In this unit our discussion shall be restricted to the balanced problems. A new technique for finding initial basic feasible. Math 30210 introduction to operations research university of notre dame, fall 2007. Revised distribution method of finding optimal solution for transportation problems s. Vam and matrix minima method always provide ibfs of a transportation problem. The method to nd an initial basic feasible solution is straightforward. Solve by lowest cost entry method and obtain an optimal solution for the following problem available from 50 30 220 1 90 45 170 3 250 200 50 4 required 4 2 2. This example is the largest and the most involved you have read so far. International journal of mathematical engineering and. Finding an initial basic feasible solution is the prime requirement to obtain an optimal solution for the transportation problems.
In this article, a new approach is proposed to find an initial basic feasible solution for the transportation problems. The modi and vam methods of solving transportation problems. On optimal solution of a transportation problem 6203. Mat lab commands, modi method, transportation problem, northwest corner. 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. This method can be used for all kinds of transportation problems, whether maximize or minimize. Solution of the transportation model b2 module b transportation and assignment solution methods. In applying the modi method, we begin with an initial solution. It includes traffic signalization, traffic regulations oneway. So, we will show that the basis to the interval transportation problem remains optimal when the interval supply and demand vary between the interval limits. The modified distribution method or modi is an efficient method of checking the optimality of the initial feasible solution. Approximation method vam, north west corner nwc method, and matrix minima method.
Produce quality pdf files in seconds and preserve the integrity of your original documents. Test for optimal solution to a transportation problem learning objective. The classic statement of the transportation problem uses a matrix with the rows representing sources and columns representing destinations. Solve facility location and other application problems with transportation methods. In addition we describe a novel method for nding an initial feasible solution which we coin modi ed russells method. The transportation models described in this module prove useful when considering alternative facility locations within the framework of an existing distribution system. Transportation problem example, in detail warehouses a, b, and c have 18, 25, and 12 units of a certain commodity, respectively.
There are basically two methods a modified distribution method modi b stepping stone method. Modi method is an improvement over stepping stone method. Transportation algorithm for minimization problem modi method step 1. The fourth is the practical field that is concerned with traffic management and operation of highway facilities. To get an optimal solution for the transportation problem, we use the modi method modified distribution method.
There are two phases to solve the transportation problem. However, tolsto 1930 was a pioneer in operations research and hence wrote a book on. Transportation problem modi method uv method optimal solution video lecture in hindi. Fortunately, a key characteristic of these problems is that most of the aij. Method in section 3 is same as the optimal value obtained by modi method. Transportation problem set 6 modi method uv method there are two phases to solve the transportation problem. In this paper, we propose a new method namely, upperlower method to develop the sensitivity analysis of supply and demand parameters in an interval transportation problem. Hindi transportation problem modi method uv method.
It deals with sources where a supply of some commodity is available and destinations where the commodity is demanded. Conclusion thus it can be concluded that asmmethod provides an optimal solution directly, in. Here we see that the optimality solution is directly obtained in zp method, however in modi, method various iterations are required. The modified distribution method, also known as modi method or u v method provides a minimum cost solution to the transportation problem. Modi method transportation algorithm for minimization problem. If you continue browsing the site, you agree to the use of cookies on this website. The membership and nonmembership function of ai is of the following form. The basic solution principle in a transportation problem is to determine whether. Select the largest negative index and proceed to solve the problem as you did using the steppingstone method.
Transportation problem, initial basic feasible solution, optimality, the degree of freedom m1 for optimality. The initial allocation is made to the cell in the tableau having the lowest cost. This technique is also best optimal solution in the literature and. Least cost method vogels approximation method northwest corner method 2. A is a continuous mapping from r to the closed interval 0,1 and. As a consequence, the shortlist method facilitates the computation of large scale transportation problems in viable time. In this class, we continue the discussion on the modified distribution. Vogels method the first iteration itself is optimal, hence optimality is reached. In this problem it is natural to assume that the v ariables x ij tak eon in teger v alues and nonnegativ e ones. In applying the simplex method, an initial solution had to be established in the initial simplex tableau. If not add a dummy column or dummy row as the case may be and balance the problem.
Each new potential plant, warehouse, or distribution center will require a different allocation of shipments, depending on its. A specialpurpose solution procedure 2 transportation, assignment, and transshipment problems a network model is one which can be represented by a set of nodes, a set of arcs, and functions e. Keywords transportation problem, transportation cost, initial basic feasible solution, optimal solution 1. A modified vogel approximation method for solving balanced.
Lecture notes on transportation and assignment problem bbe h qtm. Maximization in a transportation problem in quantitative techniques for management maximization in a transportation problem in quantitative techniques for management courses with reference manuals and examples pdf. Afterwards many researchers provide many methods and algorithms to solve transportation problems. Keywords transportation problem, revised simplex method, earth movers distance. Transportation and assignment models learning objectives students will be able to.
A new technique for finding initial basic feasible solution to transportation problem. Because of this, it can often provide considerable time savings over other methods for solving transportation problems. Arts and science college, coimbatore, tamilnadu, india abstract solving transportation problem using the new technique, results in minimum transportation cost than the least cost method. Charnes and cooper 1 developed the stepping stone method, which provides.
Maths test for optimal solution to a transportation problem using. Lecture notes on transportation and assignment problem. Pdf a new approach to solve transportation problems. The transportation problem in operational research is concerned with finding the minimum cost of transporting a single commodity from a given number of sources e.
B4 module b transportation and assignment solution methods the northwest corner method with the northwest corner method, an initial allocation is made to the cell in the upper lefthand corner of the tableau i. Pdf transportation problem in operational research. For each demand, take units from each supply, top to bottom, until the demand. Finally the purpose for optimality modi check is carried out. Transportation algorithm for minimization problem, modi. Optimization techniques for transportation problems of. The method is also illustrated with numerical examples. Examining the ibfs using modified distribution method. These types of problems can be solved by general network methods, but here we use a specific transportation algorithm. The transportation method although the transportation problem can be solved as an ordinary linear programming problem, its special structure can be exploited, resulting in a specialpurpose algorithm, the socalled transportation method.
Test for optimality modified distribution method modi modified distribution method modi it is a method for computing optimum solution of a transportation problem. Rule use the stepping stone method to nd an optimal solution of a transportation problem formulate special linear programming problems using the assignment model solve assignment problems with the hungarian method. Test for optimal solution to a transportation problem. So you must read the steps and the explanation mindfully. Determine an initial basic feasible solution by vogels technique or by any of the known. With the minimum cell cost method, the basic logic is to allocate to the cells with the lowest costs. The amount allocated is the most possible,subject tothe supply and demand constraints for that cell. Also, the zp method avoides the degeneracy in the transportation problem. An algorithm for a new proposed method and an extended modi method is developed to find optimal solutions of the problem. This problem was first presented in 1941 by hitchcock and it was further developed koopmans 1949 and dantzig 1951. The modi and vam methods of solving transportation. M et al2016 in their paper a new approach to solve transportation problems discussed a solution for solving the initial basic feasible solution of a transportation problem which. The model develops the transportation solution for the north west corner rule, least cost method, vogels approximation method, and modi method for the tp.
Optimization techniques for transportation problems of three variables. Dual of the transportation problem and the optimality of the modi. In the previous section, we provided the steps in modi method modified distribution method to solve a transportation problem. The linear programming model for this problem is formulated in the equations that follow. In this paper, a new and simple method was introduced for solving transportation problem. Transportation algorithms such as the stepping stone method and the modi modified distribution method have been developed for this purpose 1. Introduction transportation problem is famous in operation research for its wide application in real life. Satisfy each demand one by one, from left to right.
Taking the initial bfs by any method discussed above, this method find the optimal solution to the transportation problem. The paper discusses to study tp that would calculate the use of matlab codes using a mathematical modeling. That is, y ou can only ship items in whole n um ber batc hes. Lecture notes on transportation and assignment problem bbe h qtm paper of delhi. Module b transportation and assignment solution methods. The shortlist method for fast computation of the earth. Lpp, a condition referred to as mfile that can result from codes. Transportation problem set 6 modi method uv method. The structure of transportation problem involves a large number of shipping routes from several supply origins to several demand destinations 3. In the first phase, the initial basic feasible solution has to be found and the second phase involves optimization of the initial basic feasible solution that was obtained in the first phase. Revised distribution method of finding optimal solution.
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