  This paper concerns a new optimization problem arising in the management of a
multi-object spectrometer with a configurable slit unit. The field of view of
the spectrograph is divided into contiguous and parallel spatial bands, each
one associated with two opposite sliding metal bars that can be positioned to
observe one astronomical object. Thus several objects can be analyzed
simultaneously within a configuration of the bars called a mask. Due to the
high demand from astronomers, pointing the spectrograph's field of view to the
sky, rotating it, and selecting the objects to conform a mask is a crucial
optimization problem for the efficient use of the spectrometer. The paper
describes this problem, presents a Mixed Integer Linear Programming formulation
for the case where the rotation angle is fixed, presents a non-convex
formulation for the case where the rotation angle is unfixed, describes a
heuristic approach for the general problem, and discusses computational results
on real-world and randomly-generated instances.
