# Polyhedral Reformulation of a Scheduling Problem And Related Theoretical Results

Jean Damay; Alain Quilliot; Eric Sanlaville

RAIRO - Operations Research (2008)

- Volume: 42, Issue: 3, page 325-359
- ISSN: 0399-0559

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topDamay, Jean, Quilliot, Alain, and Sanlaville, Eric. "Polyhedral Reformulation of a Scheduling Problem And Related Theoretical Results." RAIRO - Operations Research 42.3 (2008): 325-359. <http://eudml.org/doc/250432>.

@article{Damay2008,

abstract = {
We deal here with a scheduling problem GPPCSP (Generalized Parallelism and Preemption Constrained Scheduling Problem) which is an extension of both the well-known Resource Constrained Scheduling Problem and the Scheduling Problem with Disjunctive Constraints. We first propose a reformulation of GPPCSP: according to it, solving GPPCSP means finding a vertex of the Feasible Vertex Subset of an Antichain Polyhedron. Next, we state several theoretical results related to this reformulation process and to structural properties of this specific Feasible Vertex Subset (connectivity, ...). We end by focusing on the preemptive case of GPPCSP and by identifying specific instances of GPPCSP which are such that any vertex of the related Antichain Polyhedron may be projected on its related Feasible Vertex Subset without any deterioration of the makespan. For such an instance, the GPPCSP problem may be solved in a simple way through linear programming.
},

author = {Damay, Jean, Quilliot, Alain, Sanlaville, Eric},

journal = {RAIRO - Operations Research},

keywords = {Partially ordered sets; hypergraphs; linear programming; polyhedra; multiprocessor scheduling; resource constrained project scheduling problem.; partially ordered sets; resource constrained project scheduling problem},

language = {eng},

month = {8},

number = {3},

pages = {325-359},

publisher = {EDP Sciences},

title = {Polyhedral Reformulation of a Scheduling Problem And Related Theoretical Results},

url = {http://eudml.org/doc/250432},

volume = {42},

year = {2008},

}

TY - JOUR

AU - Damay, Jean

AU - Quilliot, Alain

AU - Sanlaville, Eric

TI - Polyhedral Reformulation of a Scheduling Problem And Related Theoretical Results

JO - RAIRO - Operations Research

DA - 2008/8//

PB - EDP Sciences

VL - 42

IS - 3

SP - 325

EP - 359

AB -
We deal here with a scheduling problem GPPCSP (Generalized Parallelism and Preemption Constrained Scheduling Problem) which is an extension of both the well-known Resource Constrained Scheduling Problem and the Scheduling Problem with Disjunctive Constraints. We first propose a reformulation of GPPCSP: according to it, solving GPPCSP means finding a vertex of the Feasible Vertex Subset of an Antichain Polyhedron. Next, we state several theoretical results related to this reformulation process and to structural properties of this specific Feasible Vertex Subset (connectivity, ...). We end by focusing on the preemptive case of GPPCSP and by identifying specific instances of GPPCSP which are such that any vertex of the related Antichain Polyhedron may be projected on its related Feasible Vertex Subset without any deterioration of the makespan. For such an instance, the GPPCSP problem may be solved in a simple way through linear programming.

LA - eng

KW - Partially ordered sets; hypergraphs; linear programming; polyhedra; multiprocessor scheduling; resource constrained project scheduling problem.; partially ordered sets; resource constrained project scheduling problem

UR - http://eudml.org/doc/250432

ER -

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