  Let $G$ be a graph and $S\subseteq V(G)$. If every two adjacent vertices of
$G$ have different metric $S$-representations, then $S$ is a local metric
generator for $G$. A local metric generator of smallest order is a local metric
basis for $G$, its order is the local metric dimension of $G$. Lower and upper
bounds on the local metric dimension of the generalized hierarchical product
are proved and demonstrated to be sharp. The results are applied to determine
or bound the dimension of several graphs of importance in mathematical
chemistry. Using the dimension, a new model for assigning codes to customers in
delivery services is proposed.
