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 classi®ed into three cases according to the value of maximum allowable tardiness D: D-unconstrained, D-constrained and tightly D-constrained cases. It is shown that the D-unconstrained MSD=Tmax problem is equivalent to the unconstrained MSD problem and that the tightly D-constrained MSD/Tmax problem with common due date d is equivalent to the tightly constrained MSD problem with common due date D. We also provide bounds to decide when the MSD/Tmax problem is D-unconstrained or D-constrained. Then a solution procedure to the MSD/Tmax problem is presented with several examples. Ó 2001 Elsevier Science B.V. All rights reserved.