1. Chapter 2 Basic Models for the Location Problem

2. Outline 11.3 Techniques for Discrete Space Location Problems
Qualitative Analysis
Quantitative Analysis
Hybrid Analysis

3. Outline Cont... 11.4 Techniques for Continuous Space Location Problems
Median Method
Contour Line Method
Gravity Method
Weiszfeld Method

4. Weiszfeld Method

5. Weiszfeld Method:
The objective function for the single facility location problem with Euclidean distance can be written as:
As before, substituting wi=cifi and taking the derivative of TC with respect to x and y yields

6. Weiszfeld Method:

7. Weiszfeld Method:

8. Weiszfeld Method:

9. Weiszfeld Method:

10. Weiszfeld Method:
Step 0: Set iteration counter k = 1;

11. Weiszfeld Method: Step 1: Set
Step 2: If xk+1 = xk and yk+1 = yk, Stop. Otherwise, set k = k + 1 and go to Step 1

12. Example 8:
Consider Example 6. Assuming the distance metric to be used is Euclidean, determine the optimal location of the new facility using the Weiszfeld method. Data for this problem is shown in Table 11.

13. Table 11.17 Coordinates and weights for 4 departments

14. Table 11.17: Departments # xi yi wi 1 10 2 6 2 10 10 20 3 8 6 8

15. Solution:
Using the gravity method, the initial seed can be shown to be (9.8, 7.4). With this as the starting solution, we can apply Step 1 of the Weiszfeld method repeatedly until we find that two consecutive x, y values are equal.

16. Summary: Methods for Single-Facility, Continuous Space Location Problems
Rectilinear
Squared Euclidean
Euclidean
Method
Median
Gravity
Weiszfeld