Minimizing schedule length subject to minimum flow time
SIAM Journal on Computing
Preemptive scheduling with variable profile, precedence constraints and due dates
Discrete Applied Mathematics
Scheduling with Unexpected Machine Breakdowns
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
Minimizing Total Completion Time on Parallel Machines with Deadline Constraints
SIAM Journal on Computing
Multicriteria Scheduling: Theory, Models and Algorithms
Multicriteria Scheduling: Theory, Models and Algorithms
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In the past, research on multiple criteria scheduling assumes that the number of available machines is fixed during the whole scheduling horizon and research on scheduling with limited machine availability assumes that there is only a single criterion that needs to be optimized. Both assumptions may not hold in real life. In this paper we simultaneously consider both bicriteria scheduling and scheduling with limited machine availability. We focus on two parallel machines' environment and the goal is to find preemptive schedules to optimize both makespan and total completion time subject to machine availability. Our main contribution in this paper is that we showed three bicriteria scheduling problems are in P by providing polynomial time optimal algorithms.