On the solution region for certain scheduling problems with preemption

The paper deals with parallel machine and open shop scheduling problems with preemptions and an arbitrary nondecreasing objective function. An approach to describing the solution region for these problems and to reducing them to minimization over polytopes is proposed. Properties of the solution regions for certain problems are investigated. It is proved that open shop problems with unit processing times are equivalent to certain parallel machine problems, where preemption is allowed at arbitrary times. A polynomial algorithm is presented, transforming a schedule of one type into a schedule of the other type.