Manufacturing systems face growing pressure to improve operational efficiency while controlling electricity costs under Time-of-Use (TOU) tariffs, where production timing directly affects the electricity bill. This challenge is especially acute in flexible job shops, where each operation must be assigned not only to an eligible machine but also to a qualified worker. This paper studies the dual-resource flexible job shop scheduling problem under TOU tariffs (DRC-FJSP-TOU), which jointly determines machine assignments, worker assignments, and operation start times. A mathematical formulation is developed to minimize electricity cost through both energy and demand charges. To address the problem’s computational difficulty, a policy-based rough optimization with large neighborhood search (Pro-LNS) framework is proposed. The method combines a PPO-based constructive policy with an adaptive large neighborhood search phase, and the resulting solution is used to warm-start an exact mixed-integer linear programming (MILP) model. Computational experiments on 11 benchmark instances under a matched 3600-second time budget show that the standalone MILP reaches optimality only for the smallest instance, whereas the Pro-LNS-assisted MILP consistently achieves lower objective values and tighter optimality gaps, reducing final gaps to below 8% across all nontrivial instances. These results show that the proposed framework is effective for electricity-cost-aware dual-resource scheduling under TOU tariffs.