Aiming at the existing flexible integrated scheduling algorithms that use unified rules to solve the conflicts between processes and equipment, and ignore the vertical and horizontal characteristics of the process relative positions in the process tree, a flexible integrated scheduling algorithm for dynamic determination processing equipment considering the Root-Subtree vertical and horizontal pre-scheduling (FISA-DEVH) is proposed. The process sorting strategy of the Root-Subtree vertical and horizontal pre-scheduling is proposed to sort the Root-Subtree processes of the same planned processing equipment in groups and load the Root-Subtree processes into the corresponding equipment queues, so as to fully explore the vertical and horizontal characteristics of the process. In order to give full play to the characteristics of the flexible equipment and realize the effective parallel processing between the processes, the flexible equipment optimal scheduling strategy of dynamically determining process is proposed to determine the final processing equipment of the process at each equipment driving moment and complete the production scheduling process from the Root-Subtree static pre-scheduling to dynamic fusion; The strategy uses the scheduling relationship between the unplanned processes and unplanned equipment to reduce the search scope of the combination scheme and improve the efficiency of the algorithm. The example tests show that FISA-DEVH has a better scheduling effect than the flexible integrated scheduling algorithm that processes the process tree with unified rules, and has universal significance for solving the flexible integrated scheduling problem.

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 general integrated scheduling problem of tree-structured complex single-product machining and assembling, a reverse order hierarchical integrated scheduling algorithm (ROHISA) is proposed by considering the dynamic time urgency degree (TUD) of process sequences (PSs). The strategy of process sorting is put forward, and the TUD of PS is defined. The process tree is reversed using leaf alignment, and according to the order from leaf to root, the scheduling order of leaf nodes in the same layer is determined layer by layer according to the TUD values of the PSs to which the leaf nodes belong. In turn, the sorted leaf nodes in each layer are stored in a corresponding layered array (LA). Finally, the elements in each LA are reversed, and the LAs’ arranging order is reversed. A reverse order hierarchical scheduling strategy is proposed. Starting from the root node, every LA is taken as a unit to conduct trial scheduling each time. Under the condition of meeting the craft constraints, a set of quasi-scheduling schemes of same-layer processes (QSS_SLP) is obtained, and the one with the minimum end time is selected from it as the scheduling scheme of the same layer processes (SS_SLP). If it is not unique, the QSS_SLP that machines all the same layer processes (SLP) as early as possible is selected. The research shows that the ROHISA optimizes the integrated scheduling results of single-product manufacturing enterprises and improves its production efficiency.

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.