Rising costs for energy are increasingly becoming a vital factor for the production planning of manufacturing companies. Manufacturers face the challenge to react to dynamic energy prices and design energy cost efficient schedules in their production planning. In the literature, the energy cost-aware Flexible Job Shop Scheduling Problem addresses minimization of both makespan and energy costs. Recent studies provide multi-objective approaches to model the trade-off of minimizing makespan and energy costs. However, the literature is limited to coarse-grained time periods and does not consider dynamic tariffs where costs change at short intervals, so that production schedules may fall short on energy costs. We aim to close this research gap by considering frequently changing real-time energy tariffs. We propose a multi-objective memetic algorithm based on the non-dominated sorting genetic algorithm (NSGA-II) with both makespan and energy cost minimization as the objectives. We evaluate our approach by conducting computational experiments using prominent FJSP-benchmark instances from the literature, which we supplement with empiric dynamic energy prices. We show results on method performance and compare the memetic NSGA-II with the results of an exact state-of-the-art solver. To investigate the trade-off between a short makespan and low energy costs, we present solutions on the approximated Pareto front and discuss our results.

In countries with an extended use of district heating (DH), the integrated operation of DH and power systems can increase the flexibility of the power system, achieving a higher integration of renewable energy sources (RES). DH operators can not only provide flexibility to the power system by acting on the electricity market, but also profit from the situation to lower the overall system cost. However, the operational planning and bidding includes several uncertain components at the time of planning: electricity prices as well as heat and power production from RES. In this publication, we propose a planning method based on stochastic programming that supports DH operators by scheduling the production and creating bids for the day-ahead and balancing electricity markets. We apply our solution approach to a real case study in Denmark and perform an extensive analysis of the production and trading behavior of the DH system. The analysis provides insights on system costs, how DH system can provide regulating power, and the impact of RES on the planning.