Centre of gravity
x-bar = SUM(xi x wi) / SUM(wi)
y-bar = SUM(yi x wi) / SUM(wi)
Placing a single facility to serve known demand points with known volumes. Assumes cost is directly proportional to distance and volume shipped.
- xi, yi
- Grid coordinates of demand point i
- wi
- Weight or volume shipped to demand point i
Euclidean distance
d = sqrt( (x2 - x1)^2 + (y2 - y1)^2 )
Straight-line travel, and the default in load-distance problems that give coordinates rather than road distances.
- (x1, y1)
- Coordinates of the first point
- (x2, y2)
- Coordinates of the second point
Rectilinear distance
d = |x2 - x1| + |y2 - y1|
Movement along aisles, streets or a shop floor. The measure the class CRAFT spreadsheet uses between department centroids.
- |x2 - x1|
- Absolute horizontal separation
- |y2 - y1|
- Absolute vertical separation
Load-distance score
Score(site i) = SUM over j of ( load at j x distance from i to j )
Ranking a shortlist of real candidate sites. Lowest score wins; a cost per unit distance scales all scores equally.
- load at j
- Demand or tonnage carried to demand point j
- distance
- Road, Euclidean or rectilinear, as the question states
Great-circle approximation
d = 69 x sqrt( dLong^2 + dLat^2 ) miles
d = 111 x sqrt( dLong^2 + dLat^2 ) km
Decimal degrees = degrees + minutes / 60
When locations are given as latitude and longitude. Convert to decimal degrees first.
- dLat
- Difference of latitudes, in decimal degrees
- dLong
- Difference of longitudes, in decimal degrees