1. Facility Location Problems Hooman Mohajeri Moghaddam Winter 2011

2. Facility Location Problem A.K.A. Location Analysis A branch of Operations Research Mathematical modeling and solution of problems concerning optimal placement of facilities In order to minimize transportation costs, avoid placing hazardous materials near housing, outperform competitors' facilities, etc.

3. Application Warehouses for branches of a supermarket abc d

4. p p-line Center Problem Locating p > 0 linear facilities in the plane so that the maximum weighted distance from the demand points to the nearest facilities is minimized. Application? The general problem is known to be NP-Hard (Megiddo and Tamir 1982 ). p However for the case when p=1 the problem has polynomial solution (Morris and Norback 1983).

5. Problem Statement

6. How Hard is it?

7. Unweighted 1-Line-Center

8. Proof.

9. Algorithm(Unweighted)

17. Maximum Gap On a Circle Problem

18. Proof.

19. Weighted 1-Line-Center