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Lecture 13: Transportation ‘ Autopower Co. Case’

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

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

  2. Cost Coefficients *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 *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. *X23 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

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