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

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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?

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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…

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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…

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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

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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)

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Solver LHS vs RHS shortcut

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Results and Sensitivity

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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

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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…

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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

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