{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T07:19:58Z","timestamp":1780384798092,"version":"3.54.1"},"reference-count":87,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T00:00:00Z","timestamp":1750377600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Liaoning Social Science Fund","award":["L23BGL013"],"award-info":[{"award-number":["L23BGL013"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We study single-machine group green scheduling considering group setup time deterioration effects and job-processing time learning effects, where the setup time of a group is a general deterioration function on its starting setup time and the processing time of a job is a non-increasing function on its position. We focus on confirming the job schedule for each group and group schedule for minimizing the total weighted completion time. It is proved that this problem is NP-hard. According to the problem\u2019s NP-hardness, we present some optimal properties (including lower and upper bounds) and then propose a branch-and-bound algorithm and two heuristic algorithms (including the modified Nawaz\u2013Enscore\u2013Ham algorithm and simulated annealing algorithm). Finally, numerical simulations are provided to indicate the effectiveness of these algorithms, which demonstrates that the branch-and-bound algorithm can solve random instances of 100 jobs and 14 groups within reasonable time and that simulated annealing is more accurate than the modified Nawaz\u2013Enscore\u2013Ham algorithm.<\/jats:p>","DOI":"10.3390\/axioms14070480","type":"journal-article","created":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T05:17:42Z","timestamp":1750396662000},"page":"480","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Integrating Group Setup Time Deterioration Effects and Job Processing Time Learning Effects with Group Technology in Single-Machine Green Scheduling"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8072-9405","authenticated-orcid":false,"given":"Na","family":"Yin","sequence":"first","affiliation":[{"name":"School of Science, Shenyang Aerospace University, Shenyang 110136, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongyu","family":"He","sequence":"additional","affiliation":[{"name":"School of Economics, Shenyang University, Shenyang 110096, China"},{"name":"Institute of Carbon Neutrality Technology and Policy, Shenyang University, Shenyang 110044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanzhi","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Economics, Shenyang University, Shenyang 110096, China"},{"name":"Institute of Carbon Neutrality Technology and Policy, Shenyang University, Shenyang 110044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yu","family":"Chang","sequence":"additional","affiliation":[{"name":"School of Economics, Shenyang University, Shenyang 110096, China"},{"name":"Institute of Carbon Neutrality Technology and Policy, Shenyang University, Shenyang 110044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ning","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Economics, Shenyang University, Shenyang 110096, China"},{"name":"Institute of Carbon Neutrality Technology and Policy, Shenyang University, Shenyang 110044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1007\/s12293-019-00295-0","article-title":"Estimation of distribution evolution memetic algorithm for the unrelated parallel-machine green scheduling problem","volume":"11","author":"Xue","year":"2019","journal-title":"Memetic Comput."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1016\/j.apenergy.2019.04.155","article-title":"The impact of various carbon reduction policies on green flowshop scheduling","volume":"249","author":"Foumani","year":"2019","journal-title":"Appl. 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