Energy efficiency in factories is a new paradigm arising with Demand Response (DR) programs that enables energy providers to ask their clients to reduce their power consumption for a given time. In this paper, we consider demand side management of an industrial customer who owns asynchronous production line systems. Our aim is to help the customer achieve a good trade-off between production rates and power consumption during DR events. To attain this objective, we develop a framework named DR-Mgmt to schedule activities of machines on production lines so that the number of simultaneously working machines is maximized while satisfying DR constraints. Our framework first models activities of a production line using a new approach based on temporal deterministic finite station machine concept, where each state represents machine status (working/idle) and transitions capture temporal changes. Then, the problem of finding an optimal schedule from all feasible schedules is handled by selecting the optimal set of state transitions. We adapt the well-known local search heuristic to find near-optimal transitions. Numerical results show a significant benefit of our approach on production rates during DR intervals. Compared to other approaches, the proposed framework performs best and improves production rates up to 70% in some cases with higher total power consumption. We also validate our work by a real case study.