On Eulerian extensions and their application to no-wait flowshop scheduling

Authors:
Wiebke Höhn;Tobias Jacobs;Nicole Megow
Affiliations:
Technische Universität Berlin, Institut für Mathematik, Berlin, Germany 10623;National Institute of Informatics, Tokyo, Japan 101-8430;Max-Planck-Institut für Informatik, Saarbrücken, Germany 66123
Venue:
Journal of Scheduling
Year:
2012

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Abstract

We consider a variant of no-wait flowshop scheduling that is motivated by continuous casting in the multistage production process in steel manufacturing. The task is to find a feasible schedule with a minimum number of interruptions, i.e., continuous idle time intervals on the last production stage. Based on an interpretation as Eulerian Extension Problems, we fully settle the complexity status of any particular problem case: We give a very intuitive optimal algorithm for scheduling on two processing stages with one machine in the first stage, and we show that all other problem variants are strongly NP-hard. We also discuss alternative idle time related scheduling models and their justification in the considered steel manufacturing environment. Here, we derive constant factor approximations.