Integrality Property in Preemptive Parallel Machine Scheduling

@inproceedings{Baptiste2009IntegralityPI,
  title={Integrality Property in Preemptive Parallel Machine Scheduling},
  author={Philippe Baptiste and Jacques Carlier and Alexander V. Kononov and Maurice Queyranne and Sergey Sevastyanov and Maxim Sviridenko},
  booktitle={CSR},
  year={2009}
}
We consider parallel machine scheduling problems with identical machines and preemption allowed. It is shown that every such problem with chain precedence constraints and release dates and an integer-concave objective function satisfies the following integrality property : for any problem instance with integral data there exists an optimal schedule where all interruptions occur at integral dates. As a straightforward consequence of this result, for a wide class of scheduling problems with unit… 
2 Citations

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References

SHOWING 1-10 OF 28 REFERENCES

Rational preemptive scheduling

In scheduling jobs subject to precedence constraints that form a partial order, it is advantageous to interrupt (preempt) jobs, and return to complete them at a later time in order to minimize total

On preemption redundancy in scheduling unit processing time jobs on two parallel machines

On Preemptive Scheduling of Unrelated Parallel Processors by Linear Programming

TLDR
It is shown that no more than O(m 2) preemptions are necessary, in order to schedule n jobs on m unrelated processors so as to minimize makespan.

Minimizing Total Tardiness on a Single Machine with Precedence Constraints

TLDR
It is shown that the problem of minimizing the total tardiness for a set of unit-processing-time jobs on a single machine is NP-hard even for aset of chains, which gives a sharp boundary for the complexity of this problem.

Scheduling Chain-Structured Tasks to Minimize Makespan and Mean Flow Time

How useful are preemptive schedules?

Sequencing and scheduling: algorithms and complexity

TLDR
This survey focuses on the area of deterministic machine scheduling, and reviews complexity results and optimization and approximation algorithms for problems involving a single machine, parallel machines, open shops, flow shops and job shops.