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.

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.

For the existing multi-product integrated scheduling algorithm considering the delivery date, the inability to fully consider the processing order of multiple products and the potential scheduling conflicts in the processing process causes problems such as equipment resource competition during the processing of products, ultimately resulting in the extension of delivery date and the failure to the deliver products on time. Aiming at this problem, a dynamic multi-product integrated scheduling algorithm with tight delivery date (ISA-TDD) is proposed. Firstly, the initial scheduling scheme of multi-product is established according to the strategy of ‘device priority + short time + layer priority’. Secondly, the product contribution value strategy is proposed to determine the scheduling order of multiple products and improve the parallel processing of products. Finally, the dynamic adjustment strategy of the game process is proposed, which solves the conflict problem of multi-product co-processing and further improves the intensity of compact scheduling of equipment. The comparative experimental results show that the algorithm achieves the optimization goal of shorter multi-product delivery date and higher overall utilization rate of equipment, and the scheduling effect is obviously better than the comparison algorithm.

During the scheduling of the production of small batch and multi-variety products with treelike structure, many devices are idle due to the process constraints. 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 on machine idle time(ISA_DA). This algorithm adopts the critical path chain and the optimal scheduling strategy. Besides, the adjustment strategy considering the backward movement of the process is put forward to improve the intensity of the close connection of the process and the intensity 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%.