A lower bound for the job insertion problem

Tamás Kis, Alain Hertz

Research output: Contribution to journalArticle

12 Citations (Scopus)


This note deals with the job insertion problem in job-shop scheduling: Given a feasible schedule of n jobs and a new job which is not scheduled, the problem is to find a feasible insertion of the new job into the schedule which minimises the makespan. Since the problem is NP-hard, a relaxation method is proposed to compute a strong lower bound. Conditions under which the relaxation provides us with the makespan of the optimal insertion are derived. After the analysis of the polytope of feasible insertions, a polynomial time procedure is proposed to solve the relaxed problem. Our results are based on the theory of perfect graphs and elements of polyhedral theory.

Original languageEnglish
Pages (from-to)395-419
Number of pages25
JournalDiscrete Applied Mathematics
Issue number2-3
Publication statusPublished - May 1 2003


  • Job-shop scheduling
  • Perfect graphs
  • Polyhedral methods

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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