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

12011090120*110*90

ii

iiix

X W

WdC

7.70310

920,21310

200,13020,7700,1

12090100120*11090*78100*17

X

i

iixX

C

VVd

C

7.48310

100,15310

800,7800,1500,5

12090100120*6590*20100*55

Y

i

iiyY

C

VVd

C

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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

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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

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80

20

40

60

0

100 Center of Gravity Map 2

Center of Gravity

12011090120*110*90

ii

iiix

X W

WdC

2.97208

220,20208

720400,14200,1900,3

609085060*1290*1608*15050*78

X

i

iixX

C

VVd

C

7.36208640,7

208520,2250,2520350,2

609085060*4290*258*6550*47

Y

i

iiyY

C

VVd

C

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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