As renewable technology advances and decreases in cost, microgrids are becoming an appealing means of distributed generation both for isolated communities and integrated with existing electrical grid systems. Due to their small size, however, microgrids may have financial limitations which preclude them from using commercial software to optimize control of their assets. Open-source optimization solvers are a viable alternative, but increase computation time. This work expands on a rolling horizon optimization framework for economic dispatch within an existing residential microgrid located in Hoover, Alabama. The microgrid has an open-source solver requirement and a need for quick solution time on a rolling horizon as opposed to a day-ahead commitment. We present a method of reducing integer variables by relaxation which completes two goals: reduction in computation time for real-time operations, and reduction in daily operational cost for the microgrid. Seasonal data for load and photovoltaic (PV) power was also collected from the microgrid to facilitate simulation testing. Computation time was successfully reduced using multiple variations of the relaxation method, while obtaining solution quality with operational cost similar to or better than the original model.