1. Transportation and Assignment Problems
Chapter 6

2. Chapter Topics The Transportation Model
Computer Solution of a Transportation Problem
The Assignment Model
Computer Solution of an Assignment Problem
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3. Overview Part of a class of LP problems known as network flow models.
Special mathematical features that permit very efficient, unique solution methods (variations of traditional simplex procedure).
Detailed description of methods is contained on the companion website
Text focuses on model formulation and solution with Excel and QM for windows.
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4. The Transportation Model: Characteristics
A product is transported from a number of sources to a number of destinations at the minimum possible cost.
Each source is able to supply a fixed number of units of the product, and each destination has a fixed demand for the product.
The linear programming model has constraints for supply at each source and demand at each destination.
All constraints are equalities in a balanced transportation model where supply equals demand.
Constraints contain inequalities in unbalanced models where supply does not equal demand.
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5. Transportation Model Example Problem Definition and Data
Wheat is harvested in the Midwest and stored in grain elevators in three different cities Kansas City, Omaha, and Des Moines. These grain elevators supply three flour mills located in Chicago, St Louis and Cincinnati. Grain is shipped to the mills in railroad cars, each car capable of holding 1 ton of wheat. Each grain elevator is able to supply the following number of tons (i.e. railroad cars) of wheat to the mills on a monthly basis:
Supply
Grain Elevator
150
Kansas City
175
Omaha
275
Des Moines
600
Total
Demand
Mill
200
Chicago
100
St Louis
300
Cincinnati
600
Total
The cost of transporting 1 ton of wheat from each grain elevator (source) to each mill (destination) differs according to the distance and rail system. These costs are shown in the following table:
The problem is to determine how many tons of wheat to transport from each grain elevator to each mill on a monthly basis to minimize the total transportation cost

7. Transportation Model Example Transportation Network Routes
Figure Network of Transportation Routes for Wheat Shipments
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8. Transportation Model Example Computer Solution with Excel (1 of 4)
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9. Transportation Model Example Computer Solution with Excel (2 of 4)
Exhibit 6.2
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10. Transportation Model Example Computer Solution with Excel (3 of 4)
Exhibit 6.3
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11. Transportation Model Example Computer Solution with Excel (4 of 4)
Figure Transportation Network Solution
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12. The Assignment Model Characteristics
Special form of linear programming model similar to the transportation model.
Supply at each source and demand at each destination limited to one unit.
In a balanced model supply equals demand.
In an unbalanced model supply does not equal demand.
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13. Assignment Model Example Problem Definition and Data
The Atlantic Coast Conference (ACC) has four basketball games on a particular night. The conference office wants to assign four teams of officials to the four games in a way that will minimize the total distance traveled by the officials. The supply is always one team of officials and the demand is for only one team of officials at each game. The distances in miles for each team of officials to each game location are shown in the following table:
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15. Assignment Model Example Computer Solution with Excel (1 of 3)
Exhibit 6.12
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16. Assignment Model Example Computer Solution with Excel (2 of 3)
Exhibit 6.13
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17. Assignment Model Example Computer Solution with Excel (3 of 3)
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Exhibit 6.14

18. Assignment Model Example Assignment Network Solution
Figure 6.5
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19. Example Problem Solution Transportation Problem Statement
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20. Example Problem Solution
Computer Solution with Excel