On optimal common due-date determination

Given a set of n independent jobs to be processed on a single machine, the problem is to determine the optimal constant flow allowance for the CON due-date assignment method and the optimal job sequence to minimize an average missed due-date cost. A linear programming formulation of the problem is proposed and the optimal due-date is obtained by solving the LP dual problem. It is shown that the optimal job sequence can be determined analytically only under a special circumstance. Finally, a numerical example is given to demonstrate how the results can be applied to find the optimal solutions.