Thumbnail Image

On Eulerian Extension Problems and their Application to Sequencing Problems

Höhn, Wiebke; Jacobs, Tobias; Megow, Nicole

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

We introduce a new technique for solving several sequencing problems. We consider Gilmore and Gomory's variant of the Traveling Salesman Problem and two variants of no-wait two-stage flowshop scheduling, the classical makespan minimization problem and a new problem arising in the multistage production process in steel manufacturing. Our technique is based on an intuitive interpretation of sequencing problems as Eulerian Extension Problems. This view reveals new structural insights and leads to elegant and simple algorithms and proofs for this ancient type of problems. As a major effect, we compute not only a single solution; instead, we represent the entire space of optimal solutions. For the new flowshop scheduling problem we give a full complexity classification for any machine configuration.