A specialpurpose solution procedure 2 transportation, assignment, and transshipment problems a network model is one which can be represented by a set of nodes, a set of arcs, and functions e. A new method using the principle of zero point method 10 is proposed for finding an optimal solution of solid transportation problems. Northwest corner rule, least cost or vogels approximation the method is derived from the analogy of crossing a pond using stepping stones. Dantzig and thapa used the simplex method to the transportation problem as the primal simplex transportation method. The wellknown transportation problem is sometimes called the hitchcock problem. We need to work on step by step procedure to solve the transportation problem. Solve the following transportation problem for maximizing the profit. Mar 15, 2016 a read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. An efficient implementation of the transportation problem. Due to difference in raw material cost and transportation cost, the profit for unit in rupees differs which is given in the table below. Transportation problems steppingstone method step 3. Optimization techniques for transportation problems of three. Solving transportation problem using objectoriented model.
Lecture notes on transportation and assignment problem bbe. Problem here the transportation problem can be stated as a linear programming problem as. So according to the step3 of proposed algorithm, these cells values are to be continuously divided by 2 until obtain. Operation management assignment help, stepping stone method, stepping stone method. Problem is unbalanced and therefore a dummy row has to be added to make it balanced. Stepping stone method examples, transportation problem. Lecture notes on transportation and assignment problem. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. Surapati and roy 11, wahead and lee 12 and zangibadi and maleki presented a fuzzy goal programming approach to determine an optimal solution for the multiobjective transportation problem etc.
Minimise total cost z ij m i n j cijx 1 1 subject to i n j. Transportation problem in the previous section, we used the stepping stone method to find the optimal solution of a transportation problem. Optimization techniques for transportation problems of. There are msources and destn inations, each represented by a node. A new method for solving transportation problems considering. Modified vogels approximation method for solving transportation. Run the demo state machine simulation of the example state machine. If you continue browsing the site, you agree to the use of cookies on this website. Hence the given transportation problem is a balanced one.
Transportation engineering is taught in the junior year as a required course for all civil engineering students. Module b transportation and assignment solution methods. 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. Network representation and mathematical model of transportation problem generally the transportation model is represented by the network in figure 1. A modification of vogels approximation method through the use of heuristics 4 by d. The stepping stone method is used to check the optimality of the initial feasible solution determined by using any of the method viz. Introduction the first main purpose is solving transportation problem using five methods of transportation model by linear programming lp. Once the problem becomes large, the n finding the unique.
For clarity of exposition, consider the following transportation problem example 1. The stepping stone method of explaining linear programming. Also introduced is a solution procedure for assignment problems alternatively called. Procedure for finding optimal transportation tableau.
The initial northwest corner solution is shown in table t4. Steps to solve the train problem georgia institute of. 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. We use any one optimal method modi or stepping stone method. This method is designed on the analogy of crossing the pond using the stepping stone. The course provides an introduction to various aspects of transportation. An efficient implementation of the transportation problem alissa michele sustarsic university of north florida this masters thesis is brought to you for free and open access by the student scholarship at unf digital commons.
The cells at the turning points are referred to as stepping stones. Read the problem statement and draw your own state diagram to solve the. Setting up a transportation problem the executive furniture corporation. Jan 12, 2018 stepping stone method this is a procedure to be followed to find improved solution and the optimal solution in turn of a transportation problem after getting its initial solution by applying. Problembased approach to teaching transportation engineering. Transportation and assignment problems mathematics. Solved the stepping stone method is a way to evaluate. Deshmukh department of engineering mathematics, sres college of engineering, kopargaon author for correspondence abstract in this paper an innovative method named nmd method is. This method considers the row penalty and column penalty of a transportation table tt which are the differences between the lowest and next lowest cost of each row and each column of the tt respectively. Note that the only change in the transportation table is the border labeling the r i. The problem will require a dummy demand with a capacity of 10 units.
In industry, people are concerned with efficiency and. Methods for solving transportation problem there are three methods to determine the solution for balanced transportation problem. It has been accepted for inclusion in unf graduate theses and dissertations by an authorized administrator of unf. Transportation problem in excel easy excel tutorial.
Shores the transportation problem and the vogels approximation method 3. In an s x d tableau, the number of basic allocated cells. In this paper, a new algorithm is proposed to find an initial basic feasible solution for the transportation problems. A special case of the transportation problem is the assignment problem where the objective is to assign a number of resources to an equal number of activities so as to minimize total cost or.
The stepping stone method is a way to evaluate the current solution of a transportation model to see if it is a. The goal is to create the optimal solution when there are multiple suppliers and multiple destinations. The proposed method yields an optimal solution of the given solid transportation problem directly. Ops 301 chapter c transportation models flashcards quizlet. In this paper we are changing the transportation problem in linear programming problem and solving this. Several methods will be used in this paper to obtain this initial feasible problem. Transportation problem set 6 modi method uv method. A method for solving the transportation problem 6 august 2018 journal of statistics and management systems, vol. Formulate the model trial and error solve the model. A comparative study is also carried out by solving a good number of transportation problems which shows that the proposed method gives better result in comparison to the other existing heuristics available in the literature. Stepping stone method, assignment help, transportation. Modi will be used to compute an improvement index for each unused square.
The tableau for our wheat transportation model is shown in table b1. Optimal solution of transportation problem by stepping step method the universal. A company has three factories a, b, and c with production capacity 700, 400, and 600 units per week respectively. Because of the special structure of a transportation lp, the iterations of the simple method have a very special form.
May 03, 20 transportation problem stepping stone method pamantasan ng lungsod ng maynilagraduate school of engineeringgem 805 optimization techniques 2. Solving the arizona plumbing problem with modi let us try out these rules on the arizona plumbing problem. An assignment problem can be regarded as a special case of transportation problems of the hitchcock type defined above, in which mn atbjl for every i. The stepping stone method is for finding the optimal solution of a transportation problem. Northwest corner, least cost method or vogels approximation method. Stepping stone method is one of the method used to find the optimal solution for the transportation problem.
In the previous section, we used the stepping stone method to find the optimal solution of a transportation problem. A new approach for solving solid transportation problems. 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. Determine an initial basic feasible solution using any one of the following. Use the solver in excel to find the number of units to ship from each factory to. Northwest corner rule, leastcost or vogels approximation the. Transportation problem stepping stone method pamantasan ng lungsod ng maynilagraduate school of engineeringgem 805 optimization techniques 2. Destinations c and d must each receive 5 units less than they require. In the first phase, the initial basic feasible solution has to be found and the second phase involves. If you dont have a zip file utility, get winzip free at.
The modi and vam methods of solving transportation problems. Optimal solution of transportation problem by stepping step. Transportation models are solved manually within the context of a tableau, as in the simplex method. Since any transportation problem can be formulated as an lp, we can use the simplex method to find an optimal solution.
The problem is unbalanced and cannot be solved by the transportation method. Transportation 23 stepping stone method part 2 of 3. The simplex method is not suitable for the transportation problem especially for large scale transportation problem due to its special structure of the model in 1954 charnes and cooper was developed stepping stone method for the efficiency reason. Stepping stone method calculator transportation problem. Select the largest negative index and proceed to solve the problem as you did using the steppingstone method. It is very easy to understand and apply which can serve managers by providing the. The increase in the transportation cost per unit quantity of reallocation is. 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 and the modified distribution method modi stepping stone. Stepping stone number of basic allocated cells must be s. A transportation problem is said to be balanced if the total supply from all sources equals the total demand in all destinations otherwise it is called unbalanced. The second main purpose is solving transportation problem by objectoriented programming. Basic feasible solution ibfs of a transportation problem tp. The transportation problem is a distributiontype linear programming problem, concerned with transferring goods between various origins and destinations.
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. Optimal solution of transportation problem by stepping. 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. Application of the transportation and assignment problem tend to require a very large number of constraints and variables, so straightforward computer applications of simplex method may require an exorbitant computational effort. The balanced model will be used to demonstrate the solution of 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. Stepping stone method this is a one of the methods used to determine optimality ofan initial basic feasible solution i. Construct the transportation table from given transportation problem. 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. In this section, we provide another example to boost your understanding. Transportation problem, linear programming lp, objectoriented programming 1. Stepping stone method this is a procedure to be followed to find improved solution and the optimal solution in turn of a transportation problem after getting its initial solution by applying.
Read the example vhdl program and see how it implements the example state machine diagram. 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. Solving transportation problem by various methods and their. Now it is found all the cell values are even number in the transportation table 4. The modi and vam methods of solving transportation. The amount allocated is the most possible,subject tothe supply and demand constraints for that cell. The transportation simplex method uses linear programming to solve transportation problems. The transportation problem is a special type of linear programming problem, where the objective is. 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. Now there will be at least one zero in each row and in each column in the reduced cost matrix. Consider a transportation problem in which the cost, supply.
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. Thus, the stepping stone method is a procedure for finding the potential of any nonbasic variables empty. Charnes and cooper developed the stepping stone method which provides an alternative way of determining the simplex method information. A special case of the transportation problem is the assignment problem where the objective is to assign a number of resources to an equal number of activities so as to minimize total cost or maximize total profit of allocation. The problem will require a dummy supply with a capacity of 10 units. There are two phases to solve the transportation problem. The transportation problem helps companies minimise costs thereby maximise profits. Solving transportation problem by various methods and. A new method for solving fuzzy transportation problems. Frank lauren hitchcock 18751957 was an american mathematician and physicist notable for vector analysis. Transportation problem, vogels approximation method vam, maximum. From the transportation table 4, it is seen that total supply and total demand are equal. Continue the above example containing the initial basic feasible solution obtained by least cost rule. Transportation problems transportation problems pearson.