### Abstract

NP-complete problems form an extensive equivalence class of combinatorial problems for which no nonenumerative algorithms are known. The first result shows that determining a shortest-length schedule in an m-machine flowshop is NP-complete for m greater than equivalent to 3. (For m equals 2, there is an efficient algorithm for finding such schedules). The second result shows that determining a minimum mean-flow-time schedule in an m-machine flowshop is NP-complete for every m greater than equivalent to 2. Finally, it is shown that the shortest-length schedule problem for an m-machine jobshop is NP-complete for every m greater than equivalent to 2. The results are strong in that they hold whether the problem size is measured by number of tasks, number of bits required to express the task lengths, or by the sum of the task lengths.

Original language | English (US) |
---|---|

Pages (from-to) | 117-129 |

Number of pages | 13 |

Journal | Mathematics of Operations Research |

Volume | 1 |

Issue number | 2 |

State | Published - May 1976 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Management Science and Operations Research
- Mathematics(all)
- Applied Mathematics

### Cite this

*Mathematics of Operations Research*,

*1*(2), 117-129.

**COMPLEXITY OF FLOWSHOP AND JOBSHOP SCHEDULING.** / Garey, M. R.; Johnson, D. S.; Sethi, Ravi.

Research output: Contribution to journal › Article

*Mathematics of Operations Research*, vol. 1, no. 2, pp. 117-129.

}

TY - JOUR

T1 - COMPLEXITY OF FLOWSHOP AND JOBSHOP SCHEDULING.

AU - Garey, M. R.

AU - Johnson, D. S.

AU - Sethi, Ravi

PY - 1976/5

Y1 - 1976/5

N2 - NP-complete problems form an extensive equivalence class of combinatorial problems for which no nonenumerative algorithms are known. The first result shows that determining a shortest-length schedule in an m-machine flowshop is NP-complete for m greater than equivalent to 3. (For m equals 2, there is an efficient algorithm for finding such schedules). The second result shows that determining a minimum mean-flow-time schedule in an m-machine flowshop is NP-complete for every m greater than equivalent to 2. Finally, it is shown that the shortest-length schedule problem for an m-machine jobshop is NP-complete for every m greater than equivalent to 2. The results are strong in that they hold whether the problem size is measured by number of tasks, number of bits required to express the task lengths, or by the sum of the task lengths.

AB - NP-complete problems form an extensive equivalence class of combinatorial problems for which no nonenumerative algorithms are known. The first result shows that determining a shortest-length schedule in an m-machine flowshop is NP-complete for m greater than equivalent to 3. (For m equals 2, there is an efficient algorithm for finding such schedules). The second result shows that determining a minimum mean-flow-time schedule in an m-machine flowshop is NP-complete for every m greater than equivalent to 2. Finally, it is shown that the shortest-length schedule problem for an m-machine jobshop is NP-complete for every m greater than equivalent to 2. The results are strong in that they hold whether the problem size is measured by number of tasks, number of bits required to express the task lengths, or by the sum of the task lengths.

UR - http://www.scopus.com/inward/record.url?scp=0016952078&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0016952078&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0016952078

VL - 1

SP - 117

EP - 129

JO - Mathematics of Operations Research

JF - Mathematics of Operations Research

SN - 0364-765X

IS - 2

ER -