Scheduling of Star Observations under Uncertain Conditions: A Comparison of Models and Solvers

Abstract

We consider a scheduling problem for star observations using a telescope. Identical nights are available to observe stars that have been identified as of interest by astronomers. Each star yields a profit if it is observed; in that case, the observation must respect a visibility window and a minimum observation duration. The objective is to maximize the total profit of the observations that are actually performed. By interpreting nights as machines and stars as jobs to be processed, this problem is a classic scheduling setting of parallel machines. In the practical star-observation problem, the ability to observe depends on meteorological and atmospheric conditions, which are not known when the schedule is computed. A possible modeling is to consider that each night can be either perfect and everything is observable, either terrible and nothing is observable. The challenge is therefore to propose a ''high-quality'' schedule without knowing the actual number of nights (machines) that will ultimately be available. We focus here on evaluating the worst case within the robust optimization paradigm.