Minimizing Total Completion Time in Flowshop with Availability Constraint on the First Machine

We study the problem of minimizing total completion time in 2-stage flowshop with availability constraint. This problem is NP-hard in the strong sense even if both machines are always available. With availability constraint, although a bulk of research papers have studied the makespan minimization problem, there is no research done on the total completion time minimization. This paper is the first attempt to tackle this problem. We focus on the case that there is a single unavailable interval on the first machine only. We show that several special cases can be solved optimally or approximated within a constant factor. For the general case, we develop some lower hounds and dominance rules. Then we design and implement a branch and bound algorithm. We investigate the effectiveness of different lower bounds and the dominance rules by computational experiments. We also study how the start time and the duration of the unavailable interval affects the efficiency of the branch and hound algorithm.