On the complexity of non-preemptive shop scheduling with two jobs

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this note, we investigate the time complexity of non-preemptive shop scheduling problems with two jobs. First we study mixed shop scheduling where one job has a fixed order of operations and the operations of the other job may be executed in arbitrary order. This problem is shown to be binary NP-complete with respect to all traditional optimality criteria even if distinct operations of the same job require different machines. Moreover, we devise a pseudo-polynomial time algorithm which solves the problem with respect to all non-decreasing objective functions. Finally, when the job with fixed order of operations may visit a machine more than once, the problem becomes unary NP-complete. Then we discuss shop scheduling with two jobs having chain-like routings. It is shown that the problem is unary NP-complete with respect to all traditional optimality criteria even if one of the jobs has fixed order of operations and the jobs cannot visit a machine twice.

Original languageEnglish
Pages (from-to)37-49
Number of pages13
JournalComputing
Volume69
Issue number1
DOIs
Publication statusPublished - 2002

Fingerprint

Scheduling
NP-complete problem
Unary
Optimality Criteria
Polynomials
Polynomial-time Algorithm
Time Complexity
Scheduling Problem
Routing
Objective function
Binary
Distinct
Arbitrary

Keywords

  • Computational complexity
  • Mixed shop scheduling
  • Pseudo-polynomial time algorithm

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics

Cite this

On the complexity of non-preemptive shop scheduling with two jobs. / Kis, T.

In: Computing, Vol. 69, No. 1, 2002, p. 37-49.

Research output: Contribution to journalArticle

@article{622987983fbd424db92f36fb019e63b1,
title = "On the complexity of non-preemptive shop scheduling with two jobs",
abstract = "In this note, we investigate the time complexity of non-preemptive shop scheduling problems with two jobs. First we study mixed shop scheduling where one job has a fixed order of operations and the operations of the other job may be executed in arbitrary order. This problem is shown to be binary NP-complete with respect to all traditional optimality criteria even if distinct operations of the same job require different machines. Moreover, we devise a pseudo-polynomial time algorithm which solves the problem with respect to all non-decreasing objective functions. Finally, when the job with fixed order of operations may visit a machine more than once, the problem becomes unary NP-complete. Then we discuss shop scheduling with two jobs having chain-like routings. It is shown that the problem is unary NP-complete with respect to all traditional optimality criteria even if one of the jobs has fixed order of operations and the jobs cannot visit a machine twice.",
keywords = "Computational complexity, Mixed shop scheduling, Pseudo-polynomial time algorithm",
author = "T. Kis",
year = "2002",
doi = "10.1007/s00607-002-1455-z",
language = "English",
volume = "69",
pages = "37--49",
journal = "Computing (Vienna/New York)",
issn = "0010-485X",
publisher = "Springer Wien",
number = "1",

}

TY - JOUR

T1 - On the complexity of non-preemptive shop scheduling with two jobs

AU - Kis, T.

PY - 2002

Y1 - 2002

N2 - In this note, we investigate the time complexity of non-preemptive shop scheduling problems with two jobs. First we study mixed shop scheduling where one job has a fixed order of operations and the operations of the other job may be executed in arbitrary order. This problem is shown to be binary NP-complete with respect to all traditional optimality criteria even if distinct operations of the same job require different machines. Moreover, we devise a pseudo-polynomial time algorithm which solves the problem with respect to all non-decreasing objective functions. Finally, when the job with fixed order of operations may visit a machine more than once, the problem becomes unary NP-complete. Then we discuss shop scheduling with two jobs having chain-like routings. It is shown that the problem is unary NP-complete with respect to all traditional optimality criteria even if one of the jobs has fixed order of operations and the jobs cannot visit a machine twice.

AB - In this note, we investigate the time complexity of non-preemptive shop scheduling problems with two jobs. First we study mixed shop scheduling where one job has a fixed order of operations and the operations of the other job may be executed in arbitrary order. This problem is shown to be binary NP-complete with respect to all traditional optimality criteria even if distinct operations of the same job require different machines. Moreover, we devise a pseudo-polynomial time algorithm which solves the problem with respect to all non-decreasing objective functions. Finally, when the job with fixed order of operations may visit a machine more than once, the problem becomes unary NP-complete. Then we discuss shop scheduling with two jobs having chain-like routings. It is shown that the problem is unary NP-complete with respect to all traditional optimality criteria even if one of the jobs has fixed order of operations and the jobs cannot visit a machine twice.

KW - Computational complexity

KW - Mixed shop scheduling

KW - Pseudo-polynomial time algorithm

UR - http://www.scopus.com/inward/record.url?scp=0036392349&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036392349&partnerID=8YFLogxK

U2 - 10.1007/s00607-002-1455-z

DO - 10.1007/s00607-002-1455-z

M3 - Article

AN - SCOPUS:0036392349

VL - 69

SP - 37

EP - 49

JO - Computing (Vienna/New York)

JF - Computing (Vienna/New York)

SN - 0010-485X

IS - 1

ER -