07 | Transportation Problem Part 2 d | VAM | MAKAUT PYQ | Finding Optimal Solution | Optimality Test

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This video lecture of Vogel Approximation Method mostly known as VAM for Finding Optimal Solution will help Engineering and Basic Science students to understand following topic of Mathematics:
1. What is Transportation Problem
2. What are the different terminologies such as supply, demand, cost, allocations, cells in a transportation problem.
3. Different Methods of solving Transportation Problem.
4. How to solve a Transportation Problem using VAM
5. How to solve a Degenerate Transportation Problem.
6. Checking the solution optimal or not
7. Find the Optimal Solution
8. Solve Previous year question solution.

Timestamps:
0:00 - Introduction (Recap)
2:44 - Q.1. 2009 Question (Finding IBFS)
17:25 - Optimality Test
25:31 - Finding Optimal Solution
40:05 - Confirming the Solution is Optimal

“Transportation” means the transfer of materials from different sources to different destinations, keeping in view the capacity of supply, the capacity of receiving and the cost of transfer. Let a firm produce goods at m supply centre 01, 02, ... ,0m. The demand for the good is spread out at n different demand centres D1,D2, ... ,Dn. The problem of the firm is to transport goods from supply centres to demand centres at minimum cost.

The steps involved in determining an initial basic feasible solution using VAM are as follows :
Step 1. Write the given transportation problem in tabular form (if not given).

Step 2. First Compute Compute sum of availabilities and demands. If they are equal then it is a balanced transportation problem. Otherwise, add a row or column with "0" as cost in the given matrix along with the required availability and demand.

Step 3: The difference between the lowest cost and the next lowest cost corresponding to each row and each column which is known as penalty cost. Exhibit then against the respective row and column in parenthesis in the transportation table by the side of availability and below the demand respectively.

Step 4. Choose the greatest of all these row and column difference. Suppose it correspond to the i-th row. Choose the cell with minimum cost in the i-th row. If the maximum difference corresponds to a column then choose the cell with minimum cost in that column.

Step 5. Allocate min(ai, bj) in this cell. If the min.(ai, bj) = ai, then the availability of the ith origin Oi is exhausted and cover the ith row by doted lines. Demand at the j-th destination D, remains as bj - ai and the other cells of the ith row will be then unallocated. If min(ai, bj) = bj then the demand of the destination D, is fulfilled and the availability at the ith origin O, remains To be ai - bj and further no allocation will be made in the remaining cells of the j-th column and cover the j-th column by dotted lines.

Step 6. Repeat steps 3, 4, 5 with the remaining tables until al rim requirements are fulfilled.

Step 7: If m+n-1 is not equal to no. of allocations then it is a degenerate problem. Now, we convert the degenerate problem to a non-degenerate one. We draw a loop in such a way that at the corner points of the loop there should be no allocated cells.

Step 8: Check the solution optimal or not.

Step 9: If the solution is not optimal then convert it into an optimal solution by drawing loop starting from the most negative allocation in the non allocated cell. Add and subtract theta alternatively at the corner points of the loop. Then select theta as the minimum of the allocations of the allocated cell.

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Link of Playlist of Transportation Problem: https://www.youtube.com/playlist?list=PLn3Wz38keZOdxEzfXrkXJLj4GQ-Gc3Qgf

Link of Playlist of Operation Research: https://www.youtube.com/playlist?list=PLn3Wz38keZOfn1Det0MnCPapuMGbiqFfN

Link of Playlist of L.P.P.: https://www.youtube.com/playlist?list=PLn3Wz38keZOee7-gbXC25oWIUDYsEv3ye

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Видео 07 | Transportation Problem Part 2 d | VAM | MAKAUT PYQ | Finding Optimal Solution | Optimality Test канала Tending to Infinity