Modi
Transportation Problems
Transportation is considered as a “special case” of LP
Reasons? it can be formulated using LP technique so is its solution
Here, we attempt to firstly define what are them and then studying their solution methods:
Transportation Problem
We have seen a sample of transportation problem on slide 29 in lecture 2
Here, we study its alternative solution method
Consider the following transportation tableau
Review of Transportation Problem
A Transportation Example (2 of 3) Model Summary and Computer Solution with Excel
Transportation Tableau
We know how to formulate it using LP technique
Refer to lecture 2 note
Here, we study its solution by firstly attempting to determine its initial tableau
Just like the first simplex tableau!
Solution to a transportation problem
Initial tableau
Optimal solution
Important Notes
Tutorials initial tableau
Three different ways:
Northwest corner method
The Minimum cell cost method
Vogel’s approximation method (VAM)
Now, are these initial tableaus given us an Optimal solution?
Northwest corner method
Steps:
assign largest possible allocation to the cell in the upper left-hand corner of the tableau
Repeat step 1 until all allocations have been assigned
Stop. Initial tableau is obtained
Example
Northeast corner
Initial tableau of NW corner method
Repeat the above steps, we have the following tableau.
Stop. Since all allocated have been assigned
The Minimum cell cost method
Here, we use the following steps:
Steps:
Step 1 Find the cell that has the least cost
Step 2: Assign as much as allocation to this cell
Step 3: Block those cells that cannot be allocated
Step 4: Repeat above steps until all allocation have been assigned.
Example:
Step 1 Find the cell that has the least cost Step 2: Assign as much as allocation to this cell
Step 3: Block those cells that cannot be allocated Step 4: Repeat above steps until all allocation have been
Transportation is considered as a “special case” of LP
Reasons? it can be formulated using LP technique so is its solution
Here, we attempt to firstly define what are them and then studying their solution methods:
Transportation Problem
We have seen a sample of transportation problem on slide 29 in lecture 2
Here, we study its alternative solution method
Consider the following transportation tableau
Review of Transportation Problem
A Transportation Example (2 of 3) Model Summary and Computer Solution with Excel
Transportation Tableau
We know how to formulate it using LP technique
Refer to lecture 2 note
Here, we study its solution by firstly attempting to determine its initial tableau
Just like the first simplex tableau!
Solution to a transportation problem
Initial tableau
Optimal solution
Important Notes
Tutorials initial tableau
Three different ways:
Northwest corner method
The Minimum cell cost method
Vogel’s approximation method (VAM)
Now, are these initial tableaus given us an Optimal solution?
Northwest corner method
Steps:
assign largest possible allocation to the cell in the upper left-hand corner of the tableau
Repeat step 1 until all allocations have been assigned
Stop. Initial tableau is obtained
Example
Northeast corner
Initial tableau of NW corner method
Repeat the above steps, we have the following tableau.
Stop. Since all allocated have been assigned
The Minimum cell cost method
Here, we use the following steps:
Steps:
Step 1 Find the cell that has the least cost
Step 2: Assign as much as allocation to this cell
Step 3: Block those cells that cannot be allocated
Step 4: Repeat above steps until all allocation have been assigned.
Example:
Step 1 Find the cell that has the least cost Step 2: Assign as much as allocation to this cell
Step 3: Block those cells that cannot be allocated Step 4: Repeat above steps until all allocation have been