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Education of Jilin Province","award":["2022014"],"award-info":[{"award-number":["2022014"]}]},{"name":"Jilin Normal University Doctoral Program","award":["61772160"],"award-info":[{"award-number":["61772160"]}]},{"name":"Jilin Normal University Doctoral Program","award":["20BZS058"],"award-info":[{"award-number":["20BZS058"]}]},{"name":"Jilin Normal University Doctoral Program","award":["LH2024F045"],"award-info":[{"award-number":["LH2024F045"]}]},{"name":"Jilin Normal University Doctoral Program","award":["JJKH20250946KJ"],"award-info":[{"award-number":["JJKH20250946KJ"]}]},{"name":"Jilin Normal University Doctoral Program","award":["2022014"],"award-info":[{"award-number":["2022014"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/sym17050682","type":"journal-article","created":{"date-parts":[[2025,5,2]],"date-time":"2025-05-02T11:35:13Z","timestamp":1746185713000},"page":"682","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Integrated Scheduling Algorithm Based on the Improved Floyd Algorithm"],"prefix":"10.3390","volume":"17","author":[{"given":"Yingxin","family":"Wei","sequence":"first","affiliation":[{"name":"College of Mathematics and Computer, Jilin Normal University, Siping 136000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Mathematics and Computer, Jilin Normal University, Siping 136000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7422-1568","authenticated-orcid":false,"given":"Zhiqiang","family":"Xie","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Harbin University of Science and Technology, Harbin 150080, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ming","family":"Sun","sequence":"additional","affiliation":[{"name":"School of History and Culture, Jilin Normal University, Siping 136000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhenjiang","family":"Tan","sequence":"additional","affiliation":[{"name":"College of Mathematics and Computer, Jilin Normal University, Siping 136000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5666-8331","authenticated-orcid":false,"given":"Wangcheng","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Computer and Information Technology, Mudanjiang Normal University, Mudanjiang 157011, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,29]]},"reference":[{"key":"ref_1","first-page":"166","article-title":"Digitalization Transformation and ESG Performance of Manufacturing Enterprises\u2014From the ESG Segmentation Perspective","volume":"05","author":"Shi","year":"2025","journal-title":"Statist. 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