  A service system with multiple types of customers, arriving as Poisson
processes, is considered. The system has infinite number of servers, ranked by
$1,2,3, \ldots$; a server rank is its ``location." Each customer has an
independent exponentially distributed service time, with the mean determined by
its type. Multiple customers (possibly of different types) can be placed for
service into one server, subject to ``packing'' constraints. Service times of
different customers are independent, even if served simultaneously by the same
server. The large-scale asymptotic regime is considered, such that the mean
number of customers $r$ goes to infinity.
  We seek algorithms with the underlying objective of minimizing the location
(rank) $U$ of the right-most (highest ranked) occupied (non-empty) server.
Therefore, this objective seeks to minimize the total number $Q$ of occupied
servers {\em and} keep the set of occupied servers as far at the ``left'' as
possible, i.e., keep $U$ close to $Q$. In previous work, versions of {\em
Greedy Random} (GRAND) algorithm have been shown to asymptotically minimize
$Q/r$ as $r\to\infty$. In this paper we show that when these algorithms are
combined with the First-Fit rule for ``taking'' empty servers, they
asymptotically minimize $U/r$ as well.
