Makespan minimization for two parallel machines with unavailability constraints

This paper considers the two-parallel-machine scheduling problem with precedence constraints. One of the machines may not always be available due to machine breakdowns or preventive maintenance during the scheduling period. All execution and communication times between tasks are considered unitary and all unavailability dates are known in advance. The considered task graph (since tasks are related by precedence constraints) is an intree, where each task can have many predecessors but only one successor. The considered objective function in this paper is the makespan denoted C
max
. To solve the problem, a new optimal algorithm entitled Scheduling Intrees with Unavailability constraints (SIwUC) is proposed. The used strategy is to find the best trade-off between the minimization of the communications and the minimization of the difference in load between the processors in order to minimize the makespan. Algorithm details and key ideas proving the optimality of the algorithm are described.