Lecture 15: Transportation and other Networks

1. Lecture 15: Transportation and other Networks AGEC 352 Spring 2012 – March 21 R. Keeney

2. Network Models • Entry nodes, exit nodes, transition nodes • Classic example: • Production: Enter into the network • Wholesale/Warehouse: Waypoint between production and sale • Retail: Exit the network (final demand)

3. Transportation Example • Entry nodes • Jacksonville and New Orleans • Exit nodes • New York City, Chicago • Transition nodes • Atlanta, Dallas

4. Diagrammatic Example Origin Points Jacksonville Atlanta New York City Chicago New Orleans Dallas Origin Points Waypoints End Points

5. Diagrammatic Example: Additional Routes to Waypoint Jacksonville Atlanta New York City Chicago New Orleans Dallas

6. Diagrammatic Example: Additional Routes to Retail Jacksonville Atlanta New York City Chicago New Orleans Dallas

7. Diagrammatic Example: Supply and Demand Numbers 70 Units 200 Units Jacksonville Atlanta New York City Chicago New Orleans Dallas 50 Units 100 Units

8. Diagrammatic Example: Additional Retail Options 60 Units 70 Units 200 Units Jacksonville Atlanta New York City Chicago New Orleans Dallas 120 Units 50 Units 100 Units

9. Two nodes are destinations and sources • How do we deal with this? • Recall the balance equation we saw earlier in the semester for a product like corn • Corn bushels produced (S) >= corn bushels marketed (M) • S – M >= 0 • Assume we wanted to store 500 bushels • S – M >= 500

10. Balance equation • Atlanta • S = Quantity of items entering from Jacksonville and New Orleans • M = Quantity of items shipped to New York and Chicago • S – M >= 70 • Dallas?

11. Diagrammatic Example: Direct Routes 60 Units 70 Units 200 Units Jacksonville New York City Atlanta Dallas Chicago New Orleans 120 Units 50 Units 100 Units

12. Diagrammatic Example: Cost Information 60 Units 70 Units 200 Units Jacksonville New York City Atlanta $150 $75 $125 $150 Dallas $125 Chicago New Orleans $100 $100 120 Units 50 Units 100 Units

13. Diagrammatic Example: Cost Information 60 Units 70 Units 200 Units Jacksonville New York City Atlanta $150 $75 $125 $150 Dallas $125 Chicago New Orleans $100 $100 120 Units 50 Units 100 Units

14. How to model in Excel?Cost Matrix

15. Constraints • We can still use the sums at the end of rows and columns, but it will be easier to organize them in a separate location since some constraints will require both the row and column sum to calculate • We will need to force some decision variables to be zero (unavailable routes) • We can do this by constraining them to zero • Or, omitting from the decision variable matrix

16. Notes • If you constrain the routes to zero, there will be meaningless sensitivity information • Force a route to equal zero and there is a shadow price but it depends on the unit cost of using that route • If you had a credible estimate of the unit cost of transportation the shadow price might be useful

17. Comments • We’ll see a couple of different applications of network models that work just like transportation next week • Assignments and Inventory Schedules • Source = people; Destination = jobs • Source = supply today; Destination = demand in the future • Any network can be modeled, you just can’t expect them all to be cookie cutter versions…

18. Medley Swimming (U.S. 2008)

19. Olympic Swimming • Michael Phelps is the world’s greatest swimmer • If you need to win a race, you pick him • If you need to win a relay race, you pick him but where do you use him? • Medley swimming • Backstroke, Breaststroke, Butterfly, Freestyle

20. Quiz on Monday • Another Transportation Case with Waypoint nodes (serve as source and destination)