Bi-objective identical parallel machine scheduling to minimize total energy consumption and makespan

Currently, energy consumption reduction is playing a more and more important role in production and manufacturing, especially for energy-intensive industries. An optimal production scheduling can help reduce unnecessary energy consumption. This paper considers an identical parallel machine scheduling problem to minimize simultaneously two objectives: the total energy consumption (TEC) and the makespan. To tackle this NP-hard problem, an augmented ɛ-constraint method is applied to obtain an optimal Pareto front for small-scale instances. For medium- and large-scale instances, a constructive heuristic method with a local search strategy is proposed and the NSGA-II algorithm is applied to obtain good approximate Pareto fronts. Extensive computational experiments on randomly generated data and a real-world case study are conducted. The result shows the efficiency and effectiveness of the proposed methods.