Single machine flow-time scheduling with a single breakdown
Acta Informatica
Scheduling with release dates on a single machine to minimize total weighted completion time
Discrete Applied Mathematics
Single machine flow-time scheduling with scheduled maintenance
Acta Informatica
Algorithms for Scheduling Independent Tasks
Journal of the ACM (JACM)
Improved algorithms for two single machine scheduling problems
Theoretical Computer Science - Algorithmic applications in management
Note: A note on worst-case performance of heuristics for maintenance scheduling problems
Discrete Applied Mathematics
Computers and Industrial Engineering
A survey of scheduling with deterministic machine availability constraints
Computers and Industrial Engineering
Approximation schemes for parallel machine scheduling with availability constraints
Discrete Applied Mathematics
Computers and Industrial Engineering
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This paper is the first attempt to successfully design efficient approximation algorithms for the single-machine weighted flow-time minimization problem when jobs have different release dates and weights equal to their processing times under the assumption that one job is fixed (i.e., the machine is unavailable during a fixed interval corresponding to the fixed job). Our work is motivated by an interesting algorithmic application to the generation of valid inequalities in a branch-and-cut method. Our analysis shows that the trivial FIFO sequence can lead to an arbitrary large worst-case performance bound. Hence, we modify this sequence so that a new 2-approximation solution can be obtained for every instance and we prove the tightness of this bound. Then, we propose a fully polynomial-time approximation algorithm with efficient running time for the considered problem. Especially, the complexity of our algorithm is strongly polynomial.