Energy-efficient scheduling in an unrelated parallel-machine environment under time-of-use electricity tariffs

The extensive use of energy worldwide, as well as a reduction in non-renewable energy sources, has led to increased greenhouse gas emissions and global warming. Therefore, the optimal use of energy has recently become very important. A decrease in energy consumption in manufacturing environments, as one of the major energy consumers, has attracted the attention of different researchers. In addition, considering a variety of tariffs in different periods is regarded as one of the strategies which the governments apply to control energy consumption. The present study aimed to minimize the cost of consuming energy in a production environment with unrelated parallel machines. So far, various studies have evaluated the unrelated parallel machine scheduling with energy tariffs. Based on the study objective, a mixed-integer linear programming model was presented for the problem. Further, a number of dominance rules and valid inequalities were developed to improve the computational time of the model due to the assumptions for this problem. The results of the study indicated that the proposed model was better than that of the other related studies in the literature. Furthermore, a heuristic fix and relax algorithm was proposed for large-size instances, which could solve the instances up to 1000 jobs and 20 machines in size. Finally, this algorithm had a low gap compared to the lower bound of the problem. •Unrelated parallel machine scheduling under time-of-use (TOU) electricity tariffs.•The objective is minimizing the total electricity cost with bounded makespan.•An improved mixed-integer programming model is proposed.•A fix and relax heuristic method is developed.•Proposed model outperforms the other models of literature.