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In this work, we propose a supervisory control structure in islanded DC microgrids such that a well scheduled and balanced utilization of various resources is achieved. Our supervisory control layer rests on top of a voltage-controlled primary layer and comprises a secondary layer, which receives power references from an energy management system. The secondary layer translates these power into appropriate voltage references by solving an optimization problem. These references act as an input for the primary voltage controllers. We show that the unconstrained secondary optimization problem is always feasible. Moreover, since the voltages can only be enforced at the generator nodes, we provide a novel condition to guarantee the uniqueness of load voltages and power injection of the generation units. Indeed, in the absence of uniqueness, for fixed generator voltages, the load nodes and power injections may be different than planned. This can result in violation of operational limits causing damage to the connected loads. Moreover, this uniqueness condition can be verified at each load node by utilizing local load parameters, and does not require any information about microgrid topology. The functioning of the proposed architecture is tested via simulations.