Schedules with due-date assignment and position-dependent processing times

Single machine scheduling problems are considered, in which the processing of jobs depend on positions of the jobs in a schedule and the due-dates are assigned either according to the CON rule (a due-date common to all jobs is chosen) or according to the SLK rule (the due-dates are computed by increasing the actual processing times of each job by a slack, common to all jobs). Polynomial-time dynamic programming algorithms are proposed for the problems with the objective functions that include the cost of assigning the due-dates, the total cost of disgarded jobs (which are not scheduled) and, possibly, the total earliness of the scheduled jobs.

Single machine scheduling and due date assignment with positionally dependent processing times

We consider single machine scheduling and due date assignment problems in which the processing time of a job depends on its position in a processing sequence. The objective functions include the cost of changing the due dates, the total cost of discarded jobs that cannot be completed by their due dates and, possibly, the total earliness of the scheduled jobs. We present polynomial-time dynamic programming algorithms in the case of two popular due date assignment methods: CON and SLK. The considered problems are related to mathematical models of cooperation between the manufacturer and the customer in supply chain scheduling.