Bicriteria models to minimize the total weighted number of tardy jobs with convex controllable processing times and common due date assignment

We study a single-machine scheduling problem in a flexible framework where both job processing times and due dates are decision variables to be determined by the scheduler. The model can also be applied for quoting delivery times when some parts of the jobs may be outsourced. We analyze the problem with common due date assignment and a convex resource consumption function. We provide a bicriteria analysis where the first criterion is to minimize the total weighted number of tardy jobs plus due date assignment cost, and the second criterion is to minimize total weighted resource consumption. We consider four different models for treating the two criteria. Although the problem of minimizing a single integrated objective function can be solved in polynomial time, we prove that the three bicriteria models are NP-hard. We also present special cases which are polynomially solvable and frequently occur in practice.