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Quantitative Methods

Learn how to solve transportation, transshipment, and assignment problems in this comprehensive lesson covering network flow models, linear programming, Excel and QM solutions. Understand the transportation model, transshipment model, and assignment model.

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Quantitative Methods

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  1. Quantitative Methods MAT 540 Transportation, Transshipment, and Assignment Problems

  2. Objectives • When you complete this lesson, you will be able to solve: • Transportation problems • Transshipment problems • Assignment problems

  3. Overview • Network flow problems • Transportation models • Transshipment models • Assignment models

  4. The Transportation Model • Characteristics • A product is transported from a number of sources to a number of destinations at the minimum cost • Each source is able to supply a fixed amount of the product, and each destination has a fixed amount of demand for the product

  5. The Transportation Model, continued Grain ElevatorSupplyMill Demand 1. Kansas City 150 A. Chicago 200 2. Omaha 175 B. St. Louis 100 3. Des Moines 275 C. Cincinnati 300 Total 600 tons Total 600 tons

  6. The Transportation Model, continued • Linear programming model

  7. Computer Solution of a Transportation Problem • Excel solution

  8. Computer Solution of a Transportation Problem, continued • Excel QM solution

  9. Computer Solution of a Transportation Problem, continued • Excel QM solution

  10. Computer Solution of a Transportation Problem, continued • QM for Windows solution

  11. The Transshipment Model • Transshipment points • Transportation may take place from • Sources through transshipment points to destinations • One source to another • One transshipment point to another • One destination to another • Sources to destinations

  12. The Transshipment Model, continued • Nebraska, Colorado each harvest 300 tons • Kansas City, Omaha, and Des Moines are transshipment points

  13. The Transshipment Model, continued • Supply constraints for the farms • Demand constraints at mills

  14. The Transshipment Model, continued • Grain shipped into Kansas City: • Grain shipped out of Kansas City: • The two amounts must equal one another • Constraints for Omaha and Des Moines

  15. The Transshipment Model, continued • Linear programming model

  16. The Transshipment Model, continued • Excel solution

  17. The Assignment Problem • All supply and demand values equal 1 • The supply at each source and the demand at each destination are each limited to one unit

  18. The Assignment Problem, continued • Four teams of officials to four games • Minimize distance traveled • Supply and demand is one team of officials per game

  19. The Assignment Problem, continued • Linear programming model

  20. The Assignment Problem, continued • Excel solution

  21. The Assignment Problem, continued • Excel QM solution

  22. The Assignment Problem, continued • QM for Windows Solution

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