j / / / / Fifth Allocation: H K a i T ( ) ( ) / / ( ) / M ( ) ( ) / / b j / / / / / XII Std - Business Maths & Stat EM Chapter - - Operations Research Sixth Allocation: H K a i T ( ) ( ) / / ( ) ( ) / / M ( ) ( ) / / b j / / / / / / Transportation schedule : T à H , T à P , B à C , B à H , M à H , M à K The total Transportation cost = ( × ) + ( × )+ ( × ) + ( × )+ ( × ) + ( × ) = + + + + + = ` Method: Vogel’s Approximation Method (VAM) Vogel’s approximation method yields an initial basic feasible solution which is very close to the optimum solution.Various steps involved in this method are summarized as under Step : Calculate the penalties for each row and each column. Here penalty means the difference between the least and the next higher cost in a row and in a column. Step : Select the row or column with the largest penalty. Step : In the selected row or column, allocate the maximum feasible quantity to the cell with the minimum cost.
Step : Eliminate the row or column where all the allocations are made. Step : Write the reduced transportation table and repeat the steps to . Step : Repeat the procedure until all the allocations are made. Optimum solution for any transportation problem can be obtained by using MODI method.
Example . Find the initial basic feasible solution for the following transportation problem by VAM Distribution Centers Availability D D D D origin S S S Require- ment Here i j (i.e) Total Availability =Total Requirement ∴ The given problem is balanced transportation problem. Hence there exists a feasible solution to the given problem. First let us find the difference (penalty) between the first two smallest costs in each row and