This transportation problem has been solved with two techniques for solving transportation problems. One of the significant form of linear programming problem is transportation which can be expanded to inventory, assignment, traffic and so on. Solving transportation problem using objectoriented model. Suppose that it is desired to devise a transportation schedule for the distribution of a homogeneous product. Louis des moines kansas city omaha supplies demands the supply, demand and transportation costs per units are shown on the network. In these three methods, vam method is best according to the literature. The three methods for solving transportation problem are. Modi will be used to compute an improvement index for each unused square. Recently, an efficient method denoted by jhm juman and hoques method was proposed to obtain a better initial feasible solution to a transportation 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 proposed method yields an optimal solution of the given solid transportation problem directly. Kuhn 5, 6 for solving the optimal assignment problem a special type of transportation problem. The first problem they asked us about is the following transportation problem.
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. In \a new approach to solve transportation problem, a new technique using allocation table method atm was discussed to get initial basic feasible solution by mollah mesbahuddhin ahmed et. Solving transportation problem in operations research. Transportation models or problems are primarily concerned. Given here is the minimum transportation cost calculator using north west corner method to determine the transportation cost. Therefore solving transportation problem, finding minimal total cost, would be remarkable 48. Mathematical model and solving method based on software. Sharma et al 16 proposed an alternative method to north west corner method by using coeffcient of range cor. The vogels approximation method or vam is an iterative procedure calculated to find out the initial feasible solution of the transportation problem. The northwest corner rule is a method adopted to compute the initial feasible solution of the transportation problem.
Transportation problem the following must be known before using a method to find a lowcost solution. They solve an unbalanced transportation problem, after balancing it by creating dummy origin andor destination as required. Transportation problems transportation problems pearson. Use of linear programming to solve transportation problem in quantitative techniques for management use of linear programming to solve transportation problem in quantitative techniques for management courses with reference manuals and examples pdf. Problem here the transportation problem can be stated as a linear programming problem as.
Transportation problem, linear programming lp, objectoriented programming 1. The objective of such a transportation problem is to schedule shipments from sources to destinations so that total transportation costs are minimized. Vam and modi method in solving transportation problems. Consider the following network representation of a transportation problem. In this research, we have modified vogels approximation method mvam to find an initial basic feasible solution for the transportation problem whenever vam. Solving transportation problem in operations research free download as powerpoint presentation.
Solving a balanced minimization transportation problem. Hitchaxic developed the basic transportation problem in 1941. If unbalanced, add dummy source row or dummy destination column as required. 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. In \a new approach to solve transportation problem, a new technique using allocation table method atm was discussed to get initial basic feasible solution by mollah mesbahuddhin ahmed et al 14. In a transportation model, an initial feasible solution can be found by several alternative methods, including the northwest corner method, the minimum cell cost method, and vogels approximation model. Afterwards many researchers provide many methods and algorithms to solve transportation problems. The initial northwest corner solution is shown in table t4. Solving the arizona plumbing problem with modi let us try out these rules on the arizona plumbing problem. This example is the largest and the most involved you have read so far.
Formulate the given problem and set up in a matrix form. Thus our newly developed method with computer program saves time and energy and easy to apply. Module b transportation and assignment solution methods. The amount allocated is the most possible,subject tothe supply and demand constraints for that cell.
The classic statement of the transportation problem uses a matrix with the rows representing sources and columns representing destinations. Solving transportation problem with mixed constraints. Are 511 usually, we have a given capacity of goods at each source and a given requirement for the goods at each destination. Transportation problem set 6 modi method uv method. Note that the only change in the transportation table is the border labeling the r i. Some well known and long use algorithms to solve transportation problems are vogels approximation method vam, north west corner nwc method, and matrix minima method.
Kore and thakur 4 have proposed another method, which discards the need of balancing the given problem. Pdf transportation problem in operational research. The transportation problem is a special type of lpp where the objective is to minimize the cost of distributing a product from a number of sources or origins to a number of destinations. In this paper, an optimal solution of transportation programming problem has been considered.
Note on transportation problem with new method for resolution of. Similarly, mathematical model of the transportation problem that involves many variables can be solved easily using a spreadsheet as shown in fig. Maximization transportation problem can be converted into minimization transportation problem by subtracting each transportation cost from maximum transportation cost here, the maximum transportation cost is 25. Opportunitycost method, for obtaining an initial basic feasible solution for the transportation problem. The transportation problem as a major problem in linear programming problems is important. Vogels approximation method trannsportation model transportation model is a special type of networks.
Introduction the first main purpose is solving transportation problem using five methods of transportation model by linear programming lp. 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. Because of this, it can often provide considerable time savings over other methods for solving transportation problems. This algorithm is useful for solving both balanced and unbalanced transportation problems. Several methods will be used in this paper to obtain this initial feasible problem. It is used in both crisp environment as well as fuzzy environment.
The first main purpose is solving transportation problem using three 1methods of transportation model by linear programming lp. Introduction the minimum cost planning plays an important role for solving. Transportation problem transport mathematical concepts. From the transportation table 4, it is seen that total supply and total demand are equal. Minimum transportation cost calculator using north west. Because of its special structure the usual simplex method is not suitable for solving transportation problems. Modified vogels approximation method for solving transportation. In traditional method for solving fixed charge transportation problem, we introduce dummy column to make balance transportation problem from unbalance transportation problem.
For analyzing and formulation of some model, transportation problems are required. Optimal solution of transportation problem using linear. Hence the given transportation problem is a balanced one. Stepbystep guide on how to solve a balanced minimization transportation problem. Identify the row or column with the greatest penalty cost.
Three new methods to find initial basic feasible solution. The process of calculation is simplified using a spreadsheet. Introduction to transportation problem mba knowledge base. In this paper we are changing the transportation problem in linear programming problem and solving this. It deals with sources where a supply of some commodity is available and destinations where the commodity is demanded. Modi method the modi modified distribution method allows us to compute improvement indices quickly for each unused square without drawing all of the closed paths. A new method to solve transportation problem juniper publishers. Dualmatrix approach for solving the transportation problem. In order to solve transportation problems you need to consider. Check whether the problem is a balanced or unbalanced transportation problem. The name northwest corner is because the basic variables are selected from the extreme left corner. 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. Now it is found all the cell values are even number in the transportation table 4.
Transportation problem, dualmatrix approach, steppingstone method, simplex method, linear programming models. Like least cost method, here also the shipping cost is taken into consideration, but in a relative sense. Pdf a new approach to solve transportation problems. The modi and vam methods of solving transportation problems. Transportation problem set 6 modi method uv method there are two phases to solve the transportation problem. Both methods are complex in computing and can not guarantee to nd the global optimal solution in short time. A new method of solving the transportation problem. In 1958 we started popularsizing mathematical methods to the industrial departments in china. The transportation simplex method uses linear programming to solve transportation problems.
With the northwest corner method, an initial allocation is made to the cell in the upper left. 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. Solving transportation problem by various methods and their. Use the north west corner method to find an initial solution to the problem described in. The modi modified distribution method allows us to compute improvement indices quickly for each unused square without drawing all of the closed paths. Solving transportation problem by various methods and. Determine a penalty cost for each row column by subtracting the lowest unit cell cost in the row column from the next lowest unit cell cost in the same row column. The proposed method is based on a new combinatorial procedure recently developed by h. Generally a linear programming mathematical model has a large number of variables that need to be evaluated.
So according to the step3 of proposed algorithm, these cells values are to be continuously divided by 2 until obtain. Network representation and mathematical model of transportation problem. However it could be solved for optimally as an answer to complex business problem only in 1951, when george b. A new method using the principle of zero point method 10 is proposed for finding an optimal solution of solid transportation problems. A new procedure is described for the computation of a transport problem model which uses each column of the cost matrix in turn and hence is ideally suited to computers with tape storage. An efficient alternative approach to solve a transportation problem. Afterwards many researchers provide many methods to solve transportation problem. Use the northwest corner method to find an initial solution to the problem described in. Deshmukh department of engineering mathematics, sres college of engineering, kopargaon author for correspondence abstract in this paper an innovative method named nmd method is.
The economic problem is to distribute the available product to different retail shops in such a way so that the total transportation cost is minimum. Transportation problem is a particular class of linear programming, which is associated with daytoday activities in our real life and mainly deals with logistics. A new approach for solving solid transportation problems. Determine a suitable allocation to maximize the total net return. Optimization techniques for transportation problems of. The second main purpose is solving transportation problem by objectoriented programming. So you must read the steps and the explanation mindfully. To obtain initial basic feasible solution ibfs, the work shown here is donewith vogel s approximation method vam. Some of the important related works the current research has deal with are. Furthermore, the authors did not introduce the execute process by compile these algorithms software. The modi and vam methods of solving transportation. Vam and matrix minima method always provide ibfs of a transportation problem.
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. We check the optimality of the transportation problem by modi method. Dantzig applied the concept of linear programming in solving the transportation models. 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. The dualmatrix approach is used in the present algorithm.
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