  We consider a Ginzburg-Landau type energy with a piecewise constant pinning
term $a$ in the potential $(a^2 - |u|^2)^2$. The function $a$ is different from
1 only on finitely many disjoint domains, called the {\it pinning domains}.
These pinning domains model small impurities in a homogeneous superconductor
and shrink to single points in the limit $\v\to0$; here, $\v$ is the inverse of
the Ginzburg-Landau parameter. We study the energy minimization in a smooth
simply connected domain $\Omega \subset \mathbb{C}$ with Dirichlet boundary
condition $g$ on $\d \O$, with topological degree ${\rm deg}_{\d \O} (g) = d
>0$. Our main result is that, for small $\v$, minimizers have $d$ distinct
zeros (vortices) which are inside the pinning domains and they have a degree
equal to 1. The question of finding the locations of the pinning domains with
vortices is reduced to a discrete minimization problem for a finite-dimensional
functional of renormalized energy. We also find the position of the vortices
inside the pinning domains and show that, asymptotically, this position is
determined by {\it local renormalized energy} which does not depend on the
external boundary conditions.
