# Facets of the Generalized Permutahedron of a Poset

@article{Arnim1997FacetsOT, title={Facets of the Generalized Permutahedron of a Poset}, author={Annelie von Arnim and A. Schulz}, journal={Discret. Appl. Math.}, year={1997}, volume={72}, pages={179-192} }

Abstract Given a poset P as a precedence relation on a set of jobs with processing time vector p, the generalized permutahedron perm(P, p) of P is defined as the convex hull of all job completion time vectors corresponding to a linear extension of P. Thus, the generalized permutahedron allows for the single machine weighted flowtime scheduling problem to be formulated as a linear programming problem over perm(P, p). Queyranne and Wang [8]as well as von Arnim and Schrader [2]gave a collection of… CONTINUE READING

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13 Citations

Base polytopes of series—parallel posets: Linear description and optimization

- Mathematics, Computer Science
- 1998

7

Approximation Bounds for a General Class of Precedence Constrained Parallel Machine Scheduling Problems

- Computer Science
- 1998

65

Scheduling Unit Jobs with Compatible Release Dates on Parallel Machines with Nonstationary Speeds

- Computer Science
- 1995

33

Approximation Bounds for a General Class of Precedence Constrained Parallel Machine Scheduling Problems

- Computer Science, Mathematics
- 2006

30

Scheduling to Minimize Average Completion Time: Off-Line and On-Line Approximation Algorithms

- Mathematics, Computer Science
- 1997

460

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 35 REFERENCES

Sequencing Jobs to Minimize Total Weighted Completion Time Subject to Precedence Constraints

- Mathematics
- 1978

274

Polyedrische Charakterisierung von Scheduling Problemen, Diploma Thesis, Department of Mathematics

- 1993

Single{Machine Scheduling Polyhedra with Precedence Con- straints

- 1991

A Cutting Plane Procedure for Precedence{Constrained Sin- gle Machine Scheduling, Preprint, Faculty of Commerce, University of British Columbia

- 1991

A Cutting Plane Procedure for Precedence{Constrained Single Machine Scheduling

- 1991