In this article, a cost-based mathematical optimization is used to evaluate the optimal amount of imported power from the public main grid to a private microgrid (MG), that is the “LAMBDA lab MG” testbed placed at the Sapienza University of Rome. In this regard, this article considers five tests based on using different sources, including a photovoltaic (PV) array, an emergency generator set, a fuel cell, and the main grid, for load satisfaction. The “LAMBDA lab” can be considered as a “multisource multioutput energy hub” with three optional sources and both electrical and heat demands in output. This article considers PV production and load demand as indeterministic parameters and evaluates the problem under uncertainties. As a result, a stochastic programming model is defined, and a powerful optimization function is used to reach the optimal power received from the main grid. Besides, information gap decision theory is used to model the robustness of the problem against uncertainties associated with renewable generation units (PV system) and electricity loads applied on a real case for the first time. In the result section, the contribution of each source in electrical and heat load demands is presented in addition to the cost of each test by evaluating the effect of demand response of 15%. Finally, a comparison between the stochastic programming method and IGDT has been accomplished.