{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T12:32:12Z","timestamp":1777984332680,"version":"3.51.4"},"reference-count":39,"publisher":"F1000 Research Ltd","license":[{"start":{"date-parts":[[2026,1,12]],"date-time":"2026-01-12T00:00:00Z","timestamp":1768176000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["f1000research.com"],"crossmark-restriction":false},"short-container-title":["F1000Res"],"abstract":"<ns7:p>This paper investigates the Single-Machine Scheduling Problem under a multi-criteria optimization framework with due-window constraints, a class of NP-hard problems. The research introduces a mathematical formulation that integrates three performance measures\u2014maximum earliness, maximum tardiness, and maximum late work\u2014into a unified scheduling model. The due date of each job is represented as a flexible time interval bounded by minimum and maximum limits, providing a more realistic representation of production and service systems. To address the complexity of the problem, several special cases are analyzed, and a set of dominance rules is proposed to identify efficient sequences that minimize computational effort while maintaining optimality. These rules extend classical sequencing principles such as the Minimum Slack Time and Earliest Due Date rules to multi-objective contexts. So, in Results and Discussion the comparative analysis demonstrates that the proposed dominance-based approach provides reliable and efficient solutions consistent with those obtained by the Complete Enumeration Method (CEM), but with significantly reduced computational complexity. The theoretical contributions of this study offer a solid foundation for understanding trade-offs between different scheduling criteria within due-window environments. Practical implications arise in Just-in-Time (JIT) systems, where minimizing both early and late job completions directly impacts cost efficiency and workflow stability. Although the analysis is restricted to a deterministic single-machine setup, the proposed framework can be extended to multi-machine, stochastic, or dynamic scheduling environments. Future research may focus on developing heuristic and metaheuristic algorithms to solve larger instances efficiently. Overall, the study contributes to the advancement of multi-criteria scheduling theory by combining mathematical rigor with practical relevance for real-world manufacturing and service operations.<\/ns7:p>","DOI":"10.12688\/f1000research.173324.1","type":"journal-article","created":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T02:59:06Z","timestamp":1769223546000},"page":"47","update-policy":"https:\/\/doi.org\/10.12688\/f1000research.crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Single-Machine Scheduling with Multi-Criteria and Due- Windows"],"prefix":"10.12688","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-1534-3617","authenticated-orcid":false,"given":"Dhuha Athal","family":"Mohsin","sequence":"first","affiliation":[{"name":"Department of Mathematics College of Education for Pure Sciences Karbala University of Kerbala"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2530-900X","authenticated-orcid":false,"given":"Hussam Abid Ali","family":"Mohammed","sequence":"additional","affiliation":[{"name":"Department of Mathematics College of Education for Pure Sciences Karbala University of Kerbala"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2560","published-online":{"date-parts":[[2026,1,12]]},"reference":[{"key":"ref1","first-page":"19-30","article-title":"Development of heuristics for single processor scheduling problems with tardiness - related performance measures by saheed akande of the university of ibadan.","author":"M Engineering","year":"2017"},{"key":"ref2","doi-asserted-by":"publisher","author":"J J\u00f3zefowska","journal-title":"Just-In-Time Scheduling: Models and Algorithms for Computer and Manufacturing Systems.","DOI":"10.1007\/978-0-387-71718-0"},{"key":"ref3","doi-asserted-by":"publisher","first-page":"83-98","DOI":"10.4028\/p-i6uNLi","article-title":"Minimizing Conditional Mean Tardiness and Mean Earliness on a Single Machine with the due Windows Approach.","volume":"11","author":"S Akande","year":"2024","journal-title":"Eng. 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Soc."},{"key":"ref17","doi-asserted-by":"publisher","first-page":"231-241","DOI":"10.2478\/amcs-2013\u20130018","article-title":"Scheduling problems with a common due window assignment: A survey.","volume":"23","author":"A Janiak","year":"2013","journal-title":"Int. J. Appl. Math. Comput. Sci."},{"key":"ref18","doi-asserted-by":"publisher","first-page":"68-74","DOI":"10.1016\/0377-2217(95)00181","article-title":"Determination of common due window location in a single machine scheduling problem.","volume":"93","author":"S Liman","year":"1996","journal-title":"Eur. J. Oper. 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