If you continue browsing the site, you agree to the use of cookies on this website. In transportation model analysis the steppingstone method is used to a. In the video, i have explained solving transportation problem using stepping stone method in an easy and simple way. Introduction recent scientific research has made available a variety of tools which can be brought to bear on managerial problems. Various methods are available to solve the transportation problem to obtain an optimal solution 16. Solving the arizona plumbing problem with modi let us try out these rules on the arizona plumbing problem. 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. Stepping over method without symbols stack overflow. The model we are going to solve looks as follows in excel. Stepping stone algorithum for solving the transhipment. Solved what can you conclude about how much the total. The total cost of the optimal solution to a transportation problem. Solved the stepping stone method is being used to solve a. Transportation problem in excel easy excel tutorial.
For clarity of exposition, consider the following transportation problem. Problem here the transportation problem can be stated as a linear programming problem as. Stepping stone method this is a one of the methods used to determine optimality ofan initial basic feasible solution i. Stepping stone method examples, transportation problem. Northwest corner rule, leastcost or vogels approximation the. Methods for optimal solution steppingstone method the steppingstone method works by. Note that the only change in the transportation table is the border labeling the r i. Transportation problems are solved manually within a tableau format. In this section, we provide another example to boost your understanding. Now there will be at least one zero in each row and in each column in the reduced cost matrix. Progressing toward an optimal solution after having constructed an initial basic feasible solution, our next task is to progress toward an optimal solution. The series of steps are involved in checking the optimality of the initial feasible solution using the stepping.
The rest of the solution procedure for this transportation problem proceeds in the same manner as what was done earlier using the steppingstone method. A closed path consists of horizontal and vertical lines leading from an empty cell. Stepping stone number of basic allocated cells must be s. A closed path consists of horizontal and vertical lines leading from an empty cell back to itself if assignments have been. J f m dummy supply row penalty j 400 420 440 0 0 30 5 f 425 420 440 0 0 10 20 m 420 415 410 0 0 15 20.
Find the initial bfs for the problem, and then solve it. The transhipment problem is to minimise the cost of transporting goods between various sources and. What is loop rule in stepping stone in transportation problem. Transportation problem, linear programming, fuzzy cost, basis tree, nwcstepping stone. Transportation problem stepping stone method pamantasan ng lungsod ng maynilagraduate school of engineeringgem 805 optimization techniques 2. 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. There is only one empty cell having a negative improvement index and this index is 2. Aug 19, 2019 transportation problem using stepping stone method. 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. In this work, a transportation problem of the distribution of big treat bread happy chef was solved using the transportation tableau approach.
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. After computing an initial basic feasible solution, we must now proceed to determine whether the solution so obtained is optimal or not. Jan 19, 20 using stepping stone and modi methods to solve transportation problems by abdussalam muhammad mustapha 09216009 a seminar paper presented to the department of mathematics, faculty of science, usmanu danfodiyo university, sokoto in partial fulfillment of the requirements for the award of the degree of master of science mathematics. Transportation probleminitial solutionoptimality conditionfundamental knowledge stepping stone method step 1. The stepping stone method is being used to solve a transportation problem. What would happen to the total shipping cost if one. Jul 12, 20 the stepping stone method once an initial feasible solution to a transportation problem is determined by any of the previous methods, the next step is to solve the model for the optimal solution. The stepping stone optimality test begins, once an initial basic feasible solution is obtained for the transportation problem, by determining if the total transportation cost can be further reduced by entering a nonbasic variable i. In transportation model analysis the stepping stone method. The transhipment problem is to minimise the cost of transporting goods between various sources and destinations.
Optimization techniques for transportation problems of. A host such as this is referred to as a stepping stone and the series of remote logins utilizing stepping stones is termed a connection chain. Again, we will describe two methods for doing this. Stepping stone method calculator transportation problem. When applying it, we test each unused cell, or square, in the transportation. May 03, 20 transportation problem stepping stone method pamantasan ng lungsod ng maynilagraduate school of engineeringgem 805 optimization techniques 2. Stepping stone method and modified distribution 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. There is only one empty cell having a negative improvement index, and this index is 2. 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. B4 module b transportation and assignment solution methods the northwest corner method with the northwest. Construct the transportation table from given transportation problem.
The stepping stone method is used to check the optimality of the initial feasible solution determined by using any of the method viz. It is used to evaluate the cost effectiveness of shipping goods via transportation routes not currently in the solution. Download stepping stone method source codes, stepping. I write it with the help of various books on operation research. 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 problem optimal solution using stepping stone method. 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. Explain and differentiate this under the condition of certainty and uncertainty.
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. Stepping stone method transportation problem free download as pdf file. Any two hosts in a connection chain is referred to as a stepping stone connection pair. The stepping stone path for the cell indicates that the smallest quantity for the cells with minus signs is 80 units. This product is intended to help schools implement any scientifically valid reading program.
We need to work on step by step procedure to solve the transportation problem. Subtract each row entries of the transportation table from the respective row minimum and then subtract each column entries of the resulting transportation table from respective column minimum. 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 stepping stone and the modified distribution method modi stepping stone. Use the solver in excel to find the number of units to ship from each factory to each customer that minimizes the total cost. 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. Stepping stone method transportation problem mathematical. When applying it, we test each unused cell, or square, in the transportation table by asking. Northwest corner rule, least cost or vogels approximation the method is derived from the analogy of crossing a pond using stepping stones.
Transportation models are solved manually within the context of a tableau, as in the simplex method. Module b transportation and assignment solution methods. The stepping stone method of explaining linear programming. This motivates the need for a method of determining if a host on a given network is being used for such an attack. Northwest corner method pdf with the northwest corner method, an initial allocation is made to the cell in the upper. The model seeks to find a path of least resistance from points of origin and points. Online tutorial the modi and vam methods of solving. In an s x d tableau, the number of basic allocated cells. The increase in the transportation cost per unit quantity of reallocation is. The stepping stone method is for finding the optimal solution of.
A solution to a transportation problem in which fewer than m n. 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. In the previous section, we used the stepping stone method to find the optimal solution of a transportation problem. Northwest corner, least cost method or vogels approximation method. After one iteration of the steppingstone method, g. Application of stepping stone method for an optimal solution.
Transportation problem, linear programming, fuzzy cost, basis tree, nwc stepping stone. Transportation method when transportation method is employed in solving a transportation problem, the very initial step that has to be undertaken is to obtain a feasible solution satisfying demand and supply requirement lu 2010. Ops 301 chapter c transportation models flashcards quizlet. Transportation simplex method 20 phase ii stepping stone method continued step 3. The two methods for solving a transportation model are the steppingstone method and.
Pdf solving transportation problem using vogels approximation. A method for solving the transportation problem 6 august 2018 journal of statistics and management systems, vol. From to 1 2 3 capacity a 30 10 5 20 b 10 10 10 30 c 20 10. Stepping stone method codes and scripts downloads free. Procedure for finding optimal transportation tableau. The simplex method, as compared to transportation method is more general as regards the application and is employed where transportation method cannot. This method is designed on the analogy of crossing the pond using the stepping stone. 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. 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.
Stepping stones to evaluating your own school literacy program. 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. Stepping stone method 5 4 3 8 4 3 9 7 5 100 300 300 300 200. The tableau for our wheat transportation model is shown in table b1. Aare degenerate bare infeasible care unbalanced dare unbounded eprovide management with greater flexibility in selecting. Willis paint company produced the following transportation table. The balanced model will be used to demonstrate the solution of a transportation problem. Typicalwellknown transportation methods include the stepping stone method 2 charnes and. Transportation problem in the previous section, we used the stepping stone method to find the optimal solution of a transportation problem.
This program uses the stepping stone algorithum to solve the transhipment problem. It starts with an initial basic feasible solution and then evaluates, for every nonbasic variable, whether an improved solution can be obtained by introducing one of the. An occupied cell on the stepping stone path now becomes 0 unoccupied. A procedure for solving a transportation problem based on a simplification of the simplex method as applied to the constraint structure that defines a transportation problem. Thus, the stepping stone method is a procedure for finding the potential of any nonbasic variables empty cells in terms of the objective function. Using stepping stone and modi methods to solve transportation. The amount allocated is the most possible,subject tothe supply and demand constraints for that cell. The modified distribution method, also known as modi method or u v method provides a minimum cost solution to the transportation problem. The two methods for solving a transportation model are the stepping stone methodand the modified distribution.
Oct 25, 2005 a procedure for solving a transportation problem based on a simplification of the simplex method as applied to the constraint structure that defines a transportation problem. The initial northwest corner solution is shown in table t4. Techniques used in operations research project management. Stepping stone meaning in the cambridge english dictionary. Pick any empty cell and identify the closed path leading to that cell. The transportation model is a powerful tool that can be used to make business decisions in regards to location. For clarity of exposition, consider the following transportation problem example 1. Formulate a balanced transportation problem to minimize the cost of meeting steelcos weekly requirements. It is a standard method for computing a basic feasible e the stepping stone method to find an. Now, we will discuss about the methods used for finding an optimal solution. Stepping stone method, 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. The following two methods are widely used for testing the solution. Download stepping stone method source codes, stepping stone.
Chapter 10 transportation and assignment models 00036337. With the help of this method, we come to know whether the solution is optimal or not. Stepping stone method is one of the method used to find the optimal solution for the transportation problem. To formulate this transportation problem, answer the following three questions. Transportation and assignment problems mathematics. Linear programming model of transportation type and represent the transportation problem as tableau and solve it with. 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. A company has three factories a, b, and c with production capacity 700, 400, and 600 units per week respectively.