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Transportation problems are an application of linear programming that is concerned with determining the optimal strategy for distributing a commodity from a group of supply centers, called sources, to various receiving centers, called destinations.
Illustration
Illustration
Each source is able to supply a fixed number of a units of the product called the capacity, and each destination has a fixed demand called the requirement.
Example:
A company transports a commodity from three sources. A, B, C, to three destinations X, Y, Z.
Sources A, B, C are able to supply 150, 250, 300 items per day, respectively.
Destinations X, Y, Z require 200, 300, 200 units of products per day respectively.
Illustration
Illustration
When transporting products, there is always a cost. The red text in each cell represent the cost of transporting an item from each source to each destination.
Now that we have all the necessary information let's solve the problem!
Step 1. Check if the problem is balanced.
Total Supply = Total Demand
Total Supply = 150 + 250 + 300 = 700
Total Demand = 200 + 300 + 200 = 700
700 is equal to 700 therefore this problem is balanced.
Step 2. Do the northwest corner rule. The northwest corner rule is a method for computing a basic feasible solution of a transportation problem, where the basic variables are selected from the North – West corner
Read about the Northwest Corner Rule:
Start by selecting the cell in the northwest corner of the transportation table
Assign the maximum amount to this cell that is allowable based on the supply and demand constraints.
Exhaust the supply from each row before moving down to another row.
Exhaust the demand from each column before moving to another column.
Check to make sure that the supply and demand are met.
Step 3. Compute the minimum total cost of this shipping assignment by multiplying the number of units to the cost assigned to the cell.
The minimum total cost for this transportation problem is P3,650.
Although the Northwest Corner Rule is already a feasible solution, we can further minimize the total cost by optimizing our table using the Stepping-Stone Method. Watch the video to learn about the stepping stone method!
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