We introduce multiobjective disk cover problems and study their approximability. We con-
struct a polynomial-time approximation scheme (PTAS) for the multiobjective problem where
k types of points (customers) in the plane have to be covered by disks (base stations) such that
the number of disks is minimized and for each type of points, the number of covered points is
maximized. Our approximation scheme can be extended so that it works with the following
additional features: interferences, different services for different types of customers, different
shapes of supply areas, weighted customers, individual costs for base stations, and payoff for
the quality of the obtained service.

In contrast to the good approximation properties of the multiobjective disk cover problems,
we can show non-approximability results for several single-objective restrictions of these prob-
lems. For example, if there are 2 types of customers, then maximizing the supplied customers
of one type is not approximable within a constant factor, unless P = NP.