{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T11:45:55Z","timestamp":1768650355021,"version":"3.49.0"},"reference-count":28,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,2]],"date-time":"2022-02-02T00:00:00Z","timestamp":1643760000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Based on a real-world application in the semiconductor industry, this article models and discusses a hybrid flow shop problem with time dependencies and priority constraints. The analyzed problem considers a production where a large number of heterogeneous jobs are processed by a number of machines. The route that each job has to follow depends upon its type, and, in addition, some machines require that a number of jobs are combined in batches before starting their processing. The hybrid flow model is also subject to a global priority rule and a \u201csame setup\u201d rule. The primary goal of this study was to find a solution set (permutation of jobs) that minimizes the production makespan. While simulation models are frequently employed to model these time-dependent flow shop systems, an optimization component is needed in order to generate high-quality solution sets. In this study, a novel algorithm is proposed to deal with the complexity of the underlying system. Our algorithm combines biased-randomization techniques with a discrete-event heuristic, which allows us to model dependencies caused by batching and different paths of jobs efficiently in a near-natural way. As shown in a series of numerical experiments, the proposed simulation-optimization algorithm can find solutions that significantly outperform those provided by employing state-of-the-art simulation software.<\/jats:p>","DOI":"10.3390\/a15020054","type":"journal-article","created":{"date-parts":[[2022,2,3]],"date-time":"2022-02-03T05:42:33Z","timestamp":1643866953000},"page":"54","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Biased-Randomized Discrete-Event Algorithm for the Hybrid Flow Shop Problem with Time Dependencies and Priority Constraints"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3076-1754","authenticated-orcid":false,"given":"Christoph","family":"Laroque","sequence":"first","affiliation":[{"name":"Institute for Management and Information, University of Applied Sciences Zwickau, 08056 Zwickau, Germany"}]},{"given":"Madlene","family":"Lei\u00dfau","sequence":"additional","affiliation":[{"name":"Institute for Management and Information, University of Applied Sciences Zwickau, 08056 Zwickau, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4219-5056","authenticated-orcid":false,"given":"Pedro","family":"Copado","sequence":"additional","affiliation":[{"name":"IN3\u2014Computer Science Department, Universitat Oberta de Catalunya, 08018 Barcelona, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9847-0443","authenticated-orcid":false,"given":"Christin","family":"Schumacher","sequence":"additional","affiliation":[{"name":"Informatik 4\u2014Modeling and Simulation, TU Dortmund University, 44227 Dortmund, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3793-3328","authenticated-orcid":false,"given":"Javier","family":"Panadero","sequence":"additional","affiliation":[{"name":"IN3\u2014Computer Science Department, Universitat Oberta de Catalunya, 08018 Barcelona, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1392-1776","authenticated-orcid":false,"given":"Angel A.","family":"Juan","sequence":"additional","affiliation":[{"name":"Department of Applied Statistics and Operations Research, Universitat Polit\u00e8cnica de Val\u00e8ncia, 03801 Alcoy, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1007\/s10479-015-2019-x","article-title":"Simulation optimization: A review of algorithms and applications","volume":"240","author":"Amaran","year":"2016","journal-title":"Ann. 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