Past studies of microgrid generator fuel efficiencies have been based on measurements of fuel consumption by generators under static loads. There is little information on fuel efficiency of generators under time-varying loads. To help analyze the impact of time-varying loads on optimal generator operation and fuel consumption, we formulate a mixed-integer linear optimization model to plan generator and energy storage system (ESS) operation to satisfy known demands. Our model includes piecewise linear fuel penalty terms on time-varying loads. We exercise the model on a number of scenarios and compare the resulting optimal fuel consumption and generator operation profiles. Our results show that the change in fuel efficiency between scenarios with the integration of ESS is minimal regardless of the imposed penalty placed on the generator. However, without the assistance of the ESS, the fuel consumption increases dramatically as the penalty imposed on the generator becomes greater. The integration of ESS shows a drastic improvement in fuel consumption, where the ESS allows the generator to minimize power output fluctuation to maximize fuel efficiency. The insignificance of penalty type and weight imposed on the generator provides potentially useful insight for future studies in developing a real-time controller.