Millimeter wave (mmWave) wireless networks relyon narrow beams to support multi-gigabit data rates. Nevertheless, the alignment of transmitter and receiver beams is a time consuming operation, which introduces an alignment-throughput tradeoff. A wider beamwidth reduces the alignment overhead,but leads also to reduced directivity gains. Moreover, existing mmWave standards schedule a single transmission in eachtime slot, although directional communications facilitate multiple concurrent transmissions. In this paper, a joint consideration ofthe problems of beamwidth selection and scheduling is proposed to maximize effective network throughput. The resulting optimization problem requires exact knowledge of network topology,which may not be avai...