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

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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)

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

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

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

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

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

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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

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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

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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?

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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

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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

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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

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How to model in Excel? Cost Matrix From/ToAtlDalNYChi Jax75--150-- N.O.125100-- Atl-- 125150 Dal-- 100

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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

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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

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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…

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Medley Swimming (U.S. 2008) Swimmer/ Stroke BackBreastB-flyFree Peirsol53.16--57.75-- Hansen--59.2754.25-- Phelps53.1158.1550.1545.95 Lezak-- 55.4546.76

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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

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

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