In the process of the integrated scheduling of multi-variety and small-batch complex products, the process structure and attribute characteristics are often ignored, which affects the overall scheduling effect. Aiming at solving this problem, a heuristic integrated scheduling algorithm (HIS-IDA) based on the improved Dijkstra algorithm is proposed. The algorithm takes the processing time of the process itself as the path value of the preceding and the following adjacent processes. Firstly, the improved Dijkstra algorithm prioritized the scheduling of the process sequence with long longitudinal paths and realized the “longitudinal optimization” of the integrated scheduling. Secondly, the layer priority strategy is used to shorten the interval time of process processing and realize the “horizontal optimization” of integrated scheduling. On the basis of “vertical and horizontal optimization”, the idle time of the equipment is further reduced by using the process priority strategy of the leaf node, and the “idle optimization” of the integrated scheduling is realized, so as to optimize the overall effect of the integrated scheduling. The effectiveness and superiority of the algorithm are proved using comparison analysis.

To address the issue of imbalanced distribution in equipment fault data, this paper proposes an improved FedAvg aggregation algorithm. By dynamically adjusting aggregation weights, it ensures the adaptability of fault data weights across different distribution dimensions during the aggregation process. The algorithm first introduces a contribution mechanism and then combines the contribution degree of each client with the weight of their dataset for model aggregation, resulting in the FedAvg-ContribData algorithm. Experimental data demonstrate that, compared to FedAvg and FedAvg-Data algorithms, our proposed algorithm improves accuracy by 39.7% and 7.9%, precision by 40.4% and 9.1%, recall rate by 41.0% and 7.8%, and F1 score by 46.6% and 9.3%.

In the research and practice of integrated scheduling problems, the tree structure of complex products usually presents an asymmetric and complex form. This asymmetry is mainly reflected in the hierarchical relationship between the various components of the product, the degree of dependence, and the sequence of production processes. Existing studies often neglect that leaf nodes with the lowest layer priority can be scheduled at any moment, leading to underutilization of parallelism potential under symmetric structures and exacerbation of critical path delays under asymmetric structures. Aiming at solving this kind of problem, an integrated scheduling algorithm based on the improved Floyd algorithm (ISA-IFA) is proposed. According to the improved Floyd algorithm, the algorithm proposed a path-weighted strategy, which constructs the vertical path value according to the processing time of the process itself. Combined with the proposed process scheduling advantage strategy, the leaf node process is especially emphasized as the priority scheduling object, which makes the connection between the processes more closely, and then significantly reduces the idle time of the equipment. The empirical results show that the ISA-IFA algorithm shortens the completion time of complex products and simultaneously improves the equipment utilization rate to 55.9%, verifying its effectiveness in dynamic scheduling and resource co-optimization.

The existing research on the two-workshop integrated scheduling problem with symmetrical resources does not consider the complex product attribute structure and the objective situation of plant equipment resources. This results in the prolongation of the product makespan and the reduction of the utilization rate of the general equipment in the workshop. To solve the above problems, a two-workshop integrated scheduling algorithm based on process tree cyclic decomposition (STHIS-PTCD) was proposed. First, a workshop scheduling scheme based on the sub-tree cyclic decomposition strategy was proposed to improve the closeness of continuous processing further. Second, an operation allocation scheme based on the principle of workshop processing balance was presented. On the basis of ensuring the advantages of parallel processing, it also effectively reduces the idle time of equipment resources and then optimizes the overall effect of the integrated scheduling of both workshops. Through the comparison and analysis of all the existing resource-symmetric two-workshop integrated scheduling algorithms, the scheduling effect of the proposed algorithm is the best.

Aiming at the problem of current flexible integrated scheduling, most of the current research shortens the total processing time of products and ignores the loss of the equipment in the processing, which affects the scheduling ability of the equipment; in this context, a flexible integrated scheduling algorithm considering periodic maintenance (FIS-PM) is proposed. The algorithm flexibly mobilizes the processing sequence of the selected processing equipment, and uniformly maintains all equipment at a certain time. First, the ISA-PM algorithm adopts the strategy combination of the layer priority, the short-time, and the equipment priority strategy to schedule the operations. Then, based on the forest firefighting model, the maintenance start point and duration of the equipment are determined by the relationship between the number of the processed operations and the number of the unprocessed operations and the loss of equipment during the maintenance. Finally, the dynamic adjustment strategy is adopted, which not only realizes the maintenance of the equipment, but also reduces the makespan of the products. The experimental results show that the proposed ISA-PM algorithm realizes the optimization effect of reducing the makespan of complex products, completing the maintenance, and improving the overall utilization rate of equipment systems.

In the field of manufacturing, complex products with a tree structure often naturally exhibit asymmetric characteristics due to the uniqueness of their constituent elements and hierarchical relationships. In the production scheduling of such small-batch and multi-variety products, due to the influence of process constraints, many pieces of equipment will be idle for a long time in the production process. This increases the makespan of production and reduces the utilization rate of the equipment. Aiming at improving this situation, a resource cooperative scheduling algorithm is proposed to dynamically adjust the idle time of equipment: the integrated scheduling algorithm with dynamic adjustment of machine idle time based on an improved semi-numerical algorithm (ISA_DA). This algorithm adopts the critical path chain and the optimal scheduling strategy. On this basis, an adjustment strategy based on the semi-numerical algorithm considering the backward movement of the process is proposed, which improves the strength of the close connection of the process and the strength of parallel processing. Experimental results show that the effect of the proposed algorithm is better than the comparison algorithms: the hierarchical scheduling order algorithm and the process tree cyclic decomposition algorithm. It can increase the equipment utilization rate by 10% and 11.5%, respectively, and reduce the makespan by 28.6%. These experimental results strongly prove that the proposed algorithm can effectively reduce the total processing time and improve the production efficiency, whether it is for complex products with a symmetric structure or asymmetric structure.