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.