A lower bound for the job insertion problem

T. Kis, Alain Hertz

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

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
Volume128
Issue number2-3
DOIs
Publication statusPublished - May 1 2003

Fingerprint

Insertion
Computational complexity
Polynomials
Lower bound
Schedule
Job Shop Scheduling
Perfect Graphs
Relaxation Method
Polytope
Polynomial time
NP-complete problem
Minimise
Job shop scheduling

Keywords

  • Job-shop scheduling
  • Perfect graphs
  • Polyhedral methods

ASJC Scopus subject areas

  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Cite this

A lower bound for the job insertion problem. / Kis, T.; Hertz, Alain.

In: Discrete Applied Mathematics, Vol. 128, No. 2-3, 01.05.2003, p. 395-419.

Research output: Contribution to journalArticle

Kis, T. ; Hertz, Alain. / A lower bound for the job insertion problem. In: Discrete Applied Mathematics. 2003 ; Vol. 128, No. 2-3. pp. 395-419.
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