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

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. The first author is supported by the Deutsche Forschungsgemeinschaft (DFG) as part of the Priority Program “Algorithm Engineering” (1307). The second author is supported by a fellowship within the Postdoc-Programme of the German Academic Exchange Service (DAAD). W. Höhn ( ) Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623 Berlin, Germany e-mail: [email protected] T. Jacobs National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan e-mail: [email protected] N. Megow Max-Planck-Institut für Informatik, Campus E1 4, 66123 Saarbrücken, Germany e-mail: [email protected]