A Computational Study of the Two-Machine No-Wait Flow Shop Scheduling Problem Subject to Unequal Release Dates and Non-Availability Constraints

We consider the problem of scheduling a set of jobs subject to unequal release dates on a two-machine flow shop where the no-wait and non-availability constraints are considered so as to minimize the makespan. The contribution of this paper is two-fold. First, we propose a new mathematical formulation for the problem and derive valid inequalities. Second, we propose new lower bounds that are based on single and two-machine relaxations. These lower bounds are embedded onto a branch-and-bound algorithm enhanced by elimination and dominance rules. Computational results show that our exact methods consistently outperform the state-of-the-art branch-and-bound procedure.