The increasing deployment of Automated Guided Vehicles (AGVs) in smart warehouses requires integrated task scheduling and energy management strategies to ensure both operational efficiency and energy sustainability. This work addresses the problem of minimizing the energy costs of an automated warehouse equipped with a photovoltaic system and a fleet of AGV robots with Vehicle-to-Grid (V2G) capabilities. The warehouse operates under tight temporal constraints imposed by incoming and outgoing freight operations, with AGVs required to complete a set of predefined tasks within a limited scheduling horizon. To manage the inherent complexity of joint logistics and energy optimization, the proposed framework adopts a two-stage hierarchical approach. The first stage groups individual base tasks into macro-tasks, optimizing routing and reducing computational burden. The second stage, addressed in this work, formulates an energy-aware scheduling algorithm as a Mixed-Integer Linear Programming (MILP) problem that assigns and schedules macro-tasks over the available time horizon while minimizing the energy purchased from the grid. The effectiveness of the proposed optimization methodology is validated through numerical simulations and a comparative analysis with a greedy scheduling algorithm, demonstrating significant energy savings and enhanced operational flexibility while ensuring timely task completion in autonomous warehouse systems.