Scheduling, the task of producing a time table for resources and tasks, is well-known to be a difficult problem the more resources are involved (a NP-hard problem). This is about to become an issue in Radio astronomy as observatories consisting of hundreds to thousands of telescopes are planned and operated.

The Square Kilometre Array (SKA), which Australia and New Zealand bid to host, is aiming for scales where current approaches -- in construction, operation but also scheduling -- are insufficent. Although manual scheduling is common today, the problem is becoming complicated by the demand for (1) independent sub-arrays doing simultaneous observations, which requires the scheduler to plan parallel observations and (2) dynamic re-scheduling on changed conditions. Both of these requirements apply to the SKA, especially in the construction phase.

We review the scheduling approaches taken in the astronomy literature, as well as investigate techniques from human schedulers and today's observatories. The scheduling problem is specified in general for scientific observations and in particular on radio telescope arrays. Also taken into account is the fact that the observatory may be oversubscribed, requiring the scheduling problem to be integrated with a planning process.

We solve this long-term scheduling problem using a time-based encoding that works in the very general case of observation scheduling. This research then compares algorithms from various approaches, including fast heuristics from CPU scheduling, Linear Integer Programming and Genetic algorithms, Branch-and-Bound enumeration schemes. Measures include not only goodness of the solution, but also scalability and re-scheduling capabilities.

In conclusion, we have identified a fast and good scheduling approach that allows (re-)scheduling difficult and changing problems by combining heuristics with a Genetic algorithm using block-wise mutation operations. We are able to explain and eradicate two problems in the literature: The inability of a GA to properly improve schedules and the generation of schedules with frequent interruptions.

Finally, we demonstrate the scheduling framework for several operating telescopes: (1) Dynamic re-scheduling with the AUT Warkworth 12m telescope, (2) Scheduling for the Australian Mopra 22m telescope and scheduling for the Allen Telescope Array. Furthermore, we discuss the applicability of the presented scheduling framework to the Atacama Large Millimeter/submillimeter Array (ALMA, in construction) and the SKA. In particular, during the development phase of the SKA, this dynamic, scalable scheduling framework can accommodate changing conditions.