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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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location methods
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
center of gravity
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.
center of gravity example 1
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.
center of gravity ex 1
Center of Gravity – Ex 1

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center of gravity method
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
center of gravity ex 1 map 2
Center of Gravity – Ex 1, Map 2

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ctr grav ex 1 detail
CtrGrav. Ex 1 - Detail

North

Platte

Sharon

Springs

Wichita KS

Salina KS

compromise solutions
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
center of gravity map
Center of Gravity Map

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finalizing city
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
center of gravity example 2
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
center of gravity map 2
Center of Gravity Map 2

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final location
Final Location?

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break country into regions
Break Country Into Regions

Not optimal, but better than nothing, great if each division needs its own DC

johannesburg south africa
Johannesburg, South Africa

Medical waste disposal candidate site

List of all medical waste generating pts

summary
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