In this video, we'll talk about how to solve a special case of the transportation problem.
It is called the transshipment problem.
In a typical transportation problem, the products are directly shipped from the supply points
to the demand points.
In real-world situations, there may be some transshipment points through which products
can be delivered from a supply point to a demand point.
We can convert the transshipment problem to a transportation problem and then use the
transportation simplex method to find the optimal solution.
To convert the transshipment problem to a transportation problem, we need to follow
three steps.
Step 1, construct the original transportation problem by ignoring the transshipment points.
Step 2, balance the original transportation problem.
Step 3, for each transshipment point, add a row and a column in the transportation tableau,
and set the supply and demand both equal to the total original supply.
This is an example.
A company owns two factories, Factory 1 and Factory 2.
Factory 1 can produce up to 150 products per day, and Factory 2 can produce up to 200 products
per day.
Products are shipped to Customer 1 and Customer 2.
Each customer requires at least 130 products per day.
It may be cheaper to first ship to Transfer Center1 or Transfer Center 2 and then to the
final customers.
The objective is to satisfy the demand and minimize the total shipping cost.
In this table, we summarize the unit shipping cost, which is in $/product.
From Factory 1 directly to Customer 1, the cost is 25.
From Factory 1 to Transfer 1, the cost is 8.
From Transfer 1 to Customer 1, it is 16.
So, the total cost is 24, which is cheaper than directly shipping from Factory 1 to Customer
1.
From Factory 1 to Transfer 2, the cost is 13.
From Transfer 2 to Customer 1, it is 14.
So, the total cost is 27, which is more expensive than directly shipping from Factory 1 to Customer
1.
Therefore, we need to determine how many products should be shipped from each factory to each
customer, and how we should use the transfer centers.
To convert this transshipment problem to a transportation problem, we need to formulate
this original transportation problem by ignoring the transshipment points, and only considering
these two supply points and these two demand points.
This is the original transportation tableau.
It is not a balanced problem, because the total supply, which is 350, is greater than
the total demand, which is 260.
We need to introduce a dummy demand to balance the problem.
The demand will be the difference between the original total supply and the original
total demand.
It will be 90.
The unit shipping cost will be 0.
Now, for the first transfer center, we add a row and a column in the transportation tableau,
and set the supply and demand both equal to the total original supply, which is 350.
For the second transfer center, we do the same.
Add a row and a column in the transportation tableau, and set the supply and demand both
equal to the total original supply, 350.
This is the final tableau.
We have converted a transshipment problem to a balanced transportation problem.
We can solve this problem using the transportation simplex method.
This is the optimal solution.
The solution can be interpreted in this way.
From Factory 1 to Transfer 1, we will send 130 products.
This 20 means, we still have an extra capacity of making 20 products per day in this factory.
We'll send 130 products from Transfer 1 to Customer 1.
This 220 means, we still have a capacity of transferring 220 more products per day in
this transfer center.
From Factory 2 to Customer 2, we will directly send 130 products.
This 70 means, we still have an extra capacity of making 70 products per day in this factory.
This 350 means, we still have a capacity of transferring 350 more products per day in
this transfer center.
This transfer center is unused.
Okay, this is how we convert a transshipment problem to a transportation problem and solve
it using the transportation simplex method.
Thank you for watching.