A cyclic production problem: an application of max-algebra

W.M. Nawijn

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Given are m identical machines, each of which performs the same N operations Oi, 1 ≤ i ≤ N, cyclically and indefinitely, i.e. a production run on a machine looksO1, O2,…,ON, O1, O2,…,ON, O1…. There are nim to to perform operation Oi. The tools are transported between the machines by means of an infinitely fast transport device. Given a particular transport policy we prove the existence of stationary cyclic behaviour, determine the corresponding cycle time, and investigate the long run behaviour of the system starting from a given initial state.
Original languageUndefined
Pages (from-to)187-200
Number of pages14
JournalEuropean journal of operational research
Volume104
Issue number1
DOIs
Publication statusPublished - 1998

Keywords

  • Production
  • Eigenvalue problem
  • Knapsack function
  • METIS-140558
  • Cycle time
  • Minimax-algebra
  • IR-73917

Cite this

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A cyclic production problem: an application of max-algebra. / Nawijn, W.M.

In: European journal of operational research, Vol. 104, No. 1, 1998, p. 187-200.

Research output: Contribution to journalArticleAcademicpeer-review

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AB - Given are m identical machines, each of which performs the same N operations Oi, 1 ≤ i ≤ N, cyclically and indefinitely, i.e. a production run on a machine looksO1, O2,…,ON, O1, O2,…,ON, O1…. There are nim to to perform operation Oi. The tools are transported between the machines by means of an infinitely fast transport device. Given a particular transport policy we prove the existence of stationary cyclic behaviour, determine the corresponding cycle time, and investigate the long run behaviour of the system starting from a given initial state.

KW - Production

KW - Eigenvalue problem

KW - Knapsack function

KW - METIS-140558

KW - Cycle time

KW - Minimax-algebra

KW - IR-73917

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DO - 10.1016/S0377-2217(96)00336-0

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EP - 200

JO - European journal of operational research

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