Online tutorial the modi and vam methods of solving. Download stepping stone method source codes, stepping. Transportation probleminitial solutionoptimality conditionfundamental knowledge stepping stone method step 1. In this paper a different approach namely zero suffix method is applied for finding an optimal solution for transportation problems directly. 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 and assignment models l chapter 10 10. Next, we move to that cell where the next higher unit cost of transportation exists and assign the. The stepping stone method is being used to solve a transportation problem. When applying it, we test each unused cell, or square, in the transportation.
Various methods are available to solve the transportation problem to obtain an optimal solution 16. It is simple and direct unlike the current method which requires mostly two stages. Structure special lp problems using the transportation and assignment models. Note that the only change in the transportation table is the border labeling the r i. 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. Least cost method lcm, assignment help, transportation.
In case of degeneracy problem, it can resolve with the corrective degeneracy method. The cells at the turning points are referred to as stepping stones. M83 the stepping stone method is being used to solve a transportation problem. It tells you which nonbasic variable should be firstly considered as an entry variable 3. Application of classical transportation methods for solving fuzzy transportation problems journal of transportation systems engineering and information technology, vol.
Transportation and assignment problems mathematics. Pdf transportation and assignment models chapter 10. In phase ii, the stepping stone method, using the modi method for evaluating the reduced costs may be used to move from the initial feasible solution to the optimal one. Pdf optimal solution of a degenerate transportation problem. The stepping stone path for this cell indicates that the smallest quantity for the cells with minus signs is 80 units. Minimization problem in this transportation cost is given which is to be minimized. Transportation problem, vogels approximation method, unbalanced transportation problem. For the machine loading model, the simplex method reduces to a specialized algorithm which generalizes the stepping stone method of the transportation problem 2, 3.
A company has three factories a, b, and c with production capacity 700, 400, and 600 units per week respectively. To achive optimum value, there are several methods, the stepping stone method, assignment method. We need to work on step by step procedure to solve the transportation problem. This research offers a new method to accomplish the optimal solution o. 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 number of basic allocated cells must be s. In the previous section, we used the stepping stone method to find the optimal solution of a transportation problem. Solved the stepping stone method is being used to solve a. It is from this requirement that the method derives its name. The lower cost cells are chosen over the highercost cell with the objective to have the least cost of transportation. The stepping stone method again, we will use the previous example to illustrate the method.
In an s x d tableau, the number of basic allocated cells. The series of steps are involved in checking the optimality of the initial feasible solution using the stepping. If user have some questions please contact me on 1. Stepping stone method calculator transportation problem. Stepping stone and modimethod mathematical analysis.
Module b transportation and assignment solution methods. Each cell in the tableau represents the amount transported from one source to one des. For clarity of exposition, consider the following transportation problem example 1. Solve facility location and other application problems with transportation methods. With the help of this method, we come to know whether the solution is optimal or not. Linear programming model of transportation type and represent the transportation problem as tableau and solve it with. Transportation and assignment models learning objectives students will be able to. This code has been designed to solve the transportation problem with northwest corner rule. Again, we will describe two methods for doing this. Watch this video first and then move on to stepping stone and modi. Stapping stone method 2 modi modified destribution method. 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 least cost method to obtain a better ibfs to the transportation problem.
Transportation problem optimal solution using stepping stone method. Here, the allocation begins with the cell which has the minimum cost. The tableau for our wheat transportation model is shown in table b1. The process of adding and subtracting units from allocated cells is analogous to crossing a pond by stepping on stones i. There is only one empty cell having a negative improvement index, and this index is 2.
Transportation problems are solved manually within a tableau format. The transhipment problem is to minimise the cost of transporting goods between various sources and destinations. Ops 301 chapter c transportation models flashcards quizlet. In transportation model analysis the stepping stone method is. In transportation model analysis the stepping stone method is used to a. Stepbystep guide on how to solve a balanced minimization transportation problem. Answer true 25 transportation and assignment models l one. The initial northwest corner solution is shown in table t4. Journal of operational research society 406 581 590. 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. There is only one empty cell having a negative improvement index and this index is 2. 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. Improved least cost method to obtain a better ibfs to the. Stepping stone method this is a one of the methods used to determine optimality ofan initial basic feasible solution i.
An occupied cell on the stepping stone path now becomes 0 unoccupied. The balanced model will be used to demonstrate the solution of a transportation problem. Ed dansereau linear programming transportation problem and. Minimise total cost z ij m i n j cijx 1 1 subject to i n j.
Solved what problem will this cause and how should this. The modified distribution method, also known as modi method or u v method provides a minimum cost solution to the transportation problem. 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. 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.
Suplimental chapter c pages 10 to 12 see moodle for pdf file. Typicalwellknown transportation methods include the stepping stone method 2 charnes and. 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. Problem here the transportation problem can be stated as a linear programming problem as. Transportation simplex method 20 phase ii stepping stone method continued step 3.
In this particular instance two cells have the quantity 35 in them, and both have a minus sign. Transportation models are solved manually within the context of a tableau, as in the simplex method. Transportation problem least cost method to find the initial feasible solution video. It is a standard method for computing a basic feasible solution. The two methods for solving a transportation model are the steppingstone method and. Stepping stone method codes and scripts downloads free. 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. Transportation model step 4a stepping stone method youtube. Stepping stones to evaluating your own school literacy. 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. During this time, the method of solving transportation problem was conducted by northwestcorner nwc, leastcost lc, and vogel approximation vam.
Stepping stone method it is a method for computing optimum solution of a transportation problem. The stepping stone method the stepping stone methodwill help us move from an initial feasible solution to an optimal solution. The new global approach to a transportation problem. If you continue browsing the site, you agree to the use of cookies on this website. 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. Thus, the stepping stone method is a procedure for finding the potential of any nonbasic variables empty cells in terms of the objective function. It is a generalization of the transportation problem, in that weighting factors are applied to the individual elements which form the row and column sums. Stepping stones is designed flexibly so that it can be used in a variety of settings. Stepping stones can help target areas in which change is needed in. Stepping stone method transportation problem mathematical. As all these problems are particular cases of linear programming lp, the. Through stepping stone method, we determine that what effect on the transportation cost would be. J f m dummy supply row penalty j 400 420 440 0 0 30 5.
The possible number of goods that can be assigned to the cell f 3, w 1 is 100 step 3. This method is designed on the analogy of crossing the pond using the stepping stone. Answer true 27 transportation and assignment models l. When the stepping stone method is being used to solve a transportation problem, the empty squares must be evaluated to achieve the most cost effective solution. Stepping stone method is one of the method used to find the optimal solution for the transportation problem. Transportation simplex method 18 phase i minimumcost method step 1. 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. May 03, 20 transportation problem stepping stone method pamantasan ng lungsod ng maynilagraduate school of engineeringgem 805 optimization techniques 2. Pick any empty cell and identify the closed path leading to that cell.
A solution to a transportation problem in which fewer than m n 1 arcs. I write it with the help of various books on operation research. 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 transportation tableau associated with the basic feasible solution produced by the leastcost. These are sent to regional distributors in dallas, atlanta, and denver.
After computing an initial basic feasible solution, we must now proceed to determine whether the solution so obtained is optimal or not. Solving transportation problem with north west corner rule. Set up the appropriate transportation table and find the initial. Northwest corner rule, leastcost or vogels approximation the.
The augmented predecessor index method for locating stepping stone paths and assxgning dual prices in distribution problems transportation scz. Now, we will discuss about the methods used for finding an optimal solution. The two methods for solving a transportation model are the steppingstone methodand the modified distribution method also known as modi. The least cost method is another method used to obtain the initial feasible solution for the transportation problem. The increase in the transportation cost per unit quantity of reallocation is. However, tolsto 1930 was a pioneer in operations research and hence wrote a book on. Accelerated mgorithms for labehng and relabehng of trees with applications to distribution problems. The application of basis tree approach and nwcstepping stone method is used to.
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. North west corner methodmost systematic and easiest method for obtaining initial feasible basic solution. It is a modified version of stepping stone method modi has two important elements. Solving the arizona plumbing problem with modi let us try out these rules on the arizona plumbing problem. First, we consider the cell when the unit cost of transportation is the least. This method typically gets you closer to a solution than the northwest corner method. Discussion questions and problems quantitative analysis. These problems can be solved by their own algorithms. A simplex type,algorithm for general transportation problems. The stepping stone and the modified distribution method modi stepping stone. Aare degenerate bare infeasible care unbalanced dare unbounded eprovide management with greater flexibility in selecting. Northwest corner rule, least cost or vogels approximation the method is derived from the analogy of crossing a pond using stepping stones. Procedure for finding optimal transportation tableau. A closed path consists of horizontal and vertical lines leading from an empty cell back to itself if assignments have been.
In this section, we provide another example to boost your understanding. Stepping stone method transportation problem free download as pdf file. Modi will be used to compute an improvement index for each unused square. Using a sequence or path of occupied cells to identify flow adjustments necessary when flow is assigned to an unused arc in the transportation simplex method.
Following are a few examples for the use of stepping stones. Transportation problem in the previous section, we used the stepping stone method to find the optimal solution of a transportation problem. The stepping stone method of explaining linear programming calculations in. Begin the use of stepping stones as soon as summative student assessment data are available. Fuzzy cost idea in transportation problems is required. It is used to evaluate the cost effectiveness of shipping goods via transportation routes not currently in the solution. The stepping stone method for explaining linear programming. Download stepping stone method source codes, stepping stone. The generalized stepping stone method for the machine. Solving a balanced minimization transportation problem. The stepping stone method is the second video in the series and is a good teaching tool to aid in the. Stepping stone method examples, transportation problem. Pdf solving transportation problem using vogels approximation. The stepping stone method of explaining linear programming.
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