Stiller, SebastianWiese, Andreas2021-12-172021-12-1720102197-8085https://depositonce.tu-berlin.de/handle/11303/15698http://dx.doi.org/10.14279/depositonce-14471Network flows and scheduling have been studied intensely, but separately. In many applications a joint optimization model for routing and scheduling is desireable. Therefore, we study flows over time with a demand split into jobs. The objective is to minimize the weighted sum of completion times of these jobs. This is closely related to preemptive scheduling on a single machine with a processing speed increasing over time. For both, flow scheduling and increasing speed scheduling, we provide an EPTAS. Without release dates we can proof a tight approximation factor of (sqrt{3}+1)/2 for Smith's rule, by fully characterizing the worst case instances. We give exact algorithms for some special cases and a dynamic program for speed functions with a constant number of speeds. We can proof a competitive ratio of 2 for the online version. We also study the class of blind algorithms, i.e., those which schedule without knowledge of the speed function. For both online, and blind algorithm we provide a lower bound.en510 Mathematikdynamic flowsearliest arrival flowsscheduling with varying speedweighted sum of completion timesapproximation algorithmsResearch Paper