Energy savings in flexible job shop scheduling problems based on speed selection considering uncertain processing time

In existing scheduling systems, processing times and energy consumption during the production scheduling process are typically determined based on workers’ experience. However, in real manufacturing environments, various environmental factors often cause these values to deviate from those used in the actual scheduling systems. Therefore, to investigate the impact of uncertainty-induced fluctuations on completion time and energy consumption, Interval Grey Numbers (IGN) are used to represent processing times and energy consumption. Furthermore, considering the characteristics of the machines, the effects of varying processing speeds on processing time and energy consumption are studied within the framework of Interval Grey Numbers. To address the flexible job shop scheduling problem with Interval Grey Numbers and variable processing speeds (GVPS-FJSP), a two-stage reinforcement learning algorithm based on evolutionary strategy (BES-TRL) is proposed. The algorithm incorporates five initialization strategies to generate diverse sets of initial solutions, and designs five targeted neighborhood structures during the iterative stage to ensure that high-quality solutions gradually converge to the Pareto front. In the numerical experiments, the effectiveness of the designed operators and the BES-TRL algorithm is first validated. Finally, comparison experiments with other advanced algorithms demonstrate the effectiveness and usefulness of the BES-TRL algorithm in solving the GVPS-FJSP problem. Additionally, a case study is conducted to verify the practical applicability of the algorithm in real-world production scenarios. Case study on IMK20 shows that the algorithm can reduce energy consumption by 19.7% when production time is sufficient and shorten the makespan by 14.6% when production time is insufficient, which verifies its practical applicability and effectiveness.