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International Conference on Integer Programming and Combinatorial Optimization

IPCO 2004: Integer Programming and Combinatorial Optimization pp 283–297Cite as

Single Machine Scheduling with Precedence Constraints

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3064))

Abstract

We discuss the problem of sequencing precedence-constrained jobs on a single machine to minimize the average weighted completion time. This problem has attracted much attention in the mathematical programming community since Sidney’s pioneering work in 1975. We look at the problem from a polyhedral perspective and uncover a relation between Sidney’s decomposition theorem and different linear programming relaxations. More specifically, we present a generalization of Sidney’s result, which particularly allows us to reason that virtually all known 2-approximation algorithms comply with his decomposition. Moreover, we establish a connection between the single-machine scheduling problem and the vertex cover problem. Indeed, in the special case of series-parallel precedence constraints, we prove that the sequencing problem can be seen as a special case of vertex cover. We also argue that this result is true for general precedence constraints if one can show that a certain integer program represents a valid formulation of the sequencing problem. Finally, we provide a characterization of the active inequalities of a linear programming relaxation in completion time variables.

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Authors and Affiliations

  1. Operations Research Center, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139-4307, USA

    José R. Correa & Andreas S. Schulz

Authors
  1. José R. Correa
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  2. Andreas S. Schulz
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Editors and Affiliations

  1. Department of IEOR, Columbia University, 500 West 120th Street, 10027, New York, NY, USA

    Daniel Bienstock

  2. H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, USA

    George Nemhauser

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© 2004 Springer-Verlag Berlin Heidelberg

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Correa, J.R., Schulz, A.S. (2004). Single Machine Scheduling with Precedence Constraints. In: Bienstock, D., Nemhauser, G. (eds) Integer Programming and Combinatorial Optimization. IPCO 2004. Lecture Notes in Computer Science, vol 3064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25960-2_22

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  • DOI: https://doi.org/10.1007/978-3-540-25960-2_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22113-5

  • Online ISBN: 978-3-540-25960-2

  • eBook Packages: Springer Book Archive

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