Principles of Sequencing and Scheduling by Kenneth R. Baker & Dan Trietsch

Author:Kenneth R. Baker & Dan Trietsch
Language: eng
Format: epub
ISBN: 9781119262596
Publisher: Wiley
Published: 2018-10-16T00:00:00+00:00

10.3 Consider the following three‐job flow shop example.

Job j 1 2 3

aj 4 4 3

bj 7 1 2

Show that Johnson’s condition is not necessary for optimality in the two‐machine makespan problem.

10.4 Show that the jobs in the sequence produced by Algorithm 10.2 will satisfy Johnson’s rule; that is, if job i precedes job j in that sequence, then min{ai, bj} ≤ min{aj, bi}.

10.5 Consider the two‐machine problem with makespan objective and setup times. Suppose that the setup times are separable – that is, setups may be scheduled in anticipation of arriving jobs. Show that the rule for constructing an optimal sequence takes the following form:

where e1i (e2i) denotes the initial (final) idle time on machine 2 (machine 1) when job i is scheduled by itself.

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