CENTROID METHOD OF FACILITY LOCATION
Dr. Ron Lembke
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 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.
i
iixX V
VdC
i
iiyY V
VdC
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.
0 20 40 60 80 100 120 140 160
80
20
40
60
0
100Center of Gravity – Ex 1
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
12011090
120*110*90
ii
iiix
X W
WdC
7.70310
920,21
310
200,13020,7700,1
12090100
120*11090*78100*17
X
i
iixX
C
V
VdC
7.48310
100,15
310
800,7800,1500,5
12090100
120*6590*20100*55
Y
i
iiy
Y
C
V
VdC
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80
20
40
60
0
100 Center of Gravity – Ex 1, Map 2
Salina KS
North Platte
SharonSprings
Ctr Grav. Ex 1 - Detail
Wichita KS
Compromise Solutions
Closest town is Sharon Springs, KSPopulation 87230 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
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80
20
40
60
0
100 Center of Gravity Map
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
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
0 20 40 60 80 100 120 140 160
80
20
40
60
0
100 Center of Gravity Map 2
Center of Gravity
12011090
120*110*90
ii
iiix
X W
WdC
2.97208
220,20
208
720400,14200,1900,3
6090850
60*1290*1608*15050*78
X
i
iixX
C
V
VdC
7.36208
640,7
208
520,2250,2520350,2
6090850
60*4290*258*6550*47
Y
i
iiyY
C
V
VdC
0 20 40 60 80 100 120 140 160
80
20
40
60
0
100 Final Location?
Break Country Into Regions Not optimal, but better than nothing, great
if each division needs its own DC
Johannesburg, South AfricaMedical waste disposal candidate siteList of all medical waste generating pts
Summary Works well for locating one facility
For larger areas, break into separate regionsNot the final city, but an area to look in
Center of Gravity, or Centroid:Create x scale and y scale, can be differentEstimate x and y coordinates of each locationSum x coordinates times respective demandsSum y coordinates times respective demandsDivide by total demand to get location
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