An iterative lower bound algorithm for the single-machine scheduling problem under a non-availability constraint for maximum delivery time minimization

We consider the single machine scheduling problem with release dates and tails, provided that the machine is unavailable during a fixed interval. This problem is strongly NP-hard. We use the Jackson´s preemptive algorithm with precedence constraints to compute a lower bound and the Schrage´s sequence as an upper bound. Then, we propose an improved lower bound which is based on an iterative procedure. Numerical experiments show the effectiveness of the bounds.