COMPLEXITY OF FLOWSHOP AND JOBSHOP SCHEDULING.

M. R. Garey, D. S. Johnson, Ravi Sethi

Research output: Contribution to journalArticle

1686 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)117-129
Number of pages13
JournalMathematics of Operations Research
Volume1
Issue number2
StatePublished - May 1976
Externally publishedYes

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Job Shop Scheduling
Flow Shop Scheduling
Schedule
NP-complete problem
Scheduling
Equivalence classes
Flow Shop
Computational complexity
Job Shop
Flow Time
Combinatorial Problems
Equivalence class
Express
Efficient Algorithms
NP-complete
Flow shop scheduling
Job shop scheduling
Flow shop

ASJC Scopus subject areas

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

Cite this

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

In: Mathematics of Operations Research, Vol. 1, No. 2, 05.1976, p. 117-129.

Research output: Contribution to journalArticle

Garey, MR, Johnson, DS & Sethi, R 1976, 'COMPLEXITY OF FLOWSHOP AND JOBSHOP SCHEDULING.', Mathematics of Operations Research, vol. 1, no. 2, pp. 117-129.
Garey, M. R. ; Johnson, D. S. ; Sethi, Ravi. / COMPLEXITY OF FLOWSHOP AND JOBSHOP SCHEDULING. In: Mathematics of Operations Research. 1976 ; Vol. 1, No. 2. pp. 117-129.
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