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This framework proposes a heuristic algorithm based on LP (linear programming) for optimizing the electricity cost in large residential buildings, in a smart grid environment. Our heuristic tackles large multi-objective energy allocation problem (large number of appliances and high time resolution). The primary goal is to reduce the electricity bills, and discomfort factor. Also, increase the utilization of domestic renewable energy, and reduce the running time of the optimization algorithm. Our heuristic algorithm uses linear programming relaxation, and two rounding strategies. The first technique, called CR (cumulative rounding), is designed for thermostatic appliances such as air conditioners and electric heaters, and the second approach, called MCR (minimum cost rounding), is designed for other interruptible appliances. The results show that the proposed heuristic algorithm can be used to solve large MILP (mixed integer linear programming) problems and gives a decent suboptimal solution in polynomial time.