Bi-criteria Scheduling on Multiple Machines Subject to Machine Availability Constraints

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This paper studies bi-criteria scheduling problems on m parallel machines with machine unavailable intervals. The goal is to minimize the total completion time subject to the constraint that the makespan is at most a constant T. We study two different unavailability models. In the first model, each machine has a single unavailable interval which starts from time 0. In the second model, each machine can have multiple unavailable intervals, but at any time, there is at most one machine unavailable. For each model, we show that there is an optimal polynomial time algorithm.