Many operators of water distribution networks (WDNs) are unable to meet the increasing demand for water. Utility operators in such situations resort to rationing the supply as a partial solution to this problem; this, in turn, may lead to disproportionate allocation of water or inequity in supply. In this study, we propose a mixed integer non-linear program formulation and an efficient solution approach to minimize the inequity in supply, subject to hydraulic constraints and additional constraints on hours of supply and valve operation. Further, we show that the schedule can be obtained using a data-driven approach based on flow and level measurements, which eliminates the modelling effort and uncertainty associated with the use of hydraulic models. We demonstrate the proposed approaches through simulations of a real WDN, and experiments conducted on a topologically similar laboratory-scale network.