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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.

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The Intuitive Lowest Cost Method

The Intuitive Lowest Cost Method Or The Minimum Cell Cost Method

The Intuitive Lowest Cost Method is a cost based approach to finding an initial solution to a transportation problem.
It makes allocations starting with the lowest shipping costs and moving in ascending order to satisfy the demands and supplies of all sources and destinations.

This straightforward approach uses the following steps.
Identify the cell with the lowest cost.Allocate as many units as possible to that cell without exceeding the supply or demand.Then cross out the row or column or both that is exhausted by the above assignment.Move on to the next lowest cost cell and allocate the remaining units.Repeat the above steps as long as all the demands and supplies are not satisfied. 
When we use the Intuitive Approach to the Bengal Plumbing problem, we obtain the solution as below.

Transportation Matrix for Bengal Plumbing From \ To Warehouse E Warehouse F Warehouse G Factory Capacity Plant A Rs.50
Rs.40 100 Rs.30 100 Plant…

Vogel's Approximation Method (VAM)

The Vogel's Approximation Method

In addition to the North West Corner and Intuitive Lowest Cost Methods for setting an initial solution to transportation problems, we can use another important technique - Vogel's Approximation Method (VAM).
Though VAM is not quite as simple as Northwest Corner approach, but it facilitates a very good initial solution, one that is often the optimal solution.
Vogel's Approximation Method tackles the problem of finding a good initial solution by taking into account the costs associated with each alternative route, which is something that Northwest Corner Rule did not do.

To apply VAM, we must first compute for each row and column the penalty faced if the second best route is selected instead of the least cost route.

To illustrate the same, we will look at the Bengal Plumbing transportation problem.

Transportation Matrix for Bengal Plumbing From \ To Warehouse E Warehouse F Warehouse G Factory Capacity Plant A
Rs.50
Rs.40
Rs.30 100 Plant B
Rs.80
Rs.

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