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Page 1
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
Page 2
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
Page 3
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.
Page 4
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.
Page 5
• 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.
Page 6
• 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.
Page 7
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)
Page 8
• 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.
Page 9
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
Page 10
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
Page 11
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)
Page 12
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
Page 13
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.