Changeover Times and Transportation Times

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 ₁ ∪ I ₂ ∪ ... ∪ I _r and I _f ∩ I _g = ø 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:

$${s_{fgk}} + {s_{ghk}}{s_{fgk}}forallf,g,h \in \{ 1,...,r\} ,k \in \{ 1,...,m\} .$$

(9.1)

Both assumptions are realistic in practice.