Unbalanced Transportation Problem Research Articles

WITHDRAWN: Unbalanced transportation problems with multiple fuzzy goals

Abstract In most of the transportation related decision making situations, the decision maker face difficulty in case of unbalanced supply–demand units, in particular when total number of supply units is less than total number of required units. Due to shortage of availability of products, it is not possible for the decision maker to fully specify the requirement of various requirement points, with the existing available amount. In these situations, multiple objectives are considered to handle the situation. The objectives, of a multi-objective model are in general conflicting in nature. The traditional transportation approaches are not able to address the problem but goal programming approach is a well suited approach to such transportation models. In this present study, fuzzy goal programming approach is presented for an unbalanced transportation model with multiple number of objectives, in which all supply and demand quantities are specified imprecisely. We have investigated the results by implementing this method to an unbalanced transportation problem with multiple numbers of equally important fuzzy goals. To illustrate the approach, a numerical example is considered and the result is discussed.

An optimal solution of unbalanced octagonal fuzzy transportation problem

This paper presents the problems in fuzzy transportation with all the parameters are octagonal fuzzy numbers. The paper deals with the minimization of total cost in fuzzy environment. The mainaspectof this paper isto search outthe smallest amounttransportationvalueof some commodities through a capacitated networkoncethe availabilityand demand of nodesand therefore the capacityand valueof edgesarea unitrepresentedas fuzzy numbers. Also an illustrative numerical example is discussed for proposed method solving a triangular FTP with m, n origins and destinations respectively.

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

Solving unbalanced intuitionistic fuzzy transportation problem

In this paper, we find the optimal solution for an unbalanced intuitionistic fuzzy transportation problem by using monalisha’s approximation method. The main aim of this method is to avoid large number of iterations. To illustrate this method a numerical example Triangular intuitionistic fuzzy number, unbalanced intuitionistic fuzzy transportation problem, accuracy function.is given.

An algorithmic approach to solve unbalanced triangular fuzzy transportation problems

This paper presents problems in fuzzy transportation, which deals with fuzzy costs, fuzzy supplies, and demands of a fuzzy nature on any quantity transported. The paper deals with the minimization of the total fuzzy cost under the fuzzified decision-variables. The proposed method gives better optimum for fuzzy transportation problem (FTP) with unbalance and balance types. The method is intended to obtain a basic feasible solution (or “initial basic feasible solution”) (IBFS) of unbalanced fuzzy problems with triangular fuzzy number. A new and simple heuristic approach for obtaining optimum solution of triangular fuzzy unbalanced transportation problem is proposed that reduces the number of iterations in the optimization process. A given triangular fuzzy unbalanced TP is converted into a modified triangular unbalanced FTP by increasing the fuzzy-demand/fuzzy-supply of an origin and a destination, and the same is resolved by new method. Also an illustrative numerical example is discussed for proposed method solving a triangular FTP with m, n origins and destinations, respectively.

A New Technique for Solving Unbalanced Intuitionistic Fuzzy Transportation Problems

A New Technique for Solving Unbalanced Intuitionistic Fuzzy Transportation Problems

A Heuristic Approach to Obtain an Optimal Solution for Unbalanced Transportation Problem

This Method is proposed for obtaining an optimal solution for transportation problem. This method gives the optimal solution in lesser iteration. Here find the difference between two consecutive maximum for row-wise and column-wise. In that find the maximum value, for which the minimum is allocated by the minimum supply or demand. Illustration for this method is given with some examples at the end.

Absolute point algorithm for solving unbalanced fuzzy transportation problem

In real time situations, the total availability of goods or product may be more or less than the actual market demand and the unbalanced transportation situation arise more commonly. Such unbalanced Transportation Problems (TP) are solved by introducing dummy source or destination which do not exist in reality. The optimal allocation involves cells from such dummy source or destination and the allocated number of quantities are held back at one or more origins. The paper aims to propose an algorithm based on Absolute Points to solve unbalanced TP under fuzzy environment. The proposed algorithm is advantageous than the existing algorithms in such a way that it provides the added information of transporting the excess availability from dummy supply point to appropriate destination to meet future demands at minimum cost. Finally, by virtue of the proposed algorithm an example is done to illustrate the practicality and the effectiveness of the proposed algorithm.

Linear Programming Approach for Solving Balanced and Unbalanced Intuitionistic Fuzzy Transportation Problems

In this article, two methods are presented, proposed method 1 and proposed method 2. Proposed method 1 is based on linear programming technique and proposed method 2 is based on modified distribution method. Both of the methods are used to solve the balanced and unbalanced intuitionistic fuzzy transportation problems. The ideas of the proposed methods are illustrated with the help of real life numerical examples which is followed by the results and discussion and comparative study is given. The proposed method is computationally very simple when compared to the existing methods, it is shown to be and easier form of evaluation when compared to current methods.

On Solving Multiobjective Transportation Problems with Fuzzy Random Supply and Demand Using Fuzzy Goal Programming

In this article a fuzzy goal programming model is developed to solve multiobjective unbalanced transportation problems with fuzzy random parameters. In model formulation process the cost coefficients of the objectives are considered as fuzzy numbers and the supplies and demands are considered as fuzzy random variables with known fuzzy probability distribution from the view point of probabilistic as well as possibilistic uncertainties involved with the model. A fuzzy programming model is first constructed by applying chance constrained programming methodology in fuzzy environment. Then, the model is decomposed on the basis of the tolerance ranges of the fuzzy numbers associated with it. The individual optimal solution of each decomposed objectives is found in isolation to construct the membership goals of the objectives. Finally, priority based fuzzy goal programming technique is used to achieve the highest degree of each of the defined membership goals to the extent possible by minimizing the under deviational variables and thereby obtaining optimal allocation of products by using distance function in a cost minimizing decision making environment. An illustrative example is solved and compared with existing technique to explore the potentiality of the proposed methodology.

A new Approach for Obtaining Optimal Solution of Unbalanced Fuzzy Transportation Problem

The present paper attempts to study the unbalanced fuzzy transportation problem so as to minimize the transportationcost of products when supply, demand and cost of the products are represented by fuzzy numbers. In this paper, authorsuse Roubast ranking technique to transform trapezoidal fuzzy numbers to crisp numbers and propose a new algorithm tofind the fuzzy optimal solution of unbalanced fuzzy transportation problem. The proposed algorithm is more efficient thanother existing algorithms like simple VAM and is illustrated via numerical example. Also, a comparison between the resultsof the new algorithm and the result of algorithm using simple VAM is provided.

A general iterative solver for unbalanced inconsistent transportation problems

The transportation problem, as a particular case of a linear programme, has probably the highest relative frequency with which appears in applications. At least in its classical formulation, it involves demands and supplies. When, for practical reasons, the total demand cannot satisfy the total supply, the problem becomes unbalanced and inconsistent, and must be reformulated as e.g. finding a least squares solution of an inconsistent system of linear inequalities. A general iterative solver for this class of problems has been proposed by S. P. Han in his 1980 original paper. The drawback of Han’s algorithm consists in the fact that it uses in each iteration the computation of the Moore-Penrose pseudoinverse numerical solution of a subsystem of the initial one, which for bigger dimensions can cause serious computational troubles. In order to overcome these difficulties we propose in this paper a general projection-based minimal norm solution approximant to be used within Han-type algorithms for approximating least squares solutions of inconsistent systems of linear inequalities. Numerical experiments and comparisons on some inconsistent transport model problems are presented.

Optimization of unbalanced fuzzy transportation problems

Optimization of unbalanced fuzzy transportation problems

A new approach for solving unbalanced fuzzy transportation problems

Practical realization of model-based emergency forecasting in pulse systems for the case of multi-parameter variation in a possible wide range associates with the problem of a-priori forming of single-statement information on system dynamics. The fractal diagram is proposed to use for the purpose of system dynamics presentation. This diagram allows one-to-one correspondence between the both, parameter and phase,spaces establishing by line up stages.

Optimal Solution of Balanced and Unbalanced Fuzzy Transportation Problem Using Hexagonal Fuzzy Numbers

A fuzzy transportation problem (FTP) includes cost, supply and demand of transportation problems. Its numbers are fuzzy numbers. Fuzzy transportation problem works to reduce transportation cost of some commodities through a capacitate network. Present research paper points out a technique with an alpha cut, optimal solution for solving transportation problem. We suggest a technique to find the fuzzy optimal solution on scales of transportation problem and propose a new hexagonal representation of fuzzy numbers. In general, the comparison of balanced fuzzy transportation problem (BFTP) and unbalanced fuzzy transportation problem (UFTP) shows that the optimal transportation cost of UFTP is less than BFTP.

A New Approach for Solving Unbalanced Fuzzy Transportation Problem

In traditional transportation problem (TP), supplies, demands and costs are always firm. The aim of this paper develops a new approach to solve the unbalanced transportation problem where as all the parameters are not in deterministic numbers but imprecise ones. Here, all the parameters of the TP are considered to the triangular fuzzy numbers. The solution procedure is illustrated with a numerical example.

A linear time algorithm for the unbalanced Hitchcock transportation problem

The Hitchcock transportation problem is a special case of the minimum cost flow problem where the graph is bipartite and capacities are infinite. If we let m denote the size of the larger and n the...

대규모 불균형 수송문제의 간단한 해법

As the Transportation Simplex Method of the general transportation problem are inapplicable to the large-scale unbalanced transportation problem, a commercialized linear programming package remains as the only viable means. There is, however, no method made available to verify the optimality of solutions attained by the package. This paper therefore proposes a simple heuristic algorithm to the large-scale unbalanced transportation problem. From a given problem of supply and demand areas, the proposed algorithm determines the number of demands areas for each supply area and executes on the latter in the ascending order of each of their corresponding demand areas. Next, given a single corresponding demand area, it supplies the full demand volume and else, it supplies first to an area of minimum associated costs and subsequently to the rest so as to meet the demand to the fullest extent. This initial optimal value is then optimized through an adjustment process whereby costs are minimized as much as possible. When tested on the cost matrix, the proposed algorithm has obtained an optimal result improved from the commercial linear programming package by 8.9%.

Unbalanced Transportation Problems in Fuzzy Environment using Centroid Ranking Technique

In the present paper a new method proposed for the solution of unbalanced transportation problems with Trapezoidal Shaped Generalized Fuzzy Numbers (TPSGFN) using centroid ranking technique via zero suffix method. Numerical examples show that this technique offers effective way for handing the unbalanced fuzzy transportation problem with imprecise render and requirement condition. The advantage of the proposed method over the existing methods is to find fuzzy optimal solution does not involve only the dummy destination. The method has simple algorithms for computed and the study is checked with numerical examples.