Minimizing mean squared deviation of completion times with maximum tardiness constraint ?
We consider a nonpreemptive single-machine scheduling problem to minimize mean squared deviation of job completion times about a common due date with maximum tardiness constraint (MSD/Tmax problem), where the common due date is large enough so that it does not constrain the minimization of MSD. The MSD/Tmax problem is classified into three cases according to the value of maximum allowable tardiness ?: ?-unconstrained,?-constrained and tightly?-constrained cases. It is shown that the ?-unconstrained MSD/Tmax problem is equivalent to the unconstrained MSD problem and that the tightly ?-constrained MSD/Tmax problem with common due date d is equivalent to the tightly constrained MSD problem with common due date ?. We also provide bounds to decide when the MSD/Tmax problem is ?-unconstrained or ?-constrained. Then a solution procedure to the MSD/Tmax problem is presented with several examples.
maximum allowable tardiness scheduling theory earliness and tardiness penalties