## A generalized job-shop problem with more than one resource demand per task

We study a generalized job-shop problem called the Laser Sharing Problem with fixed tours (LSP-T) where the tasks may need more than one resource simultaneously. This fact will be used to model possible collisions between industrial robots. For three robots we will show that the special case where only one resource is used by more than one robot is already NP-hard. This also implies that one machine scheduling with chained min delay precedence constraints is NP-hard for at least three chains. OnWe study a generalized job-shop problem called the Laser Sharing Problem with fixed tours (LSP-T) where the tasks may need more than one resource simultaneously. This fact will be used to model possible collisions between industrial robots. For three robots we will show that the special case where only one resource is used by more than one robot is already NP-hard. This also implies that one machine scheduling with chained min delay precedence constraints is NP-hard for at least three chains. On the positive side, we present a polynomial algorithm for the two robot case and a pseudo-polynomial algorithm together with an FPTAS for an arbitrary but constant number of robots. This gives a sharp boundary of the complexity status for a constant number of robots.…

Institutes: | Mathematik |
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Author: | Joachim Schauer, Cornelius Schwarz |

Creating Corporation: | Universität Bayreuth, Mathematisches Institut |

Contributing Corporation: | Universität Graz, Institut für Statistik und Operations Research |

Year of Completion: | 2011 |

SWD-Keyword: | Approximationsalgorithmus; Kombinatorische Optimierung; Komplexitaet; Reihenfolgeproblem |

Tag: | FPTAS; complexity; job-shop; transversal graph |

Dewey Decimal Classification: | 510 Mathematik |

URN: | urn:nbn:de:bvb:703-opus-8381 |

Document Type: | Preprint |

Language: | English |

Date of Publication (online): | 04.04.2011 |