Changeover Times and Transportation Times

  • Peter Brucker

Abstract

In this chapter we consider scheduling problems in which the set I of all jobs or all operations (in connection with shop problems) is partitioned into disjoint sets I 1, ... , I r called groups, i.e. I = I 1I 2 ∪ ... ∪ I r and I f I g = ø for f, g ∈ {1, ... , r}, fg. Let N j be the number of jobs in I j . Furthermore, we have the additional restrictions that for any two jobs (operations) i, j with iI f and jI g to be processed on the same machine M k , job (operation) j cannot be started until s fgk time units after the finishing time of job (operation) i, or job (operation) i cannot be started until s gfk time units after the finishing time of job (operation) j. In a typical application, the groups correspond to different types of jobs (operations) and s fgk may be interpreted as a machine dependent changeover time. During the changeover period, the machine cannot process another job. We assume that s fgk = 0 for all f, g ∈ {1, ... , r}, k ∈ {1, ... , m} with f = g, and that the triangle inequality holds:
$${s_{fgk}} + {s_{ghk}}{s_{fgk}}forallf,g,h \in \{ 1,...,r\} ,k \in \{ 1,...,m\} .$$
(9.1)
Both assumptions are realistic in practice.

Keywords

Transportation 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Peter Brucker
    • 1
  1. 1.Fachbereich Mathematik/InformatikUniversität OsnabrückOsnabrückGermany

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