Moreover, based on the novel concepts and solutions proposed by combining the concept of a fully fuzzy solid transportation problem and a fully fuzzy transshipment problem, it describes a new class of problems, i. A note on the solution of fuzzy transportation problem using. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy. Pdf solving fuzzy transportation problem using modified. Introduction e transportation problem refers to a special case of linear programming problem. Their range of applications can be enlarged when some fuzziness in its formulation is accepted. Research article the intelligence of dual simplex method to. Fuzzy transportation problem of triangular numbers with.
A method for solving a fuzzy transportation problem via. Research article on fuzzy multiobjective multiitem solid. The optimal solution of fuzzy transportation problem is obtained from the solutions. By contrast, in boolean logic, the truth values of variables may only be the integer values 0 or 1. Algorithm for solving intuitionistic fuzzy transportation. Solving fuzzy transportation problem using ranking of. Saad and abbas discussed the solution algorithm for solving the transportation problem in fuzzy environment. In section 3, some basic definitions related to the fuzzy set theory are presented. Most of the existing techniques provide only crisp solutions for the fuzzy transportation problem.
Pdf transportation problem in operational research. International journal of computer applications 0975 8887 volume 82 no 15, november 20 solution of fuzzy transportation problem using improved. A n ew a lgorithm for s olving f uzzy t ransportation p. A comparative study of optimization methods for fuzzy transportation problems poonam kumari. A new approach for solving unbalanced fuzzy transportation. This fractional programming problem is solved by the method given by kanti swarup 12.
Consider a fuzzy transportation problem with three supplies m3 and three demands n3. A fuzzy transportation problem is a transportation problem in which the transportation cost, supply and demand quantities are fuzzy quantities. Solving fuzzy transportation problem using ranking of trapezoidal 129 2. The aim of a ftp is to find the transporting plan to minimize the total fuzzy transportation cost while satisfying fuzzy demand and supply limits. Review of literature in recent years, fuzzy transportation and fuzzy assignment problems have received much attention. A new method for solving fuzzy transportation problems.
An appropriate method for real life fuzzy transportation problems. A new dual based approach for the unbalanced fuzzy. Table 1 shows the fuzzy supplies and fuzzy demands, i1, 2, 3. A fuzzy transportation problem is a transportation problem in which the transportation expenditures, supply and demand quantities are fuzzy quantities. To illustrate the proposed method, numerical examples. Possible definition of the set kljk ohyhov in the tank in fig. A new dual based approach for the unbalanced fuzzy transportation. In conformation to model the fuzzy transportation problem can be formulated in the following mathematical programming form. Section 5 illustrates the solution of transportation problem through a numerical example. Pdf solution of fuzzy transportation problem using improved.
Pdf optimization of unbalanced fuzzy transportation. The multiobjective transportation problem refers to a special class of vector minimum linear programming problem, in which constraints are of inequality type and all the objectives are noncommensurable and conflict with each other. A geometric programming approach for a multiobjective transportation problem was considered by islam and roy 10. This paper presents fuzzy transportation problems in which direct fuzzy costs, fuzzy supplies, and. Solving fuzzy transportation problems based on extension. Solution to a multiobjective fuzzy transportation problem. Zero average method to finding an optimal solution of fuzzy. A common problem encountered in solving such multiobjective problems is that to identify a compromise solution among a large number of nondominated solutions. Introduction the time minimizing transportation problem is encountered in connection with transportation of perishable goods, with the delivery of emergency supplies. A novel approach for the fuzzy optimal solution of fuzzy.
In the next section, the general transportation problem with fuzzy trapezoidal numbers is discussed. A comparative study of optimization methods for fuzzy. Transportation models play an important role in logistics and supply chain management for reducing cost and improving service. An approach for solving fuzzy transportation problem. Optimization of unbalanced fuzzy transportation problems. An approach to solve unbalanced intuitionisitic fuzzy. Pdf fuzzy transportation problem through monalishas. In this paper, a new method is proposed for solving fuzzy transportation problems by assuming that a decision maker is uncertain about the precise values of the transportation cost, availability. The transportation research board is a unit of the national research council, a private, nonprofit. Multiobjective multiitem solid transportation problem with. An improved approach for solving fuzzy transportation. Fuzzy inequality solid transportation problem is converted to parameter solid transportation problem by an appropriate choice of flexible index, and then the crisp solid transportation problem is solved by the algorithm cao in optimal models and methods with fuzzy quantities, 2010 for decision values.
Solving fuzzy transportation problem using ranking of trapezoidal. Fuzzy transportation problem of trapezoidal numbers with. The basic transportation problem was originally developed by hitchcock 18. Details about balanced and unbalanced transportation problem you find in attached pdf notes at end of this article. In this paper, transportation problem in fuzzy environment using trapezoidal fuzzy number is discussed. Bellman and zadeh 3 proposed the concept of decision making in fuzzy. A fuzzy transportation problem is a transportation problem in which the transportation costs, supply and demand quantities are fuzzy quantities. Algorithm for solving intuitionistic fuzzy transportation problem with generalized trapezoidal intuitionistic fuzzy number via new ranking method shashi aggarwal miranda house, department of mathematics, university of delhi, delhi, india 17 shashiagg.
Pdf transportation problem in operational research download. The next section presents the standard definition of the transportation model. The transportation problems have a recognized importance. Computation of fuzzy transportation problem with dual simplex. Request pdf solution of fuzzy transportation problem using ranking methodology in this paper, we have proposed an algorithm to obtain optimal solution for fuzzy transportation problem ftp. This algorithm transforms the fully fuzzy transportation problem into a tripleobjective problem and then it utilizes a weighted method for solving multiobjective problems and solves the new problem using simplex transportation method. Fuzzy transportation linear programming models based on lr. Keywords pythagorean fuzzy numbers transportation problem fuzzy numbers score.
A new approach for solving unbalanced fuzzy transportation problems 5 step 4. A new algorithm using ranking function to find solution for fuzzy transportation problem prof. In this study, a new algorithm called fuzzy russells approximation method fram has been proposed to obtain the initial fuzzy basic feasible solution ifbfs of a fuzzy transportation problem ftp which would be a new attempt in solving the transportation problem in fuzzy environment. A parametric approach is used to obtain a fuzzy solution and the aim is to minimize the sum of. We formulate two transportation models under crisp and fuzzy environment where we consider the transportation parameters are crisp and fuzzy in nature, respectively. A new ranking method for generalized trapezoidal fuzzy number is introduced and constructed.
Transportation models have wide applications in logistics and supply chain for reducing cost. Here we consider the problem that there are so many plants and customers and the goods are transported in nstages. In this article a new algorithm is used which depending on proposed ranking. A pythagorean fuzzy approach to the transportation problem.
Solving fuzzy transportation problems using a new algorithm. Department of mathematics, magadh mahila college, patna university. The transportation problem is a special case of linearprogramming. Krishna prabha 1 solved fuzzy transportation problem through monalishas approximation method. Fuzzy multiobjective transportation problem, triangular fuzzy number, ranking function. A fuzzy transportation problem is a transportation problem in which the transportation costs, supply and demand are fuzzy quantities. Chanas and kuchta proposed the concept of the optimal solution for the transportation problem with fuzzy coefficients expressed as fuzzy numbers, and developed an algorithm for obtaining the optimal solution. The multiobjective time transportation problem with additional impurity restriction was studied by singh and saxena 6. Computation of fuzzy transportation problem with dual. The fully fuzzy transportation problem is a transportation problem in which parameters of cost, supply and demand are fuzzy values. Solving fuzzy transportation problem using zero suffix and robust ranking methodology. The transportation problems can be modeled as a standard linear programming problem, which can then be solved by the simplex method. Advanced approximation method for finding an optimal solution.
Michael 11 has proposed an algorithm for solving transportation problems with fuzzy constraints and has investigated the relationship between the. Keerthivasan 5 studied the fuzzy transportation problems. Fully fuzzy transportation problem journal of new researches in. Fuzzy transportation problem with fuzzy cost, fuzzy supply units and fuzzy demand units is given in table ii. In this paper, the author tried to categories the tp under the mixture of certain and uncertain environment and formulates the problem and utilizes the crisp. In general, transportation problems are solved with the assumption that the transportation costs, supply and demand are speci ed precisely. Chanas et al 4 developed a method for solving fuzzy transportation problems by applying the parametric programming technique using the. Iden hasan hussein, anfal hasan dheyab department of mathematics, college of science for women university of baghdad, iraq abstract. For finding the fuzzy optimal solution of fuzzy transportation problems occurring in real life situations, the proposed method is an appropriate method for solving a real fuzzy life transportation problems and also, provides an applicable optimal solution. In this paper row minima method is used to reducing the transportation cost for two stage fuzzy transportation problem, in which supplies, demands are fuzzy trapezoidal numbers. Transportation problem is used globally in solving certain concrete world problems. In this study, the basic idea is to get an optimal solution for an unbalanced fuzzy transportation problem without converting into a balanced one. A method for solving a fuzzy transportation problem via robust ranking technique and atm.
Fuzzy transportation and transshipment problems amarpreet. In conventional transportation problem tp, supplies, demands and costs are always certain. In section 4, the fuzzy transportation problem is formulated in terms of nonnegative triangular fuzzy numbers. Therefore the use of fuzzy transportation problems is more appropriate to model and solve the real world problems. Solution of fuzzy transportation problem using ranking. In solving real life transportation problem, we often face the state of uncertainty as well as hesitation due to various uncontrollable factors.
Given a transportation problem with the following costs, supply, and demand, find the initial solution using the minimum cell cost method and vogels approximation model. Fuzzy transportation problem with additional restrictions. A method for solving the fuzzy assignment problem was given by lin and wen 3. Repeat step 8 to 9 until the entire demand at various destinations or available supply at various sources is satisfied. In this work a new notion namely modified best candidate method mbcm is proposed to minimize the combination of the solutions by choosing the best candidate to reach the optimal solution in any type of transportation problems. A new algorithm called the fuzzy zero point method for finding a fuzzy optimal solution of. For the solution of the problem the technique of parametric programming is used. Lin and wen solved the assignment problem with fuzzy interval number costs by a labeling algorithm 2. Pdf this paper presents a two stage cost minimizing fuzzy transportation problem in which supplies and demands are trapezoidal fuzzy numbers. In this paper row minima method is used to reducing the transportation cost for two stage fuzzy transportation problem, in which supplies, demands are fuzzy trapezoidal numbers is defined.
In the present paper, the transportation problem with fuzzy costs with strictly increasing linear membership. Table 1 shows the fuzzy supplies and fuzzy demands, i1, 2, 3 and j1, 2, 3. Fuzzy transportation problem ftp5 is the problem of minimizing fuzzy valued objective functions with fuzzy source and fuzzy destination parameters. The crisp transportation problems are solved by usual simplex method. A fuzzy set a is defined on universal set of real numbers is said to be a generalized fuzzy number if its membership function has the following characteristics. Solving fuzzy transportation problem 2663 fuzzy transportation problem ftp. Pdf on jan 10, 2016, s vimala and others published fuzzy transportation problem through monalishas approximation method find, read. Total time minimization, fuzzy transportation problem, fuzzy number, exponential membership function, graded mean integration representation 1.
A new approach to solve thefuzzy transportation problemusing generalized trapezoidal fuzzy numbers is proposed. Research article on fuzzy multiobjective multiitem solid transportation problem deepikarani, 1 t. Finally, some conclusion and future work are discussed. Apex base least cost method for fuzzy transportation problem. Compute total fuzzy transportation cost for the feasible allocation from the original fuzzy cost table. A working group, comprised of members from both committees, identified four components to address this issue. This paper is devoted to the study of a resolution method for fuzzy transportation problems.
It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. The objective of the fuzzy transportation problem is to determine the shipping schedule that minimizes the total fuzzy transportation cost while satisfying fuzzy supply and demand limits. A transportation problem plays a vital role in production industry and many other purposes. Fuzzy transportation problem of trapezoidal numbers with f. Pandian and natarajan 2010a introduced a new algorithm to find a fuzzy optimal solution for fuzzy transportation problems. A new method is proposed to find fuzzy optimal solution of fuzzy transportation problem in in section 5. This paper develops a procedure to derive the fuzzy objective value of the fuzzy transportation problem, in that the cost coefficients and the supply and demand quantities are fuzzy. Liu and kao described a method for solving fuzzy transportation problems based on extension principle. In section 3, we introduce the fuzzy transportation problem with triangular fuzzy numbers and related results. In this section, arithmetic operations between two triangular fuzzy numbers are defined on the universal set of real numbers.
The transportation problem tp is an important networkstructured lp problem that arises in several contexts and can be applied to a wide variety of situations, such as scheduling, production. This is followed by the solution of transportation problem using fuzzy trapezoidal numbers in section 4. The balanced condition is both a necessary and sufficient condition for the existence of a feasible solution to the transportation problem. Additionally, chanas and kuchta7 designed an algorithm for solving integer fuzzy transportation problem with fuzzy demand and supply values in the sense of maximizing the joint satisfaction of the. We have taken same transportation models and used mvam to find its initial basic feasible solution and compared its result with above three methods, but mvam gives minimum transportation cost and also optimal and in some problems the result of mvam is same as vam but better than nwcm and lcm. To justify the proposed method, few numerical experiments are given to show the effectiveness of the new model. The advantage of this method is that it gives an optimal solution. Pdf a comparative study on transportation problem in.
Solution of a fuzzy assignment problem by using a new. Fuzzy transportation problem ftp is a problem in which the transportation cost, demand and supply quantities are fuzzy quantities. The transportation problem with fuzzy supply values of the deliverers and with fuzzy demand values of the receivers is analysed. Trapezoidal fuzzy numbers, ranking function, fuzzy transportationproblem. In the proposed method transportation costs, demand. The transportation research board is distributing this circular to make the information contained herein available for use by individual practitioners in state and local transportation agencies, researchers in academic institutions, and other members of the transportation research community. Then an existing optimality method is used to obtain the cost of transportation. Pdf we study a fuzzy transportation problem, and we introduce an approach for solving a wide range of such problem by using a method which apply it. Breakable fuzzy multistage transportation problem springerlink. In this chapter we apply our fuzzy monte carlo method to determine approximate solutions to a fuzzy transportation problem. In this paper, a method is proposed for solving an unbalanced fuzzy transportation problem without converting into a balanced one. Optimization of unbalanced fuzzy transportation problems 535 2. Gulati, 1 andamitkumar 2 department of mathematics, indian institute of technology roorkee, roorkee, india school of mathematics and computer applications,a par university, patiala, india. Satyanarayana murthy 1department of mathematics, national institute of technology warangal, a.
Types of transportation problem in operational research. It is an optimization problem which has been applied to solve various nphard problems. In realworld problems, optimization techniques are useful for solving problems like project schedules, assignment problems, and network flow analysis. Show full abstract to apply for finding fuzzy optimal solution of degenerate fuzzy transportation problem occurring in real world situation. Apex base least cost method for fuzzy transportation. Solving fuzzy transportation problem using zero suffix and. Pdf a new approach for solving intuitionistic fuzzy.
Fuzzy goal programming method for solving multiobjective. Fuzzy logic is a form of manyvalued logic in which the truth values of variables may be any real number between 0 and 1 both inclusive. Total time minimization of fuzzy transportation problem. An approach for solving fuzzy transportation problem using. A new method for solving fuzzy transportation problems using. Fuzzy optimal solution to fuzzy transportation problem. Abstract solution of a fuzzy transportation problem determines the transportation schedule that minimizes the total fuzzy transportation. Since the fuzzy transportation problem is a special class of fuzzy linear programming problem, the straight forward method is to apply the existing fuzzy linear programming techniques to solve the fuzzy transportation problem. Abstract solution of a fuzzy transportation problem determines the transportation schedule that minimizes the total fuzzy transportation cost. A fuzzy approach to the transportation problem sciencedirect.
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