1. ISEN 601 Location 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:

8. Location on Networks Now consider Covering problems

9. Location on Networks Closest Center Assumption: Coverage constraint:

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

11. Covering on a Tree Example tree

12. Algorithm Sketch (Book p.416)