{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T01:02:29Z","timestamp":1776128549538,"version":"3.50.1"},"reference-count":62,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,12]],"date-time":"2025-04-12T00:00:00Z","timestamp":1744416000000},"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>This work studies single-machine scheduling with general position-dependent deterioration, where job processing times are general non-decreasing functions dependent on their positions in a sequence. The goal is to find a job sequence such that makespan is minimized. The problem can be extended to deal with green scheduling environment where processing time increases due to additional carbon-reduction procedure. Under some optimal properties, we prove that the problem is solved by the largest processing time (denoted by LPT) first rule.<\/jats:p>","DOI":"10.3390\/axioms14040290","type":"journal-article","created":{"date-parts":[[2025,4,14]],"date-time":"2025-04-14T04:42:07Z","timestamp":1744605727000},"page":"290","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Minimizing Makespan Scheduling on a Single Machine with General Positional Deterioration Effects"],"prefix":"10.3390","volume":"14","author":[{"given":"Yu","family":"Sun","sequence":"first","affiliation":[{"name":"School of Science, Shenyang Aerospace University, Shenyang 110136, China"}]},{"given":"Hongyu","family":"He","sequence":"additional","affiliation":[{"name":"School of Economics, Shenyang University, Shenyang 110044, China"},{"name":"Institute of Carbon Neutrality Technology and Policy, Shenyang University, Shenyang 110044, China"}]},{"given":"Yanzhi","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Economics, Shenyang University, Shenyang 110044, China"},{"name":"Institute of Carbon Neutrality Technology and Policy, Shenyang University, Shenyang 110044, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2271-6459","authenticated-orcid":false,"given":"Ji-Bo","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Science, Shenyang Aerospace University, Shenyang 110136, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,12]]},"reference":[{"key":"ref_1","unstructured":"Baker, K.R. 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