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 l,..., I r called groups, i.e. I = I l I 2 ∪... ∪ I r and I f I g =φ 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:
$${s_{fgk}} + {s_{ghk}}{s_{fhk}}\,for\,all\,f,g,h \in \left\{ {1, \ldots ,r} \right\},k \in \left\{ {1, \ldots ,m} \right\}.$$
(9.1)
Both assumptions are realistic in practice.

Keywords

Transportation 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

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

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