North-West Corner Method

North-West Corner Method (NWC)

The North-West Corner Method is the simplest way to obtain an IBFS. It ignores cost altogether and allocates purely by position, always starting at the top-left (north-west) cell of the table.

Rule: Starting at the north-west corner, allocate the maximum possible (the smaller of the remaining row supply and remaining column demand) to that cell. If the row's supply is used up, move down to the next row in the same column; if the column's demand is used up, move right to the next column in the same row. Repeat until every supply and every demand is exhausted.

Worked example — cost matrix

A firm has three factories $O_1,O_2,O_3$ supplying three warehouses $D_1,D_2,D_3$. Per-unit transportation costs (in ₹) and the supply/demand are:

Total supply $=30+50+20=100$; total demand $=25+35+40=100$ — the problem is already balanced.

Step-by-step allocation:

1. Cell $(O_1,D_1)$: allocate $\min(30,25)=25$. $D_1$'s demand is met; $O_1$ has 5 units left.
2. Move right to $(O_1,D_2)$: allocate $\min(5,35)=5$. $O_1$'s supply is exhausted; $D_2$ has 30 units left.
3. Move down to $(O_2,D_2)$: allocate $\min(50,30)=30$. $D_2$'s demand is met; $O_2$ has 20 units left.
4. Move right to $(O_2,D_3)$: allocate $\min(20,40)=20$. $O_2$'s supply is exhausted; $D_3$ has 20 units left.
5. Move down to $(O_3,D_3)$: allocate $\min(20,20)=20$. Both are exhausted together — the allocation is complete.

Allocation table (NWC)