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

On strong exceptional collections of line bundles of maximal length on Fano toric Deligne-Mumford stacks