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

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Presentation transcript:

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 –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.

Example

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:

Location on Networks Now consider Covering problems

Location on Networks Closest Center Assumption: Coverage constraint:

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

Covering on a Tree Example tree

Algorithm Sketch (Book p.416)