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ISEN 601 Location Logistics

ISEN 601 Location Logistics. Dr. Gary M. Gaukler Fall 2011. 1-Center on Weighted Tree. Problem formulation:. Summary of Algorithm. Algorithm Refinement. It is possible to calculate the elements of matrix B “on the fly”: Choose any row r of the matrix

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ISEN 601 Location Logistics

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  1. ISEN 601Location Logistics Dr. Gary M. Gaukler Fall 2011

  2. 1-Center on Weighted Tree • Problem formulation:

  3. Summary of Algorithm

  4. Algorithm Refinement • It is possible to calculate the elements of matrix B “on the fly”: • Choose any row r of the matrix • Calculate bij for row r and find the largest element in that row -> column c • Calculate bij for column c and find the largest element in that column -> row r • Continue until you find the same element in succession. This element is bst.

  5. Example

  6. Compare with Unweighted Tree • The algorithm for calculating the matrix elements is very similar to the 1-center solution algorithm for the unweighted tree case:

  7. Location on Networks • Now consider Covering problems

  8. Location on Networks • Closest Center Assumption: • Coverage constraint:

  9. Covering on a Tree Problem formulation: Locate all centers such that the coverage constraints are satisfied, and the number of centers is minimized.

  10. Covering on a Tree Example tree

  11. Algorithm Sketch (Book p.416)

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