ISEN 601 Location Logistics Dr. Gary M. Gaukler Fall 2011.
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Transcript of ISEN 601 Location Logistics Dr. Gary M. Gaukler Fall 2011.
![Page 1: ISEN 601 Location Logistics Dr. Gary M. Gaukler Fall 2011.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649d2c5503460f94a020ab/html5/thumbnails/1.jpg)
ISEN 601Location Logistics
Dr. Gary M. Gaukler
Fall 2011
![Page 2: ISEN 601 Location Logistics Dr. Gary M. Gaukler Fall 2011.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649d2c5503460f94a020ab/html5/thumbnails/2.jpg)
1-Center on Weighted Tree
• Problem formulation:
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Summary of Algorithm
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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.
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Example
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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:
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![Page 8: ISEN 601 Location Logistics Dr. Gary M. Gaukler Fall 2011.](https://reader035.fdocuments.us/reader035/viewer/2022081516/56649d2c5503460f94a020ab/html5/thumbnails/8.jpg)
Location on Networks
• Now consider Covering problems
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Location on Networks
• Closest Center Assumption:
• Coverage constraint:
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Covering on a Tree
• Problem formulation: Locate all centers such that the coverage constraints are satisfied, and the number of centers is minimized.
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Covering on a Tree
• Example tree
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Algorithm Sketch (Book p.416)