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 available in practice. Therefore, two standard compliant approximation algorithms are developed, which relyon underestimation and overestimation of interference. The first one aims to maximize the reuse of available spectrum, whereas the second one is a more conservative approach that schedules together only links that cause no interference. Extensive performance analysis provides useful insights on the directionality level and the number of concurrent transmissions that should bepursued. Interestingly, extremely narrow beams are in general not optimal.