Thursday, July 4, 2013

The Northwest Corner Rule

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.
  1. Exhaust the Supply (factory capacity) of each row before moving down to the next row.
  2. Exhaust the Demand (warehouse requirement) of each column before moving on to the next column on the right.
  3. 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.
  1. Assign 100 units from Plant (A) to Warehouse (E), (exhausting Plant (A)'s supply).
  2. Assign 200 units from Plant (B) to Warehouse (E), (exhausting Warehouse (E)'s demand).
  3. Assign 100 units from Plant (B) to Warehouse (F), (exhausting Plant (B)'s supply).
  4. Assign 100 units from Plant (C) to Warehouse (F), (exhausting Warehouse (F)'s demand).
  5. Assign 200 units from Plant (C) to Warehouse (G), (exhausting Plant (C)'s supply and Warehouse (G)'s demand.
The following table shows the computed shipping cost according to the Northwest Corner Rule.

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.