North West Corner Rule

The north-west rule as we get the name it starts from the top left corner and collects the amount by the supply and demand to this variable i.e. X₁₁. Then the one satisfied is crossed because the remaining variables in the column or row are considered as zero. In thecase of simultaneous satisfaction of other rows and columns then they are being crossed out. Now after the adjustments the rows and columns that are left uncrossed are again crossed, and this process is continued until only one pair of uncrossed row and column is left.

Look at the steps below:

Step I: starting with the north-west corner that is the top left corner and cross with the supply source (S₁) along with the demand of the destination centre 1 (D₁). In such cases there are only three possible conditions:

• D₁ ≤ S₁ this means that the demandat the target centre is less than the supply at source. Hence, X₁₁is equal to D₁a move
• D₁ = S₁ this implies that the demand and supply are equal that means X₁₁ equals to D₁ and moves diagonally.
• D₁> S₁ here the demand is more than the As a result, the movement is vertical since X₁₁ = S₁.

Step II: the steps are to be executed in such a manner that the value of the S-E or the right bottom corner gets a value. Let’s take an example.

1. Set X₁₁ = 1000 implies that the smaller amount is present at S₁ (1000), but D₁ (2300) needs it.
2. Following the rule (c) of step I, we must proceed to cell BX vertically. As 0₁> S₁ implies that the amount available for S₂ (1500) with the quantity required. Number available at 0₁ (2300-1000=1300) and set X₁₁=1300.
3. Again if proceeded by cell BY as because 0 < S. here supply is 1500 and demand are 1400. So set X₁₂ = 1400. Hence here we must proceed horizontally to next cell, but as there are no horizontal cells present, so the allocation ends here.

The transportation cost associate with the solution is

Z = 2000 × 1000 + 2500 × 1300 + 2700 × 1400.

   = 20, 00,000 + 32, 50,000 + 37, 80,000

   = 90, 36, 000.