Network simplex method used to transportation problem. Introduction recent scientific research has made available a variety of tools which can be brought to bear on managerial problems. Jika matriks solusi awal menggunakan metode vam dan penyelesaian optimalnya menggunakan stepping stone, dapat dilakukan sebagai berikut. From 1 2 3 200 demand 200 a 6 25 7 4 75 100 300 11 175 5 12 275 to b 8 125 11 175 supply c 10 150. The transportation tableau associated with the basic feasible solution produced by the leastcost. The proposed method is a generalpurpose algorithm which uses only one operation, the gauss jordan pivoting used in the simplex method. The modi and vam methods of solving transportation problems. The two methods for solving a transportation model are the stepping stone methodand the modified distribution method. It is not the purpose of this article to explore the full ramifications of these research developments or even to explore the general field of linear programming.
The lower cost cells are chosen over the highercost cell with the objective to have the least cost of transportation. In this paper a new algorithm namely fuzzy stepping stone method is proposed for finding a fuzzy optimal solution for a fuzzy transportation problem where the transportation cost, supply and. The tableau for our wheat transportation model is shown in table b1. Transportation problem warehouse linear programming. The basic solution principle in a transportation problem is to determine whether. One of these tools, which has already proved its worth in practical applications, is linear programming. The transportation problem in linear programming is to find the optimal transportation plan for certain volumes of resources from suppliers to consumers, taking into account the cost of transportation.
B2 module b transportation and assignment solution methods the cost of transporting one ton of wheat from each grain elevator source to each mill. Here, the allocation begins with the cell which has the minimum cost. The process of adding and subtracting units from allocated cells is analogous to crossing a pond by stepping on stones i. Transportation problem, degeneracy, difference cost,optimum solution. The steppingstone method is being used to solve a transportation problem. The new global approach to a transportation problem. The stepping stone and the modified distribution method modi stepping stone. Pdf transportation and assignment models chapter 10.
Transportation models are solved manually within the context of a tableau, as in the simplex method. Ppt transportation problems powerpoint presentation free. Transportation problem optimal solution using stepping stone method. Download stepping stone method source codes, stepping stone. Dualmatrix approach for solving the transportation problem. Generally, an ebook can be downloaded in five minutes or less. Stepping stone method the stepping stone method is an iterative technique for moving from an initial feasible solution to an optimal feasible solution. This algorithm appears to be faster than simplex, more general than stepping stone. An occupied cell on the stepping stone path now becomes 0 unoccupied. The stepping stone method involves testing each unused route to see if shipping one unit on that route would increase or decrease total transportation costs. Application of stepping stone method for an optimal.
Stepping stone method transportation problem free download as pdf file. With the help of this method, we come to know whether the solution is optimal or not. Add this allocation to all cells where additions are to be made, and subtract this allocation to all cells where subtractions are to be made along the stepping stone path. A transportation problem tp with huge number of variables can be solved by modified distribution method modim and stepping stone method ssm both are simplex method which is used in operation. A simplextype algorithm for general transportation.
Nov 07, 2012 the stepping stone method is the second video in the series and is a good teaching tool to aid in the understanding of how to reach an optimal solution. The optimal solution is obtained either by using stepping stone method or by modi method in the second phase. However, the special structure of the transportation problem. In this section, we provide another example to boost your understanding. Pdf solving transportation problem using vogels approximation. The stepping stone method is the second video in the series and is a good teaching tool to aid in the understanding of how to reach an optimal solution. The amount allocated is the most possible,subject tothe supply and demand constraints for that cell. The stepping stone path for the cell indicates that the smallest quantity for the cells with minus signs is 80 units. Northwest corner rule, leastcost or vogels approximation the. The stepping stone method is an iterative technique used to evaluate the cost effectiveness of the shipping routes not currently in the solution. Stepping stone method the stepping stone method is an.
Nov 14, 20 stepping stone method to find the optimum solution in a transportation problem slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. Stepping stone method examples, transportation problem. Network model of the transportation problem is shown in figure 1. Transportation and assignment models chapter 10 transportation and assignment models. A company has three factories a, b, and c with production capacity 700, 400, and 600 units per week respectively. Test for optimality stepping stone method before learning the methods to find the optimal solution try and practice few more. Stepping stone method in transportation problem in hindi. Structure special lp problems using the transportation and assignment models. Solving the arizona plumbing problem with modi let us try out these rules on the arizona plumbing problem. In order to evaluate the cells routes using the uv method or the stepping stone method we need to imagineintroduce some used cellsroutes. Jul 14, 20 in this video, you will learn how to perform an optimality test on the basic initial feasible solution using the stepping stone method in order to find out if the solution is optimal or not.
Improved transportation flow for each city total cost of improved situation. We need to work on step by step procedure to solve the transportation problem. The series of steps are involved in checking the optimality of the initial feasible solution using the stepping. Pdf the optimum solution of degenerate transportation. 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. The transhipment problem is to minimise the cost of transporting goods between various sources and destinations. The cells at the turning points are referred to as stepping stones. Stepping stone method this is a one of the methods used to determine optimality ofan initial basic feasible solution i. B2 module b transportation and assignment solution methods.
The two methods for solving a transportation model are the stepping stone methodand the modified. When using the stepping stone method what is the maximum. It is used to evaluate the cost effectiveness of shipping goods via transportation routes not currently in the solution. Through stepping stone method, we determine that what effect on the transportation cost would be in case one unit is assigned to the empty cell. The plan is a table matrix, whose rows and columns correspond to the suppliers and consumers, the cells are placed in cargo volume. The stepping stone method of explaining linear programming. In the video, i have explained solving transportation problem using stepping stone method in an easy and simple way. Again, we will describe two methods for doing this. Transportation and assignment models learning objectives students will be able to. A the smallest number found in the squares with minus signs b the smallest number found in the squares with plus signs c the smallest number along the closed path d the minimum of the demand requirement for that column and the supply capacity for that row e the largest number found. This solution is feasible but we need to check to see if it is optimal. In such a case evaluation of the solution will not be possible. A simplex type,algorithm for general transportation problems.
Pdf optimal solution for fuzzy transportation problem using. Modi will be used to compute an improvement index for each unused square. Here we proposed the modi method with modifications to solve the degenerate transportation problem. As all these problems are particular cases of linear programming lp, the problems will be presented and then formulated as lp problems.
Transportation problem stepping stone method pamantasan ng lungsod ng maynilagraduate school of engineeringgem 805 optimization techniques 2. Using stepping stone method improvement index for unused cell will be houston to yuma houston to miami st. Stepping stone solution method using the initial solution obtained from minimum cell cost method, solve the transportation problem using stepping stone solution method. Module b transportation and assignment solution methods. Transportation problem using stepping stone method. The stepping stone path for this cell indicates that the smallest quantity for the cells with minus signs is 80 units. The initial northwest corner solution is shown in table t4. However, tolsto 1930 was a pioneer in operations research and hence wrote a book on. What is loop rule in stepping stone in transportation problem.
Stepping stone method, assignment help, transportation. Stepping stone method is one of the method used to find the optimal solution for the transportation problem. Note that the only change in the transportation table is the border labeling the r i. Starting at an unusedempty cell, trace a closed path or loop backto the. In the previous section, we used the stepping stone method to find the optimal solution of a transportation problem. This method is designed on the analogy of crossing the pond using the stepping stone.
Transportation simplex method 20 phase ii stepping stone method continued step 3. The initial basic feasible solution was obtained using the vogels approximation method and the stepping stone method was used to test and solve for optimality. Consider a transportation problem in which the cost, supply. Ops 301 chapter c transportation models flashcards quizlet. Transportation model step 4a stepping stone method youtube. The transhipment problem is to minimise the cost of transporting goods between various sources and. A simplextype algorithm for general transportation problems. Stepping stone method transportation problem mathematical. This video explains how to apply stepping stone method for finding an optional solution in transportation problem. Given the s 3 supply and d 3 demands tableau below, first create feasible tableau by using the northwest, vam, minimum cell, or russell method. The stepping stone method the stepping stone methodwill help us move from an initial feasible solution to an optimal solution. Pdf optimal solution of a degenerate transportation problem.
Application the transportation models on real data to arrival to optimize solution by three methods and compare them, add test of the optimal solution by stepping stone method. In this work, a transportation problem of the distribution of big treat bread happy chef was solved using the transportation tableau approach. Transportation problem, dualmatrix approach, stepping stone method, simplex method, linear programming models. The stepping stone method again, we will use the previous example to illustrate the method. If you continue browsing the site, you agree to the use of cookies on this website. The transportation models are concerned with determining the optimal strategy for distribution a commodity from. The dualmatrix approach is used in the present algorithm. Stepping stone method to find the optimum solution in a transportation problem slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. Solving transportation problem with north west corner rule. It is from this requirement that the method derives its name. Indeed, with the current availability of high quality lp software, it looks unnecessary to gointo the. When applying it, we test each unused cell, or square, in the transportation.
The stepping stone method of explaining linear programming calculations in transportation problems. Hitung nilai pinalti selisih 2 ongkos terkecil pada semua baris dann kolom. Northwest corner rule, least cost or vogels approximation the method is derived from the analogy of crossing a pond using stepping stones. We could set up a transportation problem and solve it using the simplex method as with any lp problem see using the simplex method to solve linear programming maximization problems, em 8720, or another of the sources listed on page 35 for information about the simplex method. The modified distribution method, also known as modi method or u v method provides a minimum cost solution to the transportation problem.
The least cost method is another method used to obtain the initial feasible solution for the transportation problem. Test for optimal solution to a transportation problem learning objective. When solving the transportation problem,the number of possible routes should be. Stepping stone number of basic allocated cells must be s. 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. Journal of operational research society 406 581 590. The stepping stone method for explaining linear programming. Stepping stone method calculator transportation problem.
The stepping stone method is being used to solve a transportation problem. Introduction the minimum cost planning plays an important role for solving the transportation problems from origins. Procedure for finding optimal transportation tableau. Download stepping stone method source codes, stepping. Finding an initial basic feasible solution by vogels approximation method. The balanced model will be used to demonstrate the solution of a transportation problem.
Stepping stone method codes and scripts downloads free. The modi and vam methods of solving transportation. Transportation problem stepping stone method stepping stone method this is a one of the methods used to determine optimality of an initial basic feasible solution i. Solve facility location and other application problems with transportation methods. This paper reexamines use of the linear programming lp formulation to solve the transportation problem tp. There is only one empty cell having a negative improvement index, and this index is 2. In an s x d tableau, the number of basic allocated cells. If it is ltmn1, it is called a degenerate solution. May 03, 20 transportation problem stepping stone method pamantasan ng lungsod ng maynilagraduate school of engineeringgem 805 optimization techniques 2. The final tableau can be used for postoptimality analysis of tp. During this time, the method of solving transportation problem was conducted by northwestcorner nwc, leastcost lc, and vogel approximation vam. There is only one empty cell having a negative improvement index and this index is 2. To achive optimum value, there are several methods, the stepping stone method, assignment method.
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