A Branch-and-Price Algorithm for Scheduling Observations on a Telescope.

We address a parallel machine scheduling problem for which the objective is to maximize the weighted number of scheduled tasks, and with the special constraint that each task has a mandatory processing instant. This problem arises, in our case, to schedule a set of astronomical observations on a telescope. We prove that the problem is NP-complete, and we propose a constraint-programming-based branch-and-price algorithm to solve it. Experiments on real and realistic datasets show that the method provides optimal solutions very efficiently.