A single machine scheduling problem with common due window and controllable processing times

A static deterministic single machine scheduling problem with a common due window is considered. Job processing times are controllable to the extent that they can be reduced, up to a certain limit, at a cost proportional to the reduction. The window location and size, along with the associated job schedule that minimizes a certain cost function, are to be determined. This function is made up of costs associated with the window location, its size, processing time reduction as well as job earliness and tardiness. We show that the problem can be formulated as an assignment problem and thus can be solved with well-known algorithms.