The Center of Gravity Method
Francisco J. Rebollo Pascual
Marriott School
Brigham Young University
Agenda
•
•
•
•
Definition
Steps and Formulas
Choosing The Best Location
The Center of Gravity Method in Your
Organization (example)
• Solved problem (using Excel)
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Definition
• The Center of Gravity Method is a tool that
seeks to compute geographic coordinates
for a potential single new facility that will
minimize costs.
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Definition
• The Center of Gravity Method takes many
factors into account including:
 Markets
 Volume of goods shipped
 Shipping costs
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Center of Gravity Method Steps (I)
• Place existing locations in a coordinate grid
 Place the grid on an ordinary map (example provided below)
 The relative distances must be noted
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Center of Gravity Method Steps (II)
• Calculate X and Y coordinates using the
following equations:
Cx= ∑ dix Vi/ ∑ Vi
Cy= ∑ diy Vi/ ∑ Vi
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Center of Gravity Method Steps (III)
• Once you have obtained the X and Y
coordinates place that location on the
previously described map.
Note: If that particular location does not fall directly on a city, simply
locate the nearest city and place the new facility there.
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The Center of Gravity Method in
Your Organization
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Choosing The Best Location
• Choosing an optimal location for your new
facility is vital to your company’s success.
Some factors you should consider include:
 Transportation
 Labor
 Quality of Life
 State and Local Government
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Choosing The Best location
• Transportation
Access to interstate highway systems
Access to major carriers and terminals
Transportation cost and service
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Choosing The best Location
• Labor
Availability of qualified workers
Prevailing labor costs
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Choosing The Best Location
• Quality of Life
Educational facilities
Housing and community appearance
Crime rate
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Choosing The Best Location
• State and Local Government
Training incentives
Building construction codes and restrictions
Planning and zoning
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How can The Center of Gravity
Method Help My Company Choose
The Best Location?
• Simple to compute
• Considers existing facilities
• Minimizes costs
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Example
• Your company wants to locate a new facility
within a network of three existing facilities. Given
the following variables and the grid provided in
the next slide, what are the coordinates for the new
location?
 Facility 1 has a daily goods volume of 2,500 units
 Facility 2 has a daily goods volume of 1,300 units
 Facility 3 has a daily goods volume of 5,000 units
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Miles
Y
150
(100, 150) Facility 3
100
(300, 100) Facility 2
50
(200, 50) Facility 1
100
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200
300
400
The Center of Gravity Method
X
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•
•
•
•
•
•
d1x= 200
d2x= 300
d3x= 100
d1y= 50
d2y= 100
d3y= 150
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• V1= 2,500
• V2= 1,300
• V3= 5,000
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Cx= (200 x 2,500) + (300 x 1,300) + (100 x 5,000)
(2,500 + 1,300 + 5,000)
= 158
Cy= (50 x 2,500) + (100 x 1,300) + (150 x 5,000)
(2,500 + 1,300 + 5,000)
= 114
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Miles
Y
150
100
(100, 150) Facility 3
50
(200, 50) Facility 1
100
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(300, 100) Facility 2
(158, 114)
New Facility
200
300
400
The Center of Gravity Method
X
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Solved Problem (using Excel)
• Wal-Mart is trying to determine where to
locate a new warehouse. The new facility is
expected to serve four cities in the state of
Utah. Calculate the center of gravity for the
new warehouse based on the information
provided in the next slide.
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City
X Coordinate
Y Coordinate
Number of Households (in thousands)
Logan
4
2
1.4
Ogden
3
3
2.1
Vernal
1
4
3.3
Provo
5
1
4.9
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First, input all the information given to you on a worksheet.
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• Remember the formulas
Cx= ∑ dix Vi/ ∑ Vi
Cy= ∑ diy Vi/ ∑ Vi
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Second, Calculate the X Coordinate
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Third, calculate the Y Coordinate
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Lastly, once you have obtained an x and y-coordinate, place that location on the
map. If that particular location does not fall directly on a city, simply locate the
nearest city and place the new Wal-Mart warehouse there.
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Summary
The Center of Gravity Method
• Seeks to compute geographic coordinates
for a potential single new facility that will
minimize costs.
• Is easy to compute
• Takes into account existing facilities
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Summary (Cont)
• Other factors you should consider before
making a final decision include:
 Transportation
 Labor
 Quality of Life
 State and Local Government
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Suggested Reading
Marc J. Schniederjans. International Facility Acquisition and Location
Analysis. New York: Quorum Books, 1999.
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References
Marc J. Schniederjans. International Facility Acquisition and Location Analysis. New York:
Quorum Books, 1999.
Cecil C. Bozarth, Robert B. Handfield. Introduction to Operations and Supply Chain
Management. New Jersey: Prentice Hall, 2005.
Bostedo, John. "Facilities Location." . . . 23 Nov. 2005
<http://www.snc.edu/socsci/chair/333/facloc98.htm>.
"The Center of Gravity Method." . . . 21 Nov. 2005
<http://online.uis.edu/spring2000/bus322/lectures/chap08/sld027.htm>
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