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North West Corner Rule

In this method, we start with the North-West Corner (top left) and allocate the maximum amount allowable by the supply and demand to this variable i.e., X11. The satisfied column/row is then crossed, meaning that remaining variables in this column/row equal zero. If a column and a row are satisfied simultaneously, only one of them is crossed out. After adjustment of the quantities of supply and that of demand for all left over (uncrossed-out) rows and columns, the minimum possible column row is allotted to the first uncrossed out element in the new column/row. The process gets completed when exactly one row or one column is left uncrossed out.

The procedure can be explained specifically in the following steps :-

Step I. Start the North West (top left) corner and compare the supply of source 1 (S1) with the demand of destination center 1 (D1). Three conditions are possible.

D1 ≤ S1 it means that the demand at destination center D1 is less than the supply at source S1. In X11 (North West/top left corner) set X11 equal to D1 and proceed horizontally.

(a)             D1 = S1 i.e., the demand is equal to supply, then set X11 equal to D1 and proceed diagonally.

(b)             D1 > S1 i.e., the demand is more than supply, then set X11 = S1 and proceed vertically.

Step II. Proceed in this manner, step by step till a value in allotted to S-E/right bottom corner. The north-west corner rule can be best demonstrated by the example in hand.

  1. Set X11 = 1000 i.e., the smaller of the amount available at S1 (1000) and that needed at D1 (2300).
  2. Proceed to cell (BX) as per rule© above which demands that you should proceed vertically. 01> S1 compare the quantity available at S2 (1500) with the amount required. Quantity available at 01(2300-1000 = 1300) and set X11 = 1300.
  3. Proceed to cell BY (rule above) as now 0 < S. Here S1 is 1500 and the demand is 1400. So set X12 = 1400. We are required to proceed horizontally to next cell. Since there is no other horizontal cell, the allocation ends here.

The transportation cost associated with the solution is

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

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

= 90,36,000.