A routine task faced by Microgrid (MG) operators is to optimally allocate incoming power demand requests while accounting for the underlying power distribution network and the associated constraints. Typically, this has been formulated as an offline optimization problem for day-ahead scheduling, assuming perfect forecasting of the demands. In practice, however, these loads are often requested in an ad-hoc manner and the control decisions are to be computed without any foresight into future inputs. With this in view, the present work contributes to the modeling and algorithmic foundations of real-time load scheduling problem in a demand response (DR) program. We model the problem within an AC Optimal Power Flow (OPF) framework and design an efficient online algorithm that outputs scheduling decisions provided with information on past and present inputs solely. Furthermore, a rigorous theoretical bound on the competitive ratio of the algorithm is derived. Practicality of the proposed approach is corroborated through numerical simulations on two benchmark MG systems against a representative greedy algorithm.