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Near-optimal solutions and large integrality gaps for almost all instances of single-machine precedence-constrained scheduling

Author(s)
Schulz, Andreas S.; Uhan, Nelson A.
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Abstract
We consider the problem of minimizing the weighted sum of completion times on a single machine subject to bipartite precedence constraints in which all minimal jobs have unit processing time and zero weight, and all maximal jobs have zero processing time and unit weight. For various probability distributions over these instances—including the uniform distribution—we show several “almost all”-type results. First, we show that almost all instances are prime with respect to a well-studied decomposition for this scheduling problem. Second, we show that for almost all instances, every feasible schedule is arbitrarily close to optimal. Finally, for almost all instances, we give a lower bound on the integrality gap of various linear programming relaxations of this problem.
Date issued
2011-02
URI
http://hdl.handle.net/1721.1/67660
Department
Massachusetts Institute of Technology. Operations Research Center; Sloan School of Management
Journal
Mathematics of Operations Research
Publisher
INFORMS
Citation
Schulz, A. S., and N. A. Uhan. “Near-Optimal Solutions and Large Integrality Gaps for Almost All Instances of Single-Machine Precedence-Constrained Scheduling.” Mathematics of Operations Research 36.1 (2011)
Version: Author's final manuscript
ISSN
0364-765X
1526-5471

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