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The Transportation Method of Linear Programming
Clarke HoldawayClarke Holdaway11/3/1111/3/11
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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
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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
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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.
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• 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.
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• 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.
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• 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.
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• 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:
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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
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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
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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.
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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?
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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.
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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.