Common due date assignment for scheduling on a single machine with jointly reducible processing times

This paper focuses on analyzing the problem of assigning a common due date to a set of jobs and scheduling them on a single machine. The processing times of the jobs are assumed to be controllable but contrary to former approaches we consider a situation in which it is only possible to reduce all processing times by the same proportional amount. This situation, which is quite interesting from a practical point of view, has to the best of our knowledge never been under study before. Besides the assignment of the common due date we concentrate on two goals, namely minimizing the sum of earliness and tardiness penalties and minimizing the number of late jobs.