Future generation Smart Grids are transforming into networks of small scale microgrids. Further, in developing nations where severe power deficits are set to remain a harsh reality, such microgrids are expected to be equipped with brownout based power management in order to avoid rolling blackouts, which affect complete denial of power to a service area during power shortage. Brownouts allow power provisioning to selective loads while curtailing power supply to others. Given the electricity demands of appliances associated with a set of establishments in a microgrid, this work presents a novel centralized, price-induced brownout based appliance scheduling mechanism. The consumers express their appliance’s priority/urgency towards uninterrupted power supply by subscribing to appropriate price tariffs and notify their preferred operation intervals. Two different types of appliances have been considered, i.e., rigid (non-deferrable but curtailable) and elastic (deferrable). We first formulate the scheduling problem as an Integer Linear Programming (ILP) problem with the objective of maximizing total revenue and show that such an optimal strategy incurs high overheads in terms of solution generation times. Therefore, we have proposed a fast yet efficient heuristic algorithm namely, Revenue-aware Appliance Scheduler (RaAS), which is able to produce appreciably good solutions which are only about 2% lower on average, than the optimal ones. However, the solution generation times taken by RaAS are about 28 times faster than the optimal ILP based strategy. The proposed algorithm is extensively evaluated by conducting experiments on various empirically generated microgrid scenarios. RaAS is found to be scalable to microgrids with significantly large number of establishments.