## North-West Corner Method

The North-West cornet method starts at the northwest corner cell of the transportation problem table.

### Step 1

Allocate as much as possible to the selected cell, and adjust the associated amounts of supply and demand by subtracting the allocated amount. The maximum possible amount is allocated in in (1,1) cell, i.e., `$x_{11} = \min(a_1, b_1)$`

.

### Step 2

- If $b_1 > a_1$, move vertically downwards to the second row and make the second allocation of amount
`$x_{21} = \min(a_2,b_1-x_{11})$`

in the cell (2,1). - If $b_1 < a_1$, move horizontally right-side to the second column and make the second allocation of amount
`$x_{12} = \min(a_1-x_{11}, b_2)$`

in the cell (1,2). - If $b_1 = a_1$, then goto step 3.

### Step 3

Start from a new northwest corner of the transportation table and repeat step 1 and 2 until all the requirements are satisfied.

The solution obtained by North-West Corner method is a basic feasible solution. In the allocation we do not consider the unit cost of transportation, hence the solution may not be an optimal solution. But this solution will serve as an initial basic feasible solution, which can be improved further.