Tuesday, January 13, 2009

Modeling quadratic penalty on lateness

> I am working on a scheduling application and want to penalize
> large lateness values extra. So I want to use quadratic penalty
> for this. How can I do that with Cplex?

In general you don't want to do that. A better way is to add a cost term to the objective using the MAX lateness.

Often one can use a mix of the following cost (penalty) terms:
  • SUM (sum of how much jobs are late)
  • COUNT (number of late jobs)
  • MAX (maximum lateness)
Changing the penalty coefficients can allow you put different weights on these criteria.

E.g. the SUM criterium may lead to many jobs just a little bit late. Adding the COUNT criterium may help prevent this. Opposed to this: adding the MAX can help prevent jobs that are very late.