Abstract
In a one-machine nonpreemptive scheduling problem, the feasible schedules may be defined by the vector of the corresponding job completion times. For given positive processing times, the associated simple scheduling polyhedronP is the convex hull of these feasible completion time vectors. The main result of this paper is a complete description of the minimal linear system definingP. We also give a complete, combinatorial description of the face lattice ofP, and a simple, O(n logn) separation algorithm. This algorithm has potential usefulness in cutting plane type algorithms for more difficult scheduling problems.
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This research was supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada, and by a Killam University Research Fellowship. The original version of this paper was completed when the author was visiting the Laboratoire d'Automatique et d'Analyse des Systèmes, Toulouse, France.
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Queyranne, M. Structure of a simple scheduling polyhedron. Mathematical Programming 58, 263–285 (1993). https://doi.org/10.1007/BF01581271
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DOI: https://doi.org/10.1007/BF01581271