1. CENTROID METHOD OF FACILITY LOCATION Dr. Ron Lembke

2. Location Methods Minimize demand-weighted distance  Center of Gravity – minimizing demand-weighted distances of one facility  Ardalan – minimize transportation of multiple facilities, but must locate by customers  P-Median Problem, Maximum Covering Factor Weighting – consider qualitative factors Break-even – Consider fixed & variable costs

3. Center of Gravity Compute X and Y coordinates separately d ix is the X coordinate of location i. d iy is the Y coordinate of i. V i is the Volume X demand at i. C X and C Y are the coordinates of the DC.

4. Center of Gravity Example 1 You need to decide where to build a new DC for Motorola. It needs to serve wholesalers in Reno, Dallas, and Chicago. Locate these cities on an unscientific, rectangular grid. Grid must maintain relative distances, but X and Y grids could be different.

5. 020406080100120140160 80 20 40 60 0 100 Center of Gravity – Ex 1

6. Center of Gravity Method CityLocationDemand Reno is at 17, 55100 Dallas is at 78, 2090 Chicago is at 110, 65.120 Demand is TL/month

7. Center of Gravity

8. 020406080100120140160 80 20 40 60 0 100 Center of Gravity – Ex 1, Map 2

9. Salina KS North Platte Sharon Springs Ctr Grav. Ex 1 - Detail Wichita KS

10. Compromise Solutions Closest town is Sharon Springs, KS  Population 872  30 miles from I-70.  Probably not a good choice Salina, KS puts us at I-70 and I-35 North Platte NE is at I-80 and 83.  Access to Dallas less convenient Wichita, KS

11. 020406080100120140160 80 20 40 60 0 100 Center of Gravity Map

12. Finalizing City Go where other warehouses are  More choice in pre-built buildings  Cheaper, easier to build a new one  More trucks to and from town, means more carriers there, means cheaper rates.  Backhaul situation Get estimates of inbound, outbound trucking costs.  Provide lists of # loads per year to each destination, from each source

13. Center of Gravity Example 2 You need to decide where to locate a DC in South Dakota XYDemand Pierre784750 Watertown150658 Sioux Falls1602590 Rapid 124260

14. 020406080100120140160 80 20 40 60 0 100 Center of Gravity Map 2

15. Center of Gravity

16. 020406080100120140160 80 20 40 60 0 100 Final Location?

17. Break Country Into Regions Not optimal, but better than nothing, great if each division needs its own DC

18. Johannesburg, South Africa Medical waste disposal candidate site List of all medical waste generating pts

19. Summary Works well for locating one facility  For larger areas, break into separate regions  Not the final city, but an area to look in Center of Gravity, or Centroid:  Create x scale and y scale, can be different  Estimate x and y coordinates of each location  Sum x coordinates times respective demands  Sum y coordinates times respective demands  Divide by total demand to get location