The Transportation Method of Linear
Programming
Clarke Holdaway
11/3/11
Presentation Overview
• The Transportation Method of Linear Programming
defined
• Why it can be useful
• How it works
• Real life example
• Exercise
• Summary
• Brainstorming Exercise
• Recommended readings list
The Transportation Method of Linear
Programming
• Definition: A special linear programming
method used to solve problems involving
transporting products from several sources to
several destinations
How is the Transportation Method of
LP Useful?
•
•
•
•
•
Adaptable
Flexible
Very fast
Easy
Lean
How it Works
• A linear function subject to constraints is used to
minimize an objective, in this case cost
• The constraints that must be met are:
– supply must meet demand
– supply cannot exceed capacity
• Microsoft Excel’s Solver
How it Works: An Example
• You are the logistics manager for a company that
manufactures widgets.
• Plants in Torrance, Fresno, and Mexicali can supply 180,
300, and 240 pallets of widgets.
• Stores in Riverside, San Diego, Oakland, and Phoenix
demand 280, 80, 200, and 140 pallets of widgets each.
Step 1: Table Set-up
• Using Microsoft Excel, set up a from/to shipping table.
• Now, on the right of your from/to table add columns for
supply capacity, pallets supplied, and excess supply.
• Input the widget supply capacity for each plant.
• Input a simple formula in the pallets supplied cell that
sums the from/to cells for each plant location.
• Next, in the excess supply box for each plant you want to
input a simple formula subtracting the pallets supplied
from the supply capacity.
• Next, we want to add demand, shipped, and cost rows on
the bottom of the table.
• Input the demand that corresponds to each store location in
the demand row.
• In each shipped cell, enter a formula that adds up the three
cells for the corresponding store location.
Step 2: The Cost Formula
• This is one of the trickiest parts. You are going to create a
large formula in the cost cell. You will need the cost table.
• In the formula, you will multiply the cost per pallet
shipped of every from/to intersection by the corresponding
from/to intersection in the shipping table.
• You will do this for every intersection and add all of the
products together.
• It should look something like this at first. See how the cost
table from/to intersection(C29) is multiplied by the
shipping table from/to intersection(C20).
• That product is then added to the next intersection product
(C29*C20 + C30* C21)
• You continue this formula until you have covered every
cost and shipping intersection product.
• It should look like this:
Step 3: Solver
• Now that the shipping table and cost formula are all set up,
we will use Microsoft Solver to optimize our shipping and
minimize the cost.
1. Set your objective as the cost cell.
2. Set to Min
3. By changing variable cells: all of the from/to shipping cells
4. Now we need to indicate two constraints.
a. customer demand must equal shipped
b. pallets supplied must be <= supply capacity
5. We need to make sure two options are set
a. check: make unconstrained variables non-negative
b. solving method: Simplex LP
6. Click solve!
• Solver has optimized our shipping and the minimum cost
is $63,100.
A Real World Example: Supply and Distribution Options
in the Oil Industry
(Balasubramanian)
Exercise
• Harlow, Guildford, Cheltenham, and Norwich can supply
1,587, 570, 908, and 1,247 pallets of widgets each.
• Cardiff, Telford, Rotherham, and Harrogate demand 1,285,
875, 1,452, and 642 pallets of widgets each.
• When optimized, what is the minimum cost?
Summary
• The transportation method of linear programming
is very useful
• Flexible
• Fast
• Adaptive
• Lean
Brainstorming Exercise
• Now that you are familiar with this tool, take 5
minutes to individually brainstorm how you can
use this method.
• Next, take 10 minutes to share your ideas and
continue brainstorming with your group.
• Each group will then present its best ideas.
Readings List
• Jacobs, F. R., & Chase, R. B. Operations and Supply
Management: The Core.
• Washington, S. P., Karlaftis, M. G., & Mannering, F. L.
Statistical and Econometric Methods for Transportation
Data Analysis, Second Edition.
• Belenky, A. Operations Research in Transportation
Systems: Ideas and Schemes of Optimization Methods for
Strategic Planning and Operations Management.