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Vogel’s Approximation Method

Definition: The Vogel’s Approximation Method or VAM is an iterative procedure calculated to find out the initial feasible solution of the transportation problem. Like Least cost Method, here also the shipping cost is taken into consideration, but in a relative sense.

The following is the flow chart showing the steps involved in solving the transportation problem using the Vogel’s Approximation Method:

VAM-1
The concept of Vogel’s Approximation Method can be well understood through an illustration given below:

  1. First of all the difference between two least cost cells are calculated for each row and column, which can be seen in the iteration given for each row and column. Then the largest difference is selected, which is 4 in this case. So, allocate 20 units to cell BD, since the minimum cost is to be chosen for the allocation. Now, only 20 units are left with the source B.VAM-2
  2. Column D is deleted, again the difference between the least cost cells is calculated for each row and column, as seen in the iteration below. The largest difference value comes to be 3, so allocate 35 units to cell AF and 15 units to the cell AE. With this, the Supply and demand of source A and origin F gets saturated, so delete both the row A and Column F.Vogel's-1
  3. Now, single column E is left, since no difference can be found out, so allocate 60 units to the cell CE and 20 units to cell BE, as only 20 units are left with source B. Hence the demand and supply are completely met.Vogel's-final

Now the total cost can be computed, by multiplying the units assigned to each cell with the cost concerned. Therefore,

Total Cost = 20*3 + 35*1 + 15*4 + 60*4 + 20*8 = Rs 555

Note: Vogel’s Approximation Method is also called as Penalty Method because the difference costs chosen are nothing but the penalties of not choosing the least cost routes.

Related terms:

  1. Least Cost Method
  2. Stepping Stone Method
  3. North-West Corner Rule
  4. Modified Distribution Method
  5. Transportation Method of Linear programming

Reader Interactions

Comments

  1. Raja Pane says

    November 1, 2016 at 8:07 am

    Why Vogel Approximation must to take 2 smallest cost in penalty?

    Reply
    • Ravi says

      June 25, 2020 at 10:20 am

      it doesnt take 2 small penalties. First you need to select the maximum penalty and then choose the smallest unit. thats all

      Reply
    • Chinnu says

      December 5, 2020 at 11:54 am

      Thank u so much. it is very clearly explained

      Reply
  2. jessy preena says

    April 24, 2017 at 1:38 am

    Easy to understand

    Reply
  3. Veer says

    May 17, 2017 at 11:51 pm

    Very beautifully described

    Reply
  4. Tenywa Jacob says

    December 6, 2017 at 7:54 pm

    The procedure was fantastic and easy to understand

    Reply
  5. kirubha says

    February 25, 2019 at 11:37 am

    easy to understand thank you so much

    Reply
  6. Kushal Niroula says

    July 24, 2019 at 5:47 pm

    Brilliant explanation

    Reply

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