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Multiprocessor scheduling under precedence constraints: polyhedral results. (English) Zbl 1120.90070
Summary: 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.

90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
90C35 Programming involving graphs or networks
Full Text: DOI
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