On Optimal Common Due-Date Determination

Given a set of n independent jobs to be processed on a singlemachine, the problem is to determine the optimal constant flowallowance for the CON due-date assignment method and the optimaljob sequence to minimize an average missed due-date cost. Alinear programming formulation of the problem is proposed andthe optimal due-date is obtained by solving the LP dual problem.It is shown that the optimal job sequence can be determinedanalytically only under a special circumstance. Finally, a numericalexample is given to demonstrate how the results can be appliedto find the optimal solutions.