In this contribution we present
two approaches allowing to find a reduced order approximant of a full
order model featuring a moving load term. First, we apply the Balanced
Truncation (BT) method to a switched linear system (SLS) using the
special structure given in the spatially discretized model. The second
approach treats the variability as a continuous parameter dependence
and uses the iterative rational Krylov algorithm (IRKA) to compute
a parameter preserving reduced order model.