Scheduling Telescope Observations for the European Southern Observatory

The European Southern Observatory (ESO) provides state-of-the-art large telescope facilities at three sites in Chile, supported by 16 European member states. Astronomers submit proposals for sets of observations which are reviewed and ranked based on scientific merit, then a schedule is constructed respecting the ranking and aiming to make the fullest use of the various telescopes and numerous instruments. Currently a schedule covers six months, but in the near future ESO will switch to annual schedules. Here we examine the most challenging scheduling problem encountered by ESO: scheduling the operations of the Very Large Telescope Interferometer (VLTI) on Paranal, Chile. Tasks to be scheduled include observations performed by ESO staff, `visitor mode' periods where astronomers visit the site to use the telescopes, various maintenance tasks, and reconfiguration tasks taking multiple days. Typically a VLTI six-month schedule would contain approximately 450 activities. We explore global constraint models and a SAT encoding of the problem.