A branch-and-bound method 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. We aim to minimize the maximum delivery time under the nonresumable senario. This problem is strongly NP-hard. The proposed algorithm is based on a branch-and-bound method. We use Jackson’s preemptive algorithm with precedence constraints to compute the lower bound and Schrage’s sequence as an upper bound. Numerical experiments show that the algorithm can solve large-size instances with up to 1000 jobs.