A note on $${\mathbb {NP}}$$NP-hardness of preemptive mean flow-time scheduling for parallel machines

@article{BellenguezMorineau2015ANO,
  title={A note on \$\$\{\mathbb \{NP\}\}\$\$NP-hardness of preemptive mean flow-time scheduling for parallel machines},
  author={Odile Bellenguez-Morineau and Marek Chrobak and Christoph D{\"u}rr and Damien Prot},
  journal={Journal of Scheduling},
  year={2015},
  volume={18},
  pages={299-304}
}
In the paper “The complexity of mean flow time scheduling problems with release times”, by Baptiste, Brucker, Chrobak, Dürr, Kravchenko and Sourd, the authors claimed to prove strong $${\mathbb {NP}}$$NP-hardness of the scheduling problem $$P|{\textit{pmtn}},r_j|\sum C_j$$P|pmtn,rj|∑Cj, namely multiprocessor preemptive scheduling where the objective is to minimize the mean flow time. We point out a serious error in their proof and give a new proof of strong $${\mathbb {NP}}$$NP-hardness for… 

Integer Programming for Scheduling Computation Alternative Machines Parallel Multi Operations

TLDR
The programming results show that a feasible solution with a weighted total tardiness measure size of eight is found, using a numerical example consisting of four multi-operation jobs and several machine alternatives in mathematical software Lingo 9.

References

SHOWING 1-4 OF 4 REFERENCES

Minimizing Mean Flow Time with Release Time Constraint

The complexity of mean flow time scheduling problems with release times

TLDR
This paper shows that when all jobs have equal processing times then the problem can be solved in polynomial time using linear programming, and shows that the problem is unary NP-hard.

Scheduling with Deadlines and Loss Functions

The problem of this paper is that of scheduling several one-stage tasks on several processors, which are capable of handling the tasks with varying degrees of efficiency, to minimize the total loss,