1. Ch 6: Transportation I. Formulation II. Northwest Corner
III. Production Smoothing

2. Formulation
Application: Decision about how many units to ship from factory to warehouse, given several factories and several warehouses
If planning new factory or new warehouse, can be used to decide location (ex: Pennsylvania Rite Aid built warehouse at Palmdale)

3. Linear Programming Objective: MINIMIZE transportation cost
Constraints: Supply, demand
Supply: Factory capacity
Demand: Warehouse requirement

4. Example Three warehouses: Albuq, Boston, Cleve
Three factories: Des Moines,Evansville,
Ft Lauderdale
Next slide: Data given

5. Transportation matrix
To From A B C
Supply D
100 E
300 F
Demand
200
700

6. Northwest Corner Start at northwest corner
Number of units = MIN (supply,demand)
Ex: Row D,Col A: MIN(100,300)=100
After allocation, subtract units

7. Transportation matrix
To From A B C
Supply D
100 E
300 F
Demand
200
700

8. Transportation matrix
To From A B C
Supply D
100 E
300 F
Demand
=200
200
700

9. Transportation matrix
To From A B C
Supply D
100 E
200
300 F
Demand
=200
700

10. Transportation matrix
To From A B C
Supply D
100 E
200
=100 F
300
Demand
=200
700

11. Transportation matrix
To From A B C
Supply D
100 E
200
=100 F
300
Demand
=200
700

12. Transportation matrix
To From A B C
Supply D
100 E
200
=100 F
300
Demand
=200
=100
700

13. Transportation matrix
To From A B C
Supply D
100 E
200
=100 F
300
Demand
=200
=100
700

14. Transportation matrix
To From A B C
Supply D
100 E
200
=100 F
=200
Demand
=100
700

15. Transportation matrix
To From A B C
Supply D
100 E
200
=100 F
=200
Demand
=100
700

16. MIN Cost Would need unit cost between factory and warehouse
Use Excel to minimize cost
Northwest Corner is initial allocation

17. Production Smoothing Factory replaced by production period
Warehouse repl by demand period

18. Two month example Month Feb Mar Supply 15 5=inventory end of Feb 20
Demand 25 40