We report on the evidence for the multiband electronic transport in $alpha$-YbAlB$_{4}$ and $alpha$-Yb$_{0.81(2)}$Sr$_{0.19(3)}$AlB$_{4}$. Multiband transport reveals itself below 10 K in both compounds via Hall effect measurements, whereas anisotropic magnetic ground state sets in below 3 K in $alpha$-Yb$_{0.81(2)}$Sr$_{0.19(3)}$AlB$_{4}$. Our results show that Sr$^{2+}$ substitution enhances conductivity, but does not change the quasiparticle mass of bands induced by heavy fermion hybridization.