1. Lecture 13: Transportation ‘Autopower Co. Case’ AGEC 352 Spring 2011 – March 9 R. Keeney

2. Cost Coefficients Sources Destinations LeipzigNancyLiegeTillburg Amsterdam120.0130.041.059.5 Antwerp61.040.0100.0110.0 Le Havre102.590.0122.042.0 *Could compare these routes or compare sources and destinations *Statistician might average costs from a source or to a destination *What should we do?

3. Information for a Model Location Port CitiesQuantity of Motors to Ship (<=) Amsterdam500 Antwerp700 Le Havre800 Factory CitiesQuantity of Motors to Receive (>=) Leipzig400 Nancy900 Liege200 Tilburg500 *All of the locations are not the same, they have different capacities and requirements. Simple averaging would be incorrect…

4. Problem Size Transportation Problem ◦ S = # of sources ◦ D = # of destinations Then ◦ SxD = # of decision variables ◦ S+D = # of constraints (not counting non- negativity constraints) Problems can get big quickly…

5. Algebraic Simplification *We use subscripts to keep track. We use s to indicate a source and d a destination. *X 23 is a shipment from source 2 to destination 3

6. Spreadsheet Setup Three matrix approach First ◦ Unit cost coefficients (from the data) Second ◦ Decision variables (including consraints) Third ◦ Cost contributions (links the first two and determines the total cost)

7. Solver LHS vs RHS shortcut

8. Results and Sensitivity

9. Constraints All of the constraints bind Source shadow prices are negative One source has shadow price zero for a binding constraint Destinations shadow prices are positive Allowable increase for destinations is zero Allowable decrease for sources is zero

10. Objective Penalty Found in the column ‘Reduced Cost’ The change in the objective variable value that occurs if you change a variable that is optimally set to zero to a value of 1 E.g. Optimal oats acreage = 0 ◦ Grow oats anyway each acre planted comes at a profit penalty…

11. Homework Questions in Lab 5 Designed as discussion questions, provide an answer of appropriate length. ◦ Even if you can answer yes or no assume that I also want to know why you chose yes/no. Some seem complicated but can be answered by referring to the sensitivity information and making comparisons