Transportation problem, linear programming lp, objectoriented programming 1. Since the total supply is more than the total demand add an extra column with zero entries and demand as the difference between their sums to make the problem balanced one. The transportation problem and the vogels approximation method, decision science 4, 441457, 1970. Transportation problem this mainly occurs in demand and supply of goods and services with the idea of significantly minimizing the cost and time to be incurred. The importance of determining efficient solutions for large scale transportation problems is borne out by many practical problems in industries, the military, etc. Afterwards many researchers provide many methods to solve transportation problem. Vogels approximation method vam is a technique for finding a good initial feasible solution to an allocation problem. Use this online vogel s approximation method calculator to find the least cost for transporting goods in an iterative procedure. To represent the unbalanced transportation problem with bipartite graph. Mar 18, 2018 transportation problem solution by using vogel s approximation method. We can find initial basic feasible solution by using. In the previous section, we used vogel approximation method unit cost penalty method to.
The objective of this paper is to find an optimal solution for the transportation problem which having objective function is to be maximized using new approach revised distribution method, and vogels approximation method. We can get an initial basic feasible solution for the transportation problem by using the northwest corner rule, row minima, column minima, matrix minima or the vogels approximation method. Vogels approximation method vam vogels approximation method is the most preferred method over the above two methods as it usually results in an optimal or a near optimal solution. Vogels approximation method allocated as much as possible to the minimum cost cell in the row or column with the largest penalty cost. Pdf comparsion of solutions by new method in transportation. In this paper, a transportation problem is applied to determine the reduction in transportation cost tc of tools which appeared to be an important component of the total cost of production. Allocate the maximum amount allowable by the supply and demand constraints to the variable x11 i. Transportation modeling is a technique that is used to way out the shipping of supplies from a number of sources to a number of destinations as well as to. Modified vogels approximation method for fuzzy transportation. The amount allocated is the most possible, subject to the supply and demand constraints for that cell. Pdf transportation problem in operational research. Define the objective function to be minimized with the constraints imposed on the problem. The basic transportation problem was originally developed by. The modi and vam methods of solving transportation problems tutorial outline modi method how to use the modi method solving the arizona plumbing problem with modi vogels approximation method.
Because of its special structure the usual simplex method is not suitable for solving transportation problems. Transportation problem solution by using vogels approximation method. Methods of finding initial basic feasible solutions. Mat lab commands, modi method, transportation problem, northwest corner method, least cost method, vogels approximation method. An improved vogels approximation method semantic scholar. An effective methodology for solving transportation problem. Freeman school of business, tulane university abstract. In the case of unbalanced transportation problems i. Transportation problemvogels approximationvamnorthwest cornerleast cost.
A improved vogels approximatio method for the transportation. Like least cost method, here also the shipping cost is taken into consideration, but in a relative sense. Mar 04, 2017 transportation problem vogel s approximation vamnorthwest cornerleast cost. The transportation problem is a special kind of the network optimization problems.
Solving transportation problem by various methods and their. The three methods for solving transportation problem are. With the northwest corner method, an initial allocation is made to the cell in the upper lefthand corner of the tableau i. The transportation problem tp is concerned with shipping a commodity between a set of sources e. Oct 27, 2016 transportation problem the following must be known before using a method to find a lowcost solution. In a transportation model, an initial feasible solution can be found by several alternative methods, including the northwest corner method, the minimum cell cost method, and vogels approximation model. With the northwest corner method, an initial allocation is made to the cell in the upper left.
A streamlined simplex method for the transportation problem. In this paper, we propose a further modification that could result in better initial solutions. This paper presents a new method to find initial basic feasible solution for transportation problem. The transportation problem is one of the oldest applications of linear programming problems.
To obtain an initial feasible solution of the problem using graph contraction method. The transportation problem deals with transporting goods from their sources to their destinations. Introduction the first main purpose is solving transportation problem using five methods of transportation model by linear programming lp. This method is preferred over the two methods discussed in the previous sections, because the initial basic feasible solution obtained by this method is either optimal or very close to the. Vam is not quite as simple as the northwest corner approach. Abstract the transportation problem with vogels approximation method vam is a special class of linear programming problem. The problem is to determine how many tons of wheat to transport from each grain. The basic transportation problem was originally developed by hitchcock 9. Improved vogels approximation method to solve fuzzy.
Transportation problem in the previous section, we used vogel approximation method unit cost penalty method to solve a transportation problem. Use this online vogels approximation method calculator to find the least cost for transporting goods in an iterative procedure. Vogels approximation method trannsportation model transportation model is a special type of networks. The first main purpose is solving transportation problem using three 1methods of transportation model by linear programming lp.
The aim of this work is to establish the superiority of the graph theoretic approach to vogels approximation method in solving unbalanced transportation problem. Least cost method vogels approximation method checking for optimality a stepping stone method b modified distribution modi method. Vogels approximation method or penalty method steps for northwest corner method. Repeat the procedures until the entire rim requirements are satisfied.
Vogel s approximation method vam vogel s approximation method is the most preferred method over the above two methods as it usually results in an optimal or a near optimal solution. Transportation models do not start at the origin where all decision. Module b transportation and assignment solution methods. Vam and modi method in solving transportation problems. Advanced approximation method for finding an optimal. Identify the boxes having minimum and next to minimum transportation cost in each row and write the difference penalty along the side of the table against the. Modified vogels approximation method for the unbalanced. Each source has a capacity dictating the amount it supplies. Aldulaymi college of engineering, alnahrain university, iraq. This method is preferred over the two methods discussed in the previous sections, because the initial basic feasible solution obtained by this method is either optimal or very close.
Improved least cost method to obtain a better ibfs to the. The supply and demand values along the outside rim of a tableau are called rim requirements. The proposed method is easier, takes less computation time and gives better initial solution than vam method. Find powerpoint presentations and slides using the power of, find free presentations research about vogel s approximation method ppt. Determine the optimal solution using vogel s approximation method sufian m. The transportation table of the given problem contains 12 cells. Solving transportation problem using objectoriented model. Improved least cost method to obtain a better ibfs to the transportation problem. Vogels approximation method vam the vogel approximation method is an iterative procedure for computing a basic feasible solution of the transportation problem. The vogel approximation method is an improved version of the minimum cell cost method and the northwest corner method that in general produces better initial basic feasible solution, which are understood as basic feasible solutions that report a smaller value in the objective minimization function of a balanced transportation problem sum of the supply sum of the demand. How to solve transportation problem using the vogels approximation method.
Pdf transportation problem in operational research download. Pdf modified vogels approximation method for solving. Nov 04, 2015 the vogel approximation method is an improved version of the minimum cell cost method and the northwest corner method that in general produces better initial basic feasible solution, which are understood as basic feasible solutions that report a smaller value in the objective minimization function of a balanced transportation problem sum of the supply sum of the demand. Vogel s approximation method vam is a technique for finding a good initial feasible solution to an allocation problem. Select the north west corner cell 1, 1 to make the first allocation. Start with all cells in the transportation tableau empty. Solving transportation problem in vogels approximation method in tamil duration. Vogels approximation method vam 1, balakrishnans version of vam 6,h. Three methods north west corner method nwcm, least cost method lcm and vogels approximation method vam have been used to find initial basic feasible solution for the transportation model.
This model gives us good result in transportation problem. Modified vogels approximation method for solving transportation problems. View and download powerpoint presentations on vogel s approximation method ppt. Transportation problem is a special type of linear programming problem. Vogels approximation method transportation problem youtube. Vogels approximation method the vogel approximation method is an iterative procedure for computing a basic feasible solution of a transportation problem. However these problems can be solved through northwest corner rule, lowest cost entry method and vogels approximation method with feasible solution, basic feasible solutions and. Transportation problem the following must be known before using a method to find a lowcost solution. Download notes for transportation problem here download notes for transportation problem here. Using transportation cost matrix find the transportation plan that is optimal considering the production costs also. Vogel approximation method transportation algorithm in lp.
Another way to find an initial solution in addition to the northwest corner and intuitive lowestcost methods of setting an initial solution to transportation problems, we introduce one other important technique vogels approximation method vam. Transportation models are solved manually within the context of a tableau, as in the. In the previous section, we used vogel approximation method unit cost penalty method to solve a transportation problem. An initial basic feasible solution ibfs for the transportation problem can be obtained by using the north west corner rule nwcr, matrix minima method mmm, vogels approximation method. Recomputed the column and row differences for the reduced fuzzy transshipment table and goto step ii. Calculate a penalty for each row and column of the transportation table. Test for optimal solution to a transportation problem learning objective. A new method for solving transportation problems considering. Introduction the transportation problem involves finding the lowestcost plan for distributing stocks of goods or supplies from. Solving transportation problem by various methods and. Improved vogels approximation method to solve fuzzy transshipment problem 83 4.
Allocate the maximum possible value to satisfy the. The corresponding supply and demand values are 250 and 200 respectively. The transportation problem is a special type of lpp where the objective is to minimize the cost of distributing a product from a number of sources or origins to a number of destinations. It is the best method of solving problem based on transportation problem. Test for optimality stepping stone method before learning the methods to find the optimal solution try and practice few more. Vogel approximation method examples, transportation problem. The modi and vam methods of solving transportation problems. Each destination has a demand dictating the amount it receives. Vogels approximation method you are encouraged to solve this task according to the task description, using any language you may know. The transportation and assignment problems in this chapter, we will discuss the transportation and assignment problems which are two special kinds of linear programming. Balakrishnan, modified vogels approximation method for unbalance transportation problem, applied mathematics letters 32, 9,11,1990. Few of them are modified vogels approximation method for unbalance transportation problem by balakrishnan. For finding the initial basic feasible solution total supply must be equal to total demand. Pdf solving transportation problem using vogels approximation.
Lets concentrate on the following example and find the optimal solution. In this section, we provide another example to enhance your knowledge. Prasad, obtaining a good primal solution to the uncapacitated transportation problem, european journal of operation research, 122 2000 611624. Enter the number of rows and columns, supply and demand constraints in the minimum transportation cost calculator to find the initial feasible solution of the transportation problem. The vogel approximation method unit cost penalty method is an iterative procedure for computing a basic feasible solution of a transportation problem. Solving transportation problem in vogel s approximation method in tamil duration.
It has the special data structure in solution characterized as a transportation. Few of them are modified vogel s approximation method for unbalance transportation problem by balakrishnan. The modi and vam methods of solving transportation. Steps in solving the transportation problem how to solve. An improved vogel s approximation method by serder korukogu and serkan balli 22.
There are several methods available to obtain an initial basic feasible solution of a transportation problem. Procedure to solve transportation problem in quantitative techniques for management procedure to solve transportation problem in quantitative techniques for management courses with reference manuals and examples pdf. The vogels approximation method or vam is an iterative procedure calculated to find out the initial feasible solution of the transportation problem. Vogels approximation method is depending on the concept of penalty cost. The vogel approximation unit penalty method is an iterative procedure for computing a basic feasible solution of a transportation problem. Modified vogels approximation method for the unbalanced transportation problem nagraj balakrishnan a. Vogels approximation method vam is the very efficient algorithm to solve the transportation problem for feasible solution which is nearer to. Balakrishnan, modified vogels approximation method for unbalance transportation problem, applied mathematics letters, 32 1990 911. Transportation problem, vogels approximation method vam, maximum penalty of largest numbers of each row, minimum penalty of smallest. Compute total fuzzy transportation cost for the feasible cost for the feasible. Transportation models do not start at the origin where all decision variables equal zero. The powers that be have identified 5 tasks that need to be solved urgently. Vogels approximation method vam is one of the conventional methods that gives better initial basic feasible solution ibfs of a transportation problem tp.