Parallel-machine scheduling under potential disruption

In this paper, we study a parallel-machine scheduling problem that arises in a disruptive environment. Such a problem deals with a situation when there is a possibility that a disruption will occur at a particular time and if it happens all machines will become unavailable for certain duration with a certain probability. Our goal is to schedule the jobs so that the expected sum of weighted completion times is minimized. We provide pseudo-polynomial time algorithms to solve the problem to optimality.