The combined increase of energy demand and environmental pollution at a global scale is entailing a rethinking of the production models in sustainable terms. As a consequence, energy suppliers are starting to adopt strategies that flatten demand peaks in power plants by means of pricing policies that stimulate a change in the consumption practices of customers. A representative example is the Time-of-Use (TOU)-based tariffs policy, which encourages electricity usage at off-peak hours by means of low prices, while penalizing peak hours with higher prices. The TOU-based tariffs policy induces a partitioning of the time horizon into a set of time slots, each associated with a cost that becomes a part of the optimization objective. This thesis focuses on a representative bi-objective energy-efficient job scheduling problem on parallel identical machines under TOU-based tariffs by delving into the description of its inherent properties, mathematical formulations, and solution approaches. Specifically, the thesis starts by reviewing the flourishing literature on the subject, and providing a useful framework for theoreticians and practitioners. Subsequently, it describes the considered problem and investigates its theoretical properties. In the same chapter, it presents a first mathematical model for the problem, as well as a possible reformulation that exploits the structure of the solution space so as to achieve a considerable increase in compactness. Afterwards, the thesis introduces a sophisticated heuristic scheme to tackle the inherent hardness of the problem, and an exact algorithm that exploits the mathematical models. Then, it shows the computational efficiency of the presented solution approaches on a wide test benchmark. Finally, it presents a perspective on future research directions for the class of energy-efficient scheduling problems under TOU-based tariffs as a whole.