The Center of Gravity Method

1. 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) The Center of Gravity Method

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. The Center of Gravity Method

4. Definition • The Center of Gravity Method takes many factors into account including: • Markets • Volume of goods shipped • Shipping costs The Center of Gravity Method

5. 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 The Center of Gravity Method

6. Center of Gravity Method Steps (II) • Calculate X and Y coordinates using the following equations: Cx= ∑ dix Vi/ ∑ Vi Cy= ∑ diy Vi/ ∑ Vi The Center of Gravity Method

7. 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. The Center of Gravity Method

8. 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 The Center of Gravity Method

9. 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 The Center of Gravity Method

10. Choosing The Best location • Transportation • Access to interstate highway systems • Access to major carriers and terminals • Transportation cost and service The Center of Gravity Method

11. Choosing The best Location • Labor • Availability of qualified workers • Prevailing labor costs The Center of Gravity Method

12. Choosing The Best Location • Quality of Life • Educational facilities • Housing and community appearance • Crime rate The Center of Gravity Method

13. Choosing The Best Location • State and Local Government • Training incentives • Building construction codes and restrictions • Planning and zoning The Center of Gravity Method

14. How can The Center of Gravity Method Help My Company Choose The Best Location? • Simple to compute • Considers existing facilities • Minimizes costs The Center of Gravity Method

15. 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 The Center of Gravity Method

16. Miles Y 150 (100, 150) Facility 3 100 (300, 100) Facility 2 50 (200, 50) Facility 1 X 100 200 300 400 The Center of Gravity Method

17. d1x= 200 d2x= 300 d3x= 100 d1y= 50 d2y= 100 d3y= 150 V1= 2,500 V2= 1,300 V3= 5,000 The Center of Gravity Method

18. 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 The Center of Gravity Method

19. 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 The Center of Gravity Method

20. 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. The Center of Gravity Method

21. The Center of Gravity Method

22. First, input all the information given to you on a worksheet. The Center of Gravity Method

23. Remember the formulas Cx= ∑ dix Vi/ ∑ Vi Cy= ∑ diy Vi/ ∑ Vi The Center of Gravity Method

24. Second, Calculate the X Coordinate The Center of Gravity Method

25. Third, calculate the Y Coordinate The Center of Gravity Method

26. 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. The Center of Gravity Method

27. 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 The Center of Gravity Method

28. Summary (Cont) • Other factors you should consider before making a final decision include: • Transportation • Labor • Quality of Life • State and Local Government The Center of Gravity Method

29. Suggested Reading Marc J. Schniederjans. International Facility Acquisition and Location Analysis. New York: Quorum Books, 1999. The Center of Gravity Method

30. 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> The Center of Gravity Method