This paper addresses the optimal power generation and load management problems in off-grid hybrid electric systems with renewable sources based on appropriately constructed optimization problems. In this venue, the capacity and operating constraints for generating, storage and load units are first formulated as mixed-integer linear programming (MILP) models. In addition, we integrate the power curtailment strategies, such as temporary pause and multiple power supplies, for the load units in the MILP models to alleviate the peak power demands and power shortage without an adverse effect on the overall operation of the system. We subsequently consider the application of this framework for representative scenarios in the context of a residential power system with solar sources. Simulation results for the case of predetermined schedules with preset power requests, as well as for the case of varying schedules with updated power requests, are presented using the proposed optimization-based approach.