Energy-efficient scheduling in an identical parallel machine environment with peak power consumption and deadline constraints

Energy-efficient scheduling is an essential means of achieving sustainability in manufacturing systems. This paper defines and addresses the problem of scheduling n jobs on m identical parallel machines in which peak power consumption and deadline constraints exist simultaneously. The objective is to maximize the total value of the selected jobs. We show that this problem is equivalent to a special case of the rectangular knapsack problem, based on which four properties are observed. To solve the problem, an effective mixed integer linear programming model is proposed based on the properties, and it is much more efficient compared to the performance of modeling methods inspired by other works. Furthermore, three effective decoding methods are proposed and embedded into genetic algorithms (GAs). Comparisons with the exact algorithm (i.e., the proposed model) show that our GAs can lead to good-quality solutions within one second for small instances. Meanwhile, experimental results for large instances indicate that the proposed GAs can obtain near-optimal or satisfactory solutions. Finally, results also show that the proposed GA-DD significantly outperforms the existing matheuristic algorithm.