cost-based algorithm embedded on Least Cost Method (LCM) is proposed which is suitable for both balanced and unbalanced TPs. Numerical instances have been carried out to demonstrate the effectiveness and efficiency of the proposed method. It is observed that, the proposed modified dynamically-updated weighted opportunity cost-based algorithm sometimes outperforms for the LCM as well as the existing weighted opportunity cost-based algorithm in unbalanced TPs.
 Journal of Engineering Science 12(2), 2021, 119-131

An Effective Alternative New Approach in Solving Transportation Problems

The Transportation problem is one of the most colorful and demanding problems in the history of Operations Research. Many researchers have paid attention to solve the problem using different approaches. In certain approaches focused on finding an initial basic feasible solution and the other to find the optimal solution. It can be noticed that these methods have advantages and disadvantages. Out of all the methods that can be found in the literature, Northwest, Least Cost and Vogel’s Approximation methods are the most prominent and renowned methods in finding an initial basic feasible solution. Also, the Modified Distribution (MODI) Method and Stepping Stone Method are the most acceptable methods in finding the optimal solution to the transportation problem. In this research paper, we propose an alternative method that finds the optimal or nearly optimal solution to the transportation problem. This method which is based on an iterative algorithm can be applied to balance as well as unbalanced transportation problems. It is also to be noticed that this method requires a minimum number of iterations to reach the optimality as compared to the other existing methods. Also, we have developed a new method of finding an optimal solution for both balanced and unbalanced transportation problems.

A New Approach for Finding the Initial Solution of the Unbalanced Transportation Problem

A transportation problem deals with two different problems balanced transportation problem or unbalanced transportation problem. This paper points out how Goyal’s modification of Vogel’s approximation method for the unbalanced transportation problem can be improved by subtracting or adding suitable constants to the cost matrix, rows and columns of the cost matrix. In this paper, a new method is proposed for solving unbalanced transportation problem which gives optimal or very near to optimal solution.

DA systematic approach for solving mixed constraint fuzzy balanced and unbalanced transportation problem

<p>In the present article, a mixed type transportation problem is considered. Most of the transportation problems in real life situation have mixed type transportation problem this type of transportation problem cannot be solved by usual methods. Here we attempt a new concept of Best Candidate Method (BCM) to obtain the optimal solution. To determine the compromise solution of balanced mixed fuzzy transportation problem and unbalanced mixed fuzzy transportation problem of trapezoidal and trivial fuzzy numbers with new BCM solution procedure has been applied. The method is illustrated by the numerical examples.</p>

A systematic approach for solving mixed constraint fuzzy balanced and unbalanced transportation problem

A systematic approach for solving mixed constraint fuzzy balanced and unbalanced transportation problem

Goal programming technique for solving fully interval-valued intuitionistic fuzzy multiple objective transportation problems

In transportation problems, the cost depends on various irresistible factors like climatic conditions, fuel expenses, etc. Consequently, the transportation problems with crisp parameters fail to handle such situations. However, the construction of the problems under an imprecise environment can significantly tackle these circumstances. The intuitionistic fuzzy number associated with a point is framed by two parameters, namely membership and non-membership degrees. The membership degree determines its acceptance level, while the non-membership measures its non-belongingness (rejection level). However, a person, because of some hesitation, instead of giving a fixed real number to the acceptance and rejection levels, may assign them intervals. This new construction not only generalizes the concept of intuitionistic fuzzy theory but also gives wider scope with more flexibility. In the present article, a balanced transportation problem having all the parameters and variables as interval-valued intuitionistic fuzzy numbers is formulated. Then, a solution methodology based on goal programming approach is proposed. This algorithm not only cares to maximize the acceptance level of the objective functions but simultaneously minimizes the deviational variables attached with each goal. To tackle the interval-valued intuitionistic fuzzy constraints corresponding to each objective function, three membership and non-membership functions, linear, exponential and hyperbolic, are used. Further, a numerical example is solved to demonstrate the computational steps of the algorithm, and a comparison is drawn amidst linear, exponential and hyperbolic membership functions.

An Effective Approach to Determine an Initial Basic Feasible Solution: A TOCM-MEDM Approach

Transportation of products from sources to destinations with minimal total cost plays an important role in logistics and supply chain management. In this article, a new and effective algorithm is introduced for finding an initial basic feasible solution of a balanced transportation problem. Number of numerical illustration is introduced and optimality of the result is also checked. Comparison of findings obtained by the new heuristic and the existing heuristics show that the method presented herein gives a better result.