Mathematical Programming

, Volume 58, Issue 1, pp 263–285

Structure of a simple scheduling polyhedron

  • Maurice Queyranne

DOI: 10.1007/BF01581271

Cite this article as:
Queyranne, M. Mathematical Programming (1993) 58: 263. doi:10.1007/BF01581271


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.

Key words

Scheduling polyhedronpolyhedrascheduling

Copyright information

© The Mathematical Programming Society, Inc. 1993

Authors and Affiliations

  • Maurice Queyranne
    • 1
  1. 1.University of British ColumbiaVancouverCanada