Optimal due date assignment and resource allocation to minimize the weighted number of tardy jobs on a single machine

With the increased emphasis on the effective management of operational issues in supply chains, the timely delivery of products has become even more important. Companies have to quote attainable delivery dates and then meet these, or face large tardiness penalties. We study systems that can be modeled by single–machine scheduling problems with due date assignment and controllable job–processing times, which are either linear or convex functions of the amount of a continuously divisible and nonrenewable resource that is allocated to the task. The due date assignment methods studied include the common due date, the slack due date, which reflects equal waiting time allowance for the jobs, and the most general method of unrestricted due dates, when each job may be assigned a different due date. For each combination of due date assignment method and processing–time function, we provide a polynomial–time algorithm to find the optimal job sequence, due date values, and resource allocations that minimize an integrated objective function, which includes the weighted number of tardy jobs, and due date assignment, makespan, and total resource consumption costs.