There has been a growing interest in microgrids because of various advantages such as environmental benefits through its integration with renewables, possible cost-efficient replacement of the electricity infrastructure in isolated areas, and improvement of reliability and resilience using multiple energy sources. However, the microgrid faces various challenges in operational management because it deals with a multitude of energy sources mainly comprising renewables (municipal solid waste incineration and solar and wind energy), fuels (natural gas, hydrogen, and biofuel), and batteries. In this work, we developed a mixed-integer linear programming model for cost-efficient and environmentally friendly scheduling in the microgrid operation. The model provides optimal schedules with minimal cost or reduced environmental impacts, e.g., global warming potential, while satisfying the balance of electricity supply and demand. Notably, an additional set of diversity constraints is incorporated within the model to ensure reasonable allocation of electricity generation from each source, thereby allowing us to maintain grid reliability. To demonstrate the applicability and utility of the model, a case study of a hypothetical microgid system in Singapore Island is presented. A comparison result with the national grid system clearly proves the cost efficiency and environmental friendliness of the microgrid. We also investigated the effects of uncertainty in local demands and seasonal weather conditions on the microgrid scheduling, suggesting capacity planning to manage the dependency on national grid and renewable sources.