Economic dispatch (ED) in a microgrid is vital to supply the load demand with a minimum cost of operation. Considering the large number of discrete variables involved in ED formulation, it is common in practice to use Mixed Integer Linear Programming (MILP) for solving the optimization problem. However, as the problem size increases, the convergence time of MILP can exponentially increase owing to the NP-hard nature of the algorithm. This paper reviews the state of the art ED formulations and proposes an equally optimal and time-efficient method, Relaxed Mixed Integer Linear Programming (RMILP) for executing the day-ahead ED in a microgrid with large problem size. Using the proposed algorithm, ED problems with smaller timesteps can be solved in a reasonable time for large systems. In addition, the load is modeled as a discrete variable which is more realistic from the perspective of load shedding and often ignored in ED formulations in the literature. We apply the proposed approach to the Banshee distribution feeders and show its advantages over conventional methods.