Here, the allocation begins with the cell which has the minimum cost. The lower cost cells are chosen over the highercost cell with the objective to have the least cost of transportation. A company has three factories a, b, and c with production capacity 700, 400, and 600 units per week respectively. Stepping stone method, assignment help, transportation. If it is ltmn1, it is called a degenerate solution. Pdf solving transportation problem using vogels approximation. The stepping stone and the modified distribution method modi stepping stone. Pdf optimal solution for fuzzy transportation problem using. A code for the transportation problem of linear programming. The transhipment problem is to minimise the cost of transporting goods between various sources and destinations. The transportation algorithm 60 after testing each unused cell by the steppingstone method in the transportation problem and finding only one cell with a negative improvement. Transportation problem in linear programming stepping stone method stepping stone method after computing the initial solution by using any of the three methods explained above, the solution needs to be tested to see whether the solution is optimum or not, by using the stepping stone method. Solving the arizona plumbing problem with modi let us try out these rules on the arizona plumbing problem. Example a company, as infigure 1, has 3 production centres, factories f, g and h, in.
Application of stepping stone method for an optimal solution to a transportation problem. Using the minimumcost method to solve transportation. Northwest corner rule, least cost or vogels approximation the method is derived from the analogy of crossing a pond using stepping stones. When using the stepping stone method what is the maximum. Note that the only change in the transportation table is the border labeling the r i. Transportation and assignment models l chapter 10 10. Structure special lp problems using the transportation and assignment models. 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. 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 amount allocated is the most possible,subject tothe supply and demand constraints for that cell. Charnes and cooper 1 also developed a method for finding an optimal solution from ibfs named as stepping stone method. Solved what can you conclude about how much the total. Solving a balanced minimization transportation problem. However, tolsto 1930 was a pioneer in operations research and hence wrote a book on. In these operational research notes pdf, you will study the broad and in depth knowledge of a range of operation research models and techniques, which can be applied to a variety of industrial applications the topics we will cover will be taken from the. Stepping stone method transportation problem mathematical. Application of stepping stone method for an optimal. Ops 301 chapter c transportation models flashcards quizlet. 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 research such as traveling salesmen problem, assignment problem, network problem and many industrial management problem. Northwest corner rule, leastcost or vogels approximation the.
Transportation problem in linear programming stepping stone method stepping stone method after computing the initial solution by using any of the three methods explained above, the solution needs to be tested to see whether the solution is optimum or. Solved the stepping stone method is being used to solve a. The augmented predecessor index method for locating stepping stone paths and assxgning dual prices in distribution problems transportation scz. There is only one empty cell having a negative improvement index, and this index is 2. Transportation problem stepping stone method pamantasan ng lungsod ng. Transportation problem warehouse linear programming. The two methods for solving a transportation model are the steppingstone method and the modified distribution method also known as modi. This method is designed on the analogy of crossing the pond using the stepping stone. Variations in transportation problem examples using modi method. Introduction to transportation problem free download as powerpoint presentation. The stepping stone method the stepping stone methodwill help us move from an initial feasible solution to an optimal solution. With the help of this method, we come to know whether the solution is optimal or not.
In the steppingstone method, cell evaluation proceeds by borrowing one unit from a full cell and using it to assess the impact of shifting units into the empty cell. Modi will be used to compute an improvement index for each unused square. The stepping stone path for the cell indicates that the smallest quantity for the cells with minus signs is 80 units. 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. The steppingstone method the steppingstone methodwill help us move from an initial feasible solution to an optimal solution. However, the stepping stones do need to be of sufficient size and quality to be of conservation value. Transportation model step 4a stepping stone method youtube. Transportation models are solved manually within the context of a tableau, as. In such a case evaluation of the solution will not be possible. This method can be used both for balanced and unbalanced transportation problem. There is only one empty cell having a negative improvement index and this index is the steppingstone path for this cell indicates that the smallest quantity for the cells with minus signs is 80 units. 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. This lesson will introduce you to the minimum cost method to solve transportation problems.
An occupied cell on the stepping stone path now becomes 0 unoccupied. Download stepping stone method source codes, stepping. Download stepping stone method source codes, stepping stone. Transportation problem using stepping stone method and its. This research offers a new method to accomplish the optimal solution o. Stepping stone method in transportation problem in hindi lecture. Overall, the results highlight the longterm importance of suitably large stepping stones in. Pdf transportation problem nourishes economic and social activity and is cardinal to operations researchand management science. Procedure to solve transportation problem in quantitative. This solution is feasible but we need to check to see if it is optimal. How to solve transportation problem by using least cost method other popular and amazing videos from ujjwal kumar sen all sfd and bmd tutorials. In this work, a transportation problem of the distribution of big treat bread happy chef was solved using the transportation tableau approach. The least cost method is another method used to obtain the initial feasible solution for the transportation problem.
The stepping stone path for this cell indicates that the smallest quantity for the cells with minus signs is 80 units. Stepping stone method 5 4 3 8 4 3 9 7 5 100 300 300 300 200. 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. Pdf operational research notes lecture free download. B4 module b transportation and assignment solution methods the northwest corner method. The transportation problem involves finding the lowestcost plan for distributing stocks of. Rekha vivek joshi, lecturer, department of mathematics, sydenham college of commerce and economics, mumbai university, india abstract. Stepping stone method codes and scripts downloads free. 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. 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. Transportation simplex method 20 phase ii stepping stone method continued step 3. The series of steps are involved in checking the optimality of the initial feasible solution using the stepping. Stepping stone number of basic allocated cells must be s. Solving a balanced minimization transportation problem youtube.
The two methods for solving a transportation model are the steppingstone methodand the modified distribution method. Consider a transportation problem in which the cost, supply. Solve facility location and other application problems with. During this time, the method of solving transportation problem was conducted by northwestcorner nwc, leastcost lc, and vogel approximation vam.
Test for optimal solution to a transportation problem learning objective. Does any extra cost required to considered in case of such type of problem. Application of stepping stone method for an optimal solution to a. Stepping stone method examples, transportation problem. The stepping stone method of explaining linear programming.
Stepping stone method 5 4 3 8 4 3 9 7 5 100 300 300 300 200 200 supply demand a from buss 211 at korea university. 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. We will explore why it is used, constraints and data needed to use the method and how the method is used. Optimization techniques for transportation problems of. This video explains how to apply stepping stone method for finding an optional solution in transportation problem. To achive optimum value, there are several methods, the stepping stone method, assignment method. For clarity of exposition, consider the following transportation problem example 1. 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. Transportation models are solved manually within the context of a tableau, as in the simplex method. Transportation and assignment models learning objectives students will be able to.
The steppingstone method is being used to solve a transportation problem. We need to work on step by step procedure to solve the transportation problem. When using the stepping stone method what is the maximum amount that can be from iimt 3636 at the university of hong kong. In these operational research notes pdf, you will study the broad and in depth knowledge of a range of operation research models and techniques, which can be applied to a variety of industrial applications. In order to evaluate the cells routes using the uv method or the stepping stone method we need to imagineintroduce some used cellsroutes. Stepping stone method this is a one of the methods used to determine optimality ofan initial basic feasible solution i. Optimization techniques for transportation problems of three variables mrs. The stepping stone method is being used to solve a transportation problem. 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. The initial northwest corner solution is shown in table t4.
It is used to evaluate the cost effectiveness of shipping goods via transportation routes not currently in the solution. Linear programming model of transportation type and represent the transportation problem as tableau. What is the cheapest transportation models and the only transportation model that can transport liquids. 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. How to solve transportation problem by using least cost method. Stepping stone patches of habitat help reduce effects of. If you continue browsing the site, you agree to the use of cookies on this website. In the previous section, we used the stepping stone method to find the optimal solution of a transportation problem.
In an s x d tableau, the number of basic allocated cells. A transportation problem is said to be unbalanced if the supply and demand are not equal. Stepbystep guide on how to solve a balanced minimization transportation problem. The illustrate example to be presented in this paper will be employed to explain the stepping stone method for solving these kind of problems. However the dual matrix approach introduced by ji and chu 2002 does not required that a transportation problem to be balanced. S by stepping stone method ssm or modified distribution method mdm. Transportation problem tp is based on supply and demand of commodities.
Stepping stone method is one of the method used to find the optimal solution for the transportation problem. Cs6704 question bank resource management techniques 3 explain the steps used to solve transportation problem using modi method. The balanced model will be used to demonstrate the solution of a transportation problem. When solving the transportation problem,the number of possible routes should be. Transportation problem optimal solution using stepping stone method.
A free powerpoint ppt presentation displayed as a flash slide show on id. The modi and vam methods of solving transportation. 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. Stepping stone method transportation problem free download as pdf file.
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 transhipment problem is to minimise the cost of transporting goods between various sources and. Ppt transportation problems powerpoint presentation free. Procedure for finding optimal transportation tableau. The tableau for our wheat transportation model is shown in table b1. 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. When applying the steppingstone method, we test each unused cell.
Subscribe to free weekly news alert 3 april 2014 issue 368 the contents and views. 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. Introduction to transportation problem mathematical. May 03, 20 transportation problem stepping stone method pamantasan ng lungsod ng maynilagraduate school of engineeringgem 805 optimization techniques 2. Transportation problem is a special kind of lp problem in which goods are. Ppt transportation problems powerpoint presentation.
Cs6704 question bank resource management techniques. Pdf the issue of transportation is a linier program. Test for optimality stepping stone method before learning the methods to find the optimal solution try and practice few more. Solve facility location and other application problems with transportation methods. Transportation and assignment problems mathematics. Aug 18, 2017 stepbystep guide on how to solve a balanced minimization transportation problem.
Transportation problem is considered a vitally important aspect that has been studied in a wide range. Transportation problem stepping stone method pamantasan ng lungsod ng maynilagraduate school of engineeringgem 805 optimization techniques 2. Module b transportation and assignment solution methods. When applying it, we test each unused cell, or square, in the transportation.
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