Friday, July 5, 2013

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.
  1. Identify the cell with the lowest cost.
  2. Allocate as many units as possible to that cell without exceeding the supply or demand.
  3. Then cross out the row or column or both that is exhausted by the above assignment.
  4. Move on to the next lowest cost cell and allocate the remaining units.
  5. 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 B
Rs.80
200
Rs.40
 100
Rs.30
300
Plant C
300
Rs.90
Rs.70
Rs.50
300
Warehouse Requirement
300
200
200
700









We will take following steps to arrive at an initial solution.
  1. Assign 100 units from Plant (A) to Warehouse (G), as it has the lowest shipping cost of Rs.30, exhausting Plant (A)'s supply.
  2. Assign the remaining 100 units to Warehouse (G) from Plant (B), as now it has the lowest shipping cost of Rs.30, exhausting Warehouse (G)'s demand.
  3. Move on the next lowest cost cell, Assign 200 units from Plant (B) to Warehouse (F), exhausting Plant (B)'s supply and Warehouse (F)'s demand.
  4. Finally enter 300 units in the only remaining cell to complete the allocations and satisfying the supply and demand of Plant (C) and Warehouse (E).
The total computed shipping cost according to the Minimum Cell Cost Method.

Transportation Route Selection based on Minimum Cell Cost Method
From
To
Units Shipped
Cost per unit
Total Cost
Plant A
Warehouse G
100
Rs.30
Rs.3000
Plant B
Warehouse G
100
Rs.30
Rs.3000
Plant B
Warehouse F
200
Rs.40
Rs.8000
Plant C
Warehouse E
300
Rs.90
Rs.27000
Total Shipping Cost
Rs.41000

The total cost of this initial solution is Rs.41000.00 as compared with a total cost of Rs.42000.00 by the Northwest Corner Rule.
It is not a coincidence that a lower total cost is derived, using the Minimum Cell Cost Method, it is a logical occurrence.
The Northwest Corner Rule does not consider costs at all while making allocations, while Minimum Cell Cost method does.
This initial solution is closer to the optimal solution and requires fewer subsequent iterations.

Both the Northwest Corner and the Intuitive Lowest Cost approaches are meant only to provide us with a starting point, we often have to employ an additional procedure to reach an optimal solution.