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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

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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

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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.

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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.

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• 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.

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• 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.

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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)

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• 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.

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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

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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

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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)

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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

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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.