The Northwest Corner Rule
The Northwest Corner Rule requires that we start with the upper left hand cell (or northwest corner) of the Transportation Matrix and allocate units to shipping routes as follows.
To make our initial shipping assignment, we need five steps.
The Northwest Corner Rule requires that we start with the upper left hand cell (or northwest corner) of the Transportation Matrix and allocate units to shipping routes as follows.
 Exhaust the Supply (factory capacity) of each row before moving down to the next row.
 Exhaust the Demand (warehouse requirement) of each column before moving on to the next column on the right.
 Check to ensure all Supplies and Demands are met.
The following table uses the northwest corner rule to find an initial feasible solution to the Bengal Plumbing Problem.
Transportation
Matrix for Bengal Plumbing


From \ To

Warehouse
E

Warehouse
F

Warehouse
G

Factory
Capacity


Plant A

100

Rs.50

Rs.40

Rs.30

100


Plant B

200

Rs.80

100

Rs.40

Rs.30

300


Plant C

Rs.90

100

Rs.70

200

Rs.50

300


Warehouse Requirement

300

200

200

700

To make our initial shipping assignment, we need five steps.
 Assign 100 units from Plant (A) to Warehouse (E), (exhausting Plant (A)'s supply).
 Assign 200 units from Plant (B) to Warehouse (E), (exhausting Warehouse (E)'s demand).
 Assign 100 units from Plant (B) to Warehouse (F), (exhausting Plant (B)'s supply).
 Assign 100 units from Plant (C) to Warehouse (F), (exhausting Warehouse (F)'s demand).
 Assign 200 units from Plant (C) to Warehouse (G), (exhausting Plant (C)'s supply and Warehouse (G)'s demand.
Initial Feasible Transportation Route Selection


From

To

Units Shipped

Cost per unit

Total Cost

Plant A

Warehouse E

100

Rs.50

Rs.5000

Plant B

Warehouse E

200

Rs.80

Rs.16000

Plant B

Warehouse F

100

Rs.40

Rs.4000

Plant C

Warehouse F

100

Rs.70

Rs.7000

Plant C

Warehouse G

200

Rs.50

Rs.10000

Total Shipping Cost

Rs.42000

The Total Shipping Cost for Bengal Plumbing comes out to be Rs. 42000.00
The Solution given is feasible because it satisfies all demand and supply constraints.