Multiprocessor scheduling under precedence constraints: polyhedral results

Authors:
Pablo E. Coll;Celso C. Ribeiro;Cid C. de Souza
Affiliations:
Universidad de Buenos Aires, Departamento de Computación, Pabellón I, Ciudad Universitaria, Buenos Aires, Argentina;Department of Computer Science, Catholic University of Rio de Janeiro, Rio de Janeiro, RJ, Brazil;University of Campinas, Institute of Computing, Campinas, SP, Brazil
Venue:
Discrete Applied Mathematics - Special issue: IV ALIO/EURO workshop on applied combinatorial optimization
Year:
2006

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Abstract

We consider the problem of scheduling a set of tasks related by precedence constraints to a set of processors, so as to minimize their makespan. Each task has to be assigned to a unique processor and no preemption is allowed. A new integer programming formulation of the problem is given and strong valid inequalities are derived. A subset of the inequalities in this formulation has a strong combinatorial structure, which we use to define the polytope of partitions into linear orders. The facial structure of this polytope is investigated and facet defining inequalities are presented which may be helpful to tighten the integer programming formulation of other variants of multiprocessor scheduling problems. Numerical results on real-life problems are presented.