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Centre of Gravity Method

Concept

The Center of Gravity method is a mathematical technique used to determine the optimal location for a distribution center, warehouse, or facility that minimizes transportation costs. It considers the locations of markets, the volume of goods shipped, and associated costs.

Method

Coordinate System: Place existing locations on a coordinate system (x, y).
Data Collection: Gather data on demand/supply volume (Q) for each location. Calculate Center of Gravity (Cx, Cy): Use these formulas:
Cx = ∑ (xi * Qi) / ∑Qi
Cy = ∑ (yi * Qi) / ∑Qi

Where:
* xi = x-coordinate of location i
* yi = y-coordinate of location i
* Qi = quantity of goods moved to or from location i

Optimal Location: The resulting (Cx, Cy) coordinates represent the calculated center of gravity, which is the suggested new location.

Practical Example

Scenario: A healthcare company wants to find the optimal location for a new facility to serve seven census tracts.

Data:

Census Tract (x, y) Population (Q) (in 1000's)
A (2.5, 4.5) 2
B (2.5, 2.5) 5
C (5.5, 4.5) 10
D (5, 2) 7
E (8, 5) 10
F (7, 2) 20
G (9, 2.5) 14

Calculations

Census Tract (x,y) Population (Q) Lx Ly
A (2.5, 4.5) 2 5 9
B (2.5, 2.5) 5 12.5 12.5
C (5.5, 4.5) 10 55 45
D (5, 2) 7 35 14
E (8, 5) 10 80 50
F (7, 2) 20 140 40
G (9, 2.5) 14 126 35
Total 68 453.5 205.5
  • Cx = 453.5 / 68 = 6.67
  • Cy = 205.5 / 68 = 3.02

Proposed Location: The suggested location for the health-care facility is (6.67, 3.02).

Practical Example with Diagram

Scenario: A company has 4 distribution centers in the cities of Chicago, Pittsburg, New York and Atlanta. They want to build a new warehouse. Their demand information is below:

Data:

Location X Coordinate Y Coordinate Containers Shipped Monthly
Chicago 30 120 2000
Pittsburgh 90 110 1000
New York 130 130 1000
Atlanta 60 40 2000

Calculations *Cx = ((30 * 2000) + (90 * 1000) + (130 * 1000) + (60 * 2000)) / (2000 + 1000 + 1000 + 2000) = (60,000 + 90,000 + 130,000 + 120,000)/ 6000 = 400,000 / 6000 Cx = 66.7

*Cy = ((120 * 2000) + (110 * 1000) + (130 * 1000) + (40 * 2000)) / (2000 + 1000 + 1000 + 2000) = (240,000 + 110,000 + 130,000 + 80,000) / 6000 = 560,000 / 6000 Cy= 93.3 The new warehouse location is suggested at (66.7, 93.3)

Graph:

  • Where C represents Chicago, P represents Pittsburg, Y represents New York, and A represents Atlanta
  • The plus sign(+) indicates the center of gravity at coordinates (66.7, 93.3).

Advantages

  • Simple to calculate.
  • Easy to understand and apply.
  • Considers demand volume.

Limitations

  • Assumes linear transportation costs, which may not always be accurate.
  • Does not consider other factors like infrastructure or land costs.
  • Relies on the accuracy of the coordinate system and demand data.
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