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 Δ: Δ-unconstrained, Δ-constrained and tightly Δ-constrained cases. It is shown that the Δ-unconstrained MSD/Tmax problem is equivalent to the unconstrained MSD problem and that the tightly Δ-constrained MSD/Tmax problem with common due date d is equivalent to the tightly constrained MSD problem with common due date Δ. We also provide bounds to decide when the MSD/Tmax problem is Δ-unconstrained or Δ-constrained. Then a solution procedure to the MSD/Tmax problem is presented with several examples.
