The department shape ratio is the maximum of the length to width and width to length ratios of the smallest rectangle enclosing the department. Let 
and
be the length and width of the smallest rectangle enclosing the department, then the shape ratio 
is given by
(3.1)
For rectangular departments the smallest rectangle enclosing the department is of course the department itself. For example the shape ratio of a square department is one and the shape ratio of a three by one rectangular department is equal to three.
The shape ratio is an output variable, computed by the program based on the current shape of the department. If the department shape ratio exceeds the maximum shape ratio then the shape adjusted distance score is the sum of the normal distance score and the excess of the department shape ratio over the maximum shape ratio multiplied by the shape penalty.