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

2. 2-Center Problem
Alternative formulation (P1):
Note:

3. 2-Center Problem Looks almost like a covering problem!
Consider the covering problem C(z):
Note that for the 2-center case, the minimal objective function value of C(z) must be <=2

4. 2-Center Problem
Equivalence of C(z) and P1:

5. 2-Center Problem
Hence:

6. 2-Center Problem
Example:

7. 2-Center Problem
Example:

8. 2-Center Problem
Example:

9. 2-Center Problem
Example:

10. 2-Center Problem
Example:

11. n-Center Problem
General approach:

12. n-Center Problem
Algorithm:

13. n-Center Problem
Algorithm:

14. Location on General Networks
Example:

15. Median Problem on GNs
Recall: node optimality for median problems

16. Node Optimality on GNs
Let’s look at a 1-median problem:

17. Node Optimality on GNs
Distances for the sample network:

18. Node Optimality on GNs

19. Solving the 1-median Problem