We would demonstrate all the three methods. Allocate the minimum of remaining balance of supply in last column and demand in last row. Let us select S1D5 route.

Vogel Approximation Method The Vogel approximation method Unit cost penalty method is an iterative procedure for computing a basic feasible solution of a transportation problem. This method is preferred over the two methods discussed in the previous sections, because the initial basic feasible solution obtained by this method is either optimal or very close to the optimal solution.

This method is a little complex than the previously discussed methods. So go slowly and reread the explanation atleast twice. Identify the boxes having minimum and next to minimum transportation cost in each row and write the difference penalty along the side of the table against the corresponding row.

Identify the boxes having minimum and next to minimum transportation cost in each column and write the difference penalty against the corresponding column Identify the maximum penalty. If it is along the side of the table, make maximum allotment to the box having minimum cost of transportation in that row.

If it is below the table, make maximum allotment to the box having minimum cost of transportation in that column.

If the penalties corresponding to two or more rows or columns are equal, you are at liberty to break the tie arbitrarily. Repeat the above steps until all restrictions are satisfied.However, among the five methods listed above, the North West Corner Method (NWCM), the Lowest Cost Method (LCM), and the Vogel’s Approximation method are the most commonly used methods used in finding the initial basic feasible solutions of the CTP.

The North-West Corner Rule is a method adopted to compute the initial feasible solution of the transportation problem. The name North-west corner is given to this method because the basic variables are selected from the extreme left corner.

include: Northwest corner method, least cost method, Vogel method and modi method. This will mainly aim at finding the best and cheapest route on how .

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We found that the International Journal of Computer Science and Network Security, object oriented program of VAM given by Nabendu Sen et al.

10(4), , ) to code the well-known VAM (Vogel’s approximation method) using C++.

Initial basic feasible solution by VAM (Vogel's Approximation Method) of Transportation Problem Gourav Manjrekar 2 years ago. , Optimality test by stepping stone method and MODI method (Math) Northwest Corner, Min Cost and Vogel's Shokoufeh Mirzaei 4 .

When the solution of a transportation problem by Vogel's approximation method is done, we know that (a) we have the optimal solution.

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(b) we have the same initial solution as we would have obtained using the northwest corner rule.

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