## Abstract

In this chapter we consider scheduling problems in which the set Both assumptions are realistic in practice.

*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*},*f*≠*g*. 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*i*∈*I*_{ f }and*j*∈*I*_{ 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)

### Keywords

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## Copyright information

© Springer-Verlag Berlin Heidelberg 1998