Lecture 15: Transportation and other Networks AGEC 352 Spring 2011 – March 23 R. Keeney

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)

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

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

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

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

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

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

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

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?

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

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

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

How to model in Excel? Cost Matrix From/ToAtlDalNYChi Jax N.O Atl Dal-- 100

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 a 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

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

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…

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