Minimizing the maximum deviation of job completion time about a common due-date

Given a set of n jobs with deterministic processing times and the same ready times, the problem is to find the optimal common due-date k*and the optimal job sequences σ*to minimize the maximum deviation of job completion time about the common due-date. It is shown that the problem can be formulated as an equivalent linear programming (LP) minimization problem. Using the strong duality property of LP, we derive the optimal due-date by considering the dual of the LP problem. When the optimal due-date is determined the optimal job sequence is readily available. After the theoretical treatment numerical examples are presented to demonstrate the validity of the theories.