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Centroid method of facility location

Dr. Ron Lembke. Centroid method of facility location. 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

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Centroid method of facility location

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  1. Dr. Ron Lembke Centroid method of facility location

  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 • dix is the X coordinate of location i. • diy is the Y coordinate of i. • Vi is the Volume X demand at i. • CX and CY 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. Center of Gravity – Ex 1 100 80 60 40 20 0 0 20 40 60 80 100 120 140 160

  6. Center of Gravity Method City Location Demand • Reno is at 17, 55 100 • Dallas is at 78, 20 90 • Chicago is at 110, 65. 120 • Demand is TL/month

  7. Center of Gravity

  8. Center of Gravity – Ex 1, Map 2 100 80 60 40 20 0 0 20 40 60 80 100 120 140 160

  9. CtrGrav. Ex 1 - Detail North Platte Sharon Springs Wichita KS Salina 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. Center of Gravity Map 100 80 60 40 20 0 0 20 40 60 80 100 120 140 160

  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 X Y Demand • Pierre 78 47 50 • Watertown 150 65 8 • Sioux Falls 160 25 90 • Rapid 12 42 60

  14. Center of Gravity Map 2 100 80 60 40 20 0 0 20 40 60 80 100 120 140 160

  15. Center of Gravity

  16. Final Location? 100 80 60 40 20 0 0 20 40 60 80 100 120 140 160

  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

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