  In this paper, we investigate the Mechanism Design aspects of the
$m$-Capacitated Facility Location Problem ($m$-CFLP) on a line. We focus on two
frameworks. In the first framework, the number of facilities is arbitrary, all
facilities have the same capacity, and the number of agents is equal to the
total capacity of all facilities. In the second framework, we aim to place two
facilities, each with a capacity of at least half of the total agents. For both
of these frameworks, we propose truthful mechanisms with bounded approximation
ratios with respect to the Social Cost (SC) and the Maximum Cost (MC). When
$m>2$, the result sharply contrasts with the impossibility results known for
the classic $m$-Facility Location Problem \cite{fotakis2014power}, where
capacity constraints are not considered. Furthermore, all our mechanisms are
(i) optimal with respect to the MC (ii) optimal or nearly optimal with respect
to the SC among anonymous mechanisms. For both frameworks, we provide a lower
bound on the approximation ratio that any truthful and deterministic mechanism
can achieve with respect to the SC and MC.
