Single Machine Scheduling with Precedence Constraints

  • José R. Correa
  • Andreas S. Schulz
Conference paper

DOI: 10.1007/978-3-540-25960-2_22

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

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • José R. Correa
    • 1
  • Andreas S. Schulz
    • 1
  1. 1.Operations Research CenterMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations