The Center of Gravity Method

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The Center of Gravity Method

• Francisco J. Rebollo Pascual
• Marriott School
• Brigham Young University

2
Agenda

• Definition
• Steps and Formulas
• Choosing The Best Location
• The Center of Gravity Method in Your Organization
  (example)
• Solved problem (using Excel)

3
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
Minimize distance
Effectiveness
Happy customers
Faster shipments
Organized delivery
Better distribution
Easy
Minimize transportation activity
Minimize costs
Best location
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Choosing The Best Location

• Choosing an optimal location for your new
  facility is vital to your companys 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
X
100
200
300
400
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• d1x 200
• d2x 300
• d3x 100
• d1y 50
• d2y 100
• d3y 150

• 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)
• Cy (50 x 2,500) (100 x 1,300) (150 x 5,000)
• (2,500 1,300 5,000)

158
114
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Miles
Y
150
(100, 150) Facility 3
100
(300, 100) Facility 2
(158, 114) New Facility
50
(200, 50) Facility 1
X
100
200
300
400
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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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SummaryThe 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 lthttp//www.snc.edu/socsci/chair/333/fac
  loc98.htmgt.
• "The Center of Gravity Method." . . . 21 Nov.
  2005 lthttp//online.uis.edu/spring2000/bus322/lect
  ures/chap08/sld027.htmgt