The rapid increase of renewable energy sources made coordinated control of the distributed and intermittent generation units a more demanded task. Matching demand and supply is particularly challenging in islanded microgrids. In this study, we have demonstrated a mixed-integer quadratic programming (MIQP) method to achieve efficient use of sources within an islanded microgrid. A unique objective function involving fuel consumption of diesel generator, degradation in a lithium-ion battery energy storage system, carbon emissions, load shifting, and curtailment of the renewable sources is constructed, and an optimal operating point is pursued using the MIQP approach. A systematic and extensive methodology for building the objective function is given in a sequential and explicit manner with an emphasis on a novel model-based battery aging formulation. Performance of the designed system and a sensitivity analysis of resulting battery dispatch, diesel generator usage, and storage aging against a range of optimization parameters are presented by considering real-world specifications of the Semakau Island, an island in the vicinity of Singapore.