1. Transportation Models
Module C
Transportation Models

2. The Transportation Method
Ship items at lowest cost
Sources have fixed supplies
Destinations have fixed demand

3. Note for the readings
The Northwest Corner Rule, Stepping Stone Method, etc. are not covered.
These are algorithms to use if you didn’t have good automatic software, but we do.

4. Transportation Problem
GRAIN ELEVATOR SUPPLY
1. Kansas City 150
2. Omaha 175
Des Moines 275
600 tons
MILL DEMAND
A. Chicago 200
B. St. Louis 100
Cincinnati 300

5. Transportation Problem
GRAIN ELEVATOR SUPPLY
1. Kansas City 150
2. Omaha 175
Des Moines 275
600 tons
MILL DEMAND
A. Chicago 200
B. St. Louis 100
Cincinnati 300
MILL
GRAIN Chicago St. Louis Cincinnati
ELEVATOR A B C
Kansas City $6 $8 $10
Omaha
Des Moines

6. The Transportation TableauTO
FROM Chicago St. Louis Cincinnati SUPPLY
Kansas City
Omaha
Des Moines
DEMAND

7. Solution for Grain ShipmentTO
GRAIN
FROM Chicago St. Louis Cincinnati SUPPLY SHIPPED
Kansas City
Omaha
Des Moines
DEMAND
GRAIN
SHIPPED
COST $4525

8. Transportation Variants
GRAIN ELEVATOR SUPPLY
1. Kansas City 250
2. Omaha 175
Des Moines 275
700 tons
MILL DEMAND
A. Chicago 200
B. St. Louis 100
Cincinnati 300
600 tons
MILL
GRAIN Chicago St. Louis Cincinnati
ELEVATOR A B C
Kansas City $6 $8 $10
Omaha
Des Moines

9. Transportation Variants
GRAIN ELEVATOR SUPPLY
1. Kansas City 250
2. Omaha 175
Des Moines 275
700 tons
MILL DEMAND
A. Chicago 200
B. St. Louis 100
Cincinnati 300
600 tons
Solution: When supply is greater than demand there is no problem. Let Solver figure it out!

10. Transportation Variants
GRAIN ELEVATOR SUPPLY
1. Kansas City 150
2. Omaha 175
Des Moines 275
600 tons
MILL DEMAND
A. Chicago 200
B. St. Louis 200
Cincinnati 300
700 tons
MILL
GRAIN Chicago St. Louis Cincinnati
ELEVATOR A B C
Kansas City $6 $8 $10
Omaha
Des Moines

11. Transportation Variants
GRAIN ELEVATOR SUPPLY
1. Kansas City 150
2. Omaha 175
Des Moines 275
600 tons
MILL DEMAND
A. Chicago 200
B. St. Louis 200
Cincinnati 300
700 tons
Solution: When demand is greater than supply Solver cannot do it. Add a “dummy origin.”
Supply at the dummy origin =
total demand – total supply

12. Transportation Variants
Blocking an Origin Destination Pair:
Solver minimizes cost, so if you put a large enough cost on a certain pair, no units will be shipped from that origin to that destination.

13. Other Problems
The Transportation setup works for a variety of different problems
If we know the costs (or profits) of assigning workers to a set of jobs we can use the transportation problem, for example
Use the Transp. Macro to solve B.16
Before the next test we will use transportation macros to solve planning problems (such as manufacturing to meet future demand.)