The Transportation Method of Linear Programming

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The Transportation Method of Linear Programming
Clarke Holdaway 11/3/11
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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 Excels 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 (C29C20 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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• Now we need to indicate two constraints.
• a. customer demand must equal shipped

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• b. pallets supplied must be lt 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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• 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.