COMPLEXITY OF FLOWSHOP AND JOBSHOP SCHEDULING.

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

Research output: Contribution to journalArticle

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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
DOIs
StatePublished - Jan 1 1976
Externally publishedYes

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ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research

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