There is a decision variable $x_i$ which denotes the time when a person is allowed to do his work.
The objective function is
$\min (x_i - a_i)$
where $a_i$ is the time when the person arrives at the workplace.
Suppose after solving, the values of decision variable come out to be:
x1 = 10 x2 = 6 x3 = 8 x4 = 3 x5 = 9
Now I need to formulate an additional objective function and a constraint with another decision variable $r_i$ which denotes the rank or order in which these people start doing the work.
For instance from the above example,
r1 = 5 r2 = 2 r3 = 3 r4 = 1 r5 = 4
How do I determine the value of $r_i$ from $x_i$ in the form of a constraint in this multiobjective optimization problem?