  We study strong exceptional collections of line bundles on Fano toric
Deligne-Mumford stacks $\mathbb{P}_{\mathbf{\Sigma}}$ with rank of Picard group
at most two. We prove that any strong exceptional collection of line bundles
generates the derived category of $\mathbb{P}_{\mathbf{\Sigma}}$, as long as
the number of elements in the collection equals the rank of the (Grothendieck)
$K$-theory group of $\mathbb{P}_{\mathbf{\Sigma}}$.
