How do I calculate required outdoor air for a VAV multi-zone system?

Per ASHRAE 62.1 Appendix A, you calculate each zone's breathing zone outdoor airflow (V_bz), then zone outdoor airflow (V_oz = V_bz / Ez), and the uncorrected outdoor air intake V_ou = Σ V_oz. The system ventilation efficiency (Ev) is determined by the critical zone with the highest outdoor air fraction (Zp = V_oz / V_dz), using Ev = 1 + Xs − Zd where Xs is the average outdoor air fraction and Zd is the critical zone's fraction. The final design outdoor air intake is V_ot = V_ou / Ev, and the larger the disparity between critical zone and average zone demand, the lower the efficiency and the more outdoor air the system must handle. ASHRAE 62.1’s Appendix A provides the full algebraic derivation and tables for common system configurations.