Makespan minimization for two parallel machines with an availability constraint

In this paper, we consider a two parallel machine problem where one machine is not available during a time period. The unavailable time period is fixed and known in advance. A machine is not available probably because it needs preventive maintenance or periodical repair. The objective of the problem is to minimize the makespan. For both nonresumable and resumable cases, we partition the problem into four sub-problems, each of which is solved optimally by an algorithm. Although all the algorithms have exponential time complexities, they are quite efficient in solving large-sized problems.