In this work, a transportation problem of the distribution of big treat bread happy chef was solved using the transportation tableau approach. The model seeks to find a path of least resistance from points of origin and points. Stepping stone method this is a one of the methods used to determine optimality ofan initial basic feasible solution i. Transportation problem stepping stone method pamantasan ng lungsod ng.

This method is designed on the analogy of crossing the pond using the stepping stone. Download stepping stone method source codes, stepping stone. Note that the only change in the transportation table is the border labeling the r i. These problems can be solved by their own algorithms. It is used to evaluate the cost effectiveness of shipping goods via transportation routes not currently in the solution. 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. In this section, we provide another example to boost your understanding. In transportation model analysis the steppingstone method is used to. Thus, well have to evaluate each unoccupied cell represents unused routes in the transportation table in terms of an opportunity of reducing total transportation cost. The increase in the transportation cost per unit quantity of reallocation is. 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. Modi will be used to compute an improvement index for each unused square. Procedure for finding optimal transportation tableau. Ppt transportation problems powerpoint presentation.

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. Formulation, solution, unbalanced transportation problem. Stepping stone method transportation problem mathematical. 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. Procedure to solve transportation problem in quantitative. Solving the arizona plumbing problem with modi let us try out these rules on the arizona plumbing 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. Operations management online assignment answers online objective question answers. Pdf solving transportation problem using vogels approximation. A company has three factories a, b, and c with production capacity 700, 400, and 600 units per week respectively. Transportation problem stepping stone method pamantasan ng lungsod ng maynilagraduate school of engineeringgem 805 optimization techniques 2.

The stepping stone method is being used to solve a transportation problem. For clarity of exposition, consider the following transportation problem. The initial solution to a transportation problem can be generated in any manner, so long as. 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. If the problem is not unbalanced then the concept of a dummy row or a dummy column to transform the unbalanced problem to. Northwest corner rule, leastcost or vogels approximation the. Stepping stone method, assignment help, transportation.

Stepping stone method examples, transportation problem. If this indicates a better solution is possible, use the steppingstone path to move from this solution to improved solutions until an optimal solution is found. May 03, 20 transportation problem stepping stone method pamantasan ng lungsod ng maynilagraduate school of engineeringgem 805 optimization techniques 2. If unbalanced, add dummy source row or dummy destination column as required. Module b transportation and assignment solution methods. The stepping stone and the modified distribution method modi stepping stone. Least cost method lcm, assignment help, transportation. A 14 a transportation problem with a total supply of 500 and a total demand of 400 will have an optimal solution that leaves 100 units of supply unused. Some illustrative numerical examples are also presented.

Transportation problem in the previous section, we used the stepping stone method to find the optimal solution of a transportation problem. Here, the allocation begins with the cell which has the minimum cost. Stepping stone method 5 4 3 8 4 3 9 7 5 100 300 300 300. The steppingstone method is being used to solve a transportation problem. The transportation model is a powerful tool that can be used to make business decisions in regards to location. Solving a balanced minimization transportation problem youtube. The transhipment problem is to minimise the cost of transporting goods between various sources and destinations.

Solved the stepping stone method is being used to solve a. The least cost method is another method used to obtain the initial feasible solution for the transportation problem. First, we consider the cell when the unit cost of transportation is the least. Download stepping stone method source codes, stepping. The modi and vam methods of solving transportation. The transportation algorithm 61 in the transportation problem, using the. If you continue browsing the site, you agree to the use of cookies on this website. 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. Jun 06, 2016 operations management online assignment answers.

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. Stepping stone method it is a method for computing optimum solution of a transportation problem. 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. The britisheuropeans refer to operational research, the americans to operations research but both are often shortened to just or which is the term we will use. An occupied cell on the stepping stone path now becomes 0 unoccupied.

The augmented predecessor index method for locating stepping stone paths and assxgning dual prices in distribution problems transportation scz. The modi and vam methods of solving transportation problems. In this work, a transportation problem of the distribution of big treat. Stepping stone number of basic allocated cells must be s. When applying it, we test each unused cell, or square, in the transportation. Transportation problem set 6 modi method uv method there are two phases to solve the transportation problem. The lower cost cells are chosen over the highercost cell with the objective to have the least cost of transportation.

Stepping stone method codes and scripts downloads free. The americans sometimes combine the terms or and ms together and. The augmented predecessor index method for locating steppingstone paths and assxgning dual prices in distribution problems transportation scz. Application of stepping stone method for an optimal. Transportation problem set 6 modi method uv method. The initial northwest corner solution is shown in table t4. The stepping stone method is used to check the optimality of the initial feasible solution determined by using any of the method viz.

If the total sum of all the supply from sources o1, o2, and o3 is equal to the total sum of all the demands for destinations d1, d2, d3 and d4 then the transportation problem is a balanced transportation problem note. Solving a balanced minimization transportation problem. The initial solution of for the fuzzy transportation problem the fuzzy north west corner method was used and for determining the. The smallest quantity in a cell with a minus sign is 35, but two different cells with minus signs have 35 units in them. The balanced model will be used to demonstrate the solution of a transportation problem. Ppt transportation problems powerpoint presentation free. The stepping stone method of explaining linear programming.

Introduction recent scientific research has made available a variety of tools which can be brought to bear on managerial problems. The tableau for our wheat transportation model is shown in table b1. Aug 18, 2017 stepbystep guide on how to solve a balanced minimization transportation problem. Transportation and assignment problems mathematics. The stepping stone path for the cell indicates that the smallest quantity for the cells with minus signs is 80 units. Transportation problem optimal solution using stepping stone method. When using the stepping stone method what is the maximum. Transportation problem using stepping stone method. The possible number of goods that can be assigned to the cell f 3, w 1 is 100 step 3. S by stepping stone method ssm or modified distribution method mdm.

Optimality test by stepping stone method and modi method, and some special cases of transportation problem. Stepping stone method calculator transportation problem. In an s x d tableau, the number of basic allocated cells. 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. The pushandpull algorithm is free from pivotal degeneracy which. We need to work on step by step procedure to solve the transportation problem. 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. In the previous section, we used the stepping stone method to find the optimal solution of a transportation problem. The series of steps are involved in checking the optimality of the initial feasible solution using the stepping. Transportation models are solved manually within the context of a tableau, as in the simplex method. As all these problems are particular cases of linear programming lp, the. 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. The lower cost cells are chosen over the highercost cell with the objective to.

Check whether the problem is a balanced or unbalanced transportation problem. Formulate the given problem and set up in a matrix form. The stepping stone path for this cell indicates that the smallest quantity for the cells with minus signs is 80 units. Finding basic feasible solutions northwest corner rule, least cost method, and vogels approximation method. It is simple and direct unlike the current method which requires mostly two stages. Transportation simplex method 20 phase ii stepping stone method continued step 3. The transportation algorithm 60 after testing each unused cell by the stepping stone method in the transportation problem and finding only one cell with a negative improvement index, diff.

Application of stepping stone method for an optimal solution. Stepping stone method is one of the method used to find the optimal solution for the transportation problem. There is only one empty cell having a negative improvement index and this index is 2. 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.

Transportation type problems have certain features which makes it possible to device special computational techniques which are extremely simple. Pdf operational research notes lecture free download. Another term that is used for this field is management science ms. Stepbystep guide on how to solve a balanced minimization transportation problem. Northwest corner rule, least cost or vogels approximation the method is derived from the analogy of crossing a pond using stepping stones. There is only one empty cell having a negative improvement index, and this index is 2. 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 index, diff. Optimal solution, stepping stone method, feasible solution. Thus, the stepping stone method is a procedure for finding the potential of any nonbasic variables empty cells in terms of the objective function. Solved what problem will this cause and how should. Pdf solving a fuzzy transportation problem by stepping stone.

The amount allocated is the most possible,subject tothe supply and demand constraints for that cell. Next, we move to that cell where the next higher unit cost of transportation exists and assign the possible. What problem will this cause and how should this difficulty be resolved. Application of stepping stone method for an optimal solution to a. However, tolsto 1930 was a pioneer in operations research and hence wrote a book on. Linear programming model of transportation type and represent the transportation problem as tableau. Unlike many lp problems, the transportation problem is feasible to solve by hand using a series of tables and welldocumented strategies such as the northwestcorner method to find an initial basic feasible solution and then using techniques like the leastcost method or the stepping stone method. 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. A code for the transportation problem of linear programming. 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. Ops 301 chapter c transportation models flashcards quizlet. The steppingstone method the steppingstone methodwill help us move from an initial feasible solution to an optimal solution.

Stepping stone method transportation problem free download as pdf file. The transhipment problem is to minimise the cost of transporting goods between various sources and. Northwest corner, least cost method or vogels approximation method. Optimality test by stepping stone method and modi method math. In the northwestcorner rule, the largest possible allocation. Stepping stone method 5 4 3 8 4 3 9 7 5 100 300 300 300 200. This research offers a new method to accomplish the optimal solution o. Stepping stone method 5 4 3 8 4 3 9 7 5 100 300 300 school korea university. For clarity of exposition, consider the following transportation problem example 1. The cells at the turning points are referred to as stepping stones.

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