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North-West Corner Rule

Definition: 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.

The concept of North-West Corner can be well understood through a transportation problem given below:

North-West Corner-1a

In the table, three sources A, B and C with the production capacity of 50 units, 40 units, 60 units of product respectively is given. Every day the demand of three retailers D, E, F is to be furnished with at least 20 units, 95 units and 35 units of product respectively. The transportation costs are also given in the matrix.

The prerequisite condition for solving the transportation problem is that demand should be equal to the supply. In case the demand is more than supply, then dummy origin is added to the table. The supply of dummy origin will be equal to the difference between the total supply and total demand. The cost associated with the dummy origin will be zero.

Similarly, in case the supply is more than the demand, then dummy source is created whose demand will be equivalent to the difference between supply and demand. Again the cost associated with the dummy source will be zero.

Once the demand and supply are equal, the following procedure is followed:

North-West Corner-1b

  1. Select the north-west or extreme left corner of the matrix, assign as many units as possible to cell AD, within the supply and demand constraints. Such as 20 units are assigned to the first cell, that satisfies the demand of destination D while the supply is in surplus.
  2. Now move horizontally and assign 30 units to the cell AE. Since 30 units are available with the source A, the supply gets fully saturated.
  3. Now move vertically in the matrix and assign 40 units to Cell BE. The supply of source B also gets fully saturated.
  4. Again move vertically, and assign 25 units to cell CE, the demand of destination E is fulfilled.
  5. Move horizontally in the matrix and assign 35 units to cell CF, both the demand and supply of origin and destination gets saturated. Now the total cost can be computed.

The Total cost can be computed by multiplying the units assigned to each cell with the concerned transportation cost. Therefore,

Total Cost = 20*5+ 30*8+ 40*6+ 25*9+ 35*6 = Rs 1015

Related terms:

  1. Least Cost Method
  2. Transportation Method of Linear programming
  3. Stepping Stone Method
  4. Vogel’s Approximation Method
  5. Modified Distribution Method

Reader Interactions

Comments

  1. ABDUSSAMAD IBRAHIM AHMAD says

    November 19, 2017 at 10:05 pm

    thanks very useful ):(

    Reply
  2. Karan says

    August 26, 2018 at 5:55 am

    Superb 😍😍😍

    Reply
  3. Ibrahim says

    November 20, 2018 at 10:00 pm

    Thanks it was usefull

    Reply
  4. Maneesh Kareer says

    March 29, 2019 at 5:43 pm

    I’m doing MBA via distance, was try to understand from book provided but couldn’t able to. It’s exam time now, going to enter in exam hall in 30 mins. I just googled it and came to link. 3 mins of reading and done. Thanks.

    Reply
  5. Abiodun Olasunkanmi says

    May 25, 2019 at 3:02 am

    Very meaningful and helpful…God bless you

    Reply
    • SAMUEL SULE says

      May 5, 2021 at 3:42 pm

      Very Educative.

      Reply
  6. Rabiu hamisu kankarofi says

    June 23, 2019 at 11:59 pm

    Thanks today you solve at least 60% of my problem in this topic

    Reply
  7. Joseph Distor says

    September 27, 2019 at 6:18 am

    Thank you

    Reply
  8. scol says

    November 8, 2019 at 7:20 am

    Thank you.

    Reply
  9. Jerry says

    February 20, 2020 at 3:25 pm

    Well explained thank you so much

    Reply
  10. HR says

    September 8, 2020 at 4:36 pm

    THANK YOU SO MUCH FOR THE EXPLANATION

    Reply
  11. Anjel says

    November 25, 2020 at 2:10 pm

    What if the supply is greater than demand?

    Reply
  12. Kas says

    December 7, 2020 at 12:02 pm

    Thanks. Very useful.

    Reply
  13. Temitope says

    May 10, 2021 at 3:15 pm

    Thank you so much. Pretty simple

    Reply
  14. Isa Musa says

    May 21, 2021 at 10:24 pm

    Thanks very much.
    The is well explained and I have understand within no time

    Reply

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