CENTROID METHOD OF FACILITY LOCATION Dr. Ron Lembke.
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Transcript of CENTROID METHOD OF FACILITY LOCATION Dr. Ron Lembke.
![Page 1: CENTROID METHOD OF FACILITY LOCATION Dr. Ron Lembke.](https://reader035.fdocuments.net/reader035/viewer/2022081513/5697bfde1a28abf838cb1f5e/html5/thumbnails/1.jpg)
CENTROID METHOD OF FACILITY LOCATION
Dr. Ron Lembke
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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
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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
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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.
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100Center of Gravity – Ex 1
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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
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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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100 Center of Gravity – Ex 1, Map 2
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Salina KS
North Platte
SharonSprings
Ctr Grav. Ex 1 - Detail
Wichita KS
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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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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
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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
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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
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Break Country Into Regions Not optimal, but better than nothing, great
if each division needs its own DC
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Johannesburg, South AfricaMedical waste disposal candidate siteList of all medical waste generating pts
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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