Integrated Continuous Berth Allocation and Time-Invariant Specific Quay Crane Assignment: A Mixed-Integer Model and a Greedy Genetic Algorithm

Integrated Continuous Berth Allocation and Time-Invariant Specific Quay Crane Assignment: A Mixed-Integer Model and a Greedy Genetic Algorithm | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Integrated Continuous Berth Allocation and Time-Invariant Specific Quay Crane Assignment: A Mixed-Integer Model and a Greedy Genetic Algorithm Yan Zhou, Xu Cheng, Yu Cao This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9235581/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 10 You are reading this latest preprint version Abstract Efficient coordination of berth and quay crane resources is essential for improving the operational performance of container terminals under increasing vessel traffic and limited shoreline capacity. This paper studies an integrated optimization problem that combines continuous berth allocation with specific quay crane assignment. Unlike studies that determine only the number of quay cranes assigned to each vessel, the present work explicitly determines the identities of assigned quay cranes while considering practical operational constraints, including continuous berth positions, ship-specific crane quantity limits, contiguous crane assignment, vessel non-overlap, and crane non-crossing requirements. A mixed-integer programming model is formulated with the objective of minimizing the total time that vessels spend in port. Since exact optimization becomes computationally expensive as the problem size increases, a greedy genetic algorithm (GGA) is developed to obtain high-quality feasible solutions within limited computational time. The proposed algorithm combines greedy initialization with a feasibility-repair procedure for offspring generated during crossover and mutation, thereby improving feasibility maintenance during the evolutionary search process. Computational experiments are conducted using real operational data collected from a container port in Liaoning, China, together with synthetic instances of different scales. The results indicate that the proposed method provides better average solution quality and higher stability than a standard genetic algorithm while maintaining competitive computational efficiency. For medium- and large-scale instances, the proposed GGA can generate high-quality feasible schedules within practical time limits, which supports its potential applicability to real-world port operations. Physical sciences/Engineering Physical sciences/Mathematics and computing continuous berth allocation specific quay crane assignment container terminal mixed-integer programming greedy genetic algorithm Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 28 Apr, 2026 Reviews received at journal 25 Apr, 2026 Reviews received at journal 09 Apr, 2026 Reviewers agreed at journal 08 Apr, 2026 Reviewers agreed at journal 07 Apr, 2026 Reviewers invited by journal 07 Apr, 2026 Editor assigned by journal 04 Apr, 2026 Editor invited by journal 02 Apr, 2026 Submission checks completed at journal 01 Apr, 2026 First submitted to journal 01 Apr, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9235581","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":622304046,"identity":"a5bdaa67-7565-4acd-a0a6-890b8f512283","order_by":0,"name":"Yan Zhou","email":"","orcid":"","institution":"Guangzhou Institute of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Yan","middleName":"","lastName":"Zhou","suffix":""},{"id":622304047,"identity":"e2c0495b-e7d9-4f2d-9767-999a68f9c5f8","order_by":1,"name":"Xu Cheng","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2ElEQVRIiWNgGAWjYHACNhAhB+UwE6/FmHQtiQ1EazG4kfzswccdtenzZyQ/k2CosE5sYD97AK8WyRlp5oYzzxzP3XAjzUyC4Ux6YgNPXgJeLfwSOWzSvG3HcjdIJJhJMLYdTmyQ4DHA7xGQlr9tx9LlZ6R/k2D8R4QWsC2MbTUJDDdygLY0EKFFsueZmWRv2wHDDWfeFFskHEs3buPJwa/F4DgwoH621cnLt6dvvPGhxlq2n/0Mfi1QcJiBQSCBgSGBARpNRIA6oK8OEKl2FIyCUTAKRhwAADQVQkJTEwTVAAAAAElFTkSuQmCC","orcid":"","institution":"Shenyang Agricultural University","correspondingAuthor":true,"prefix":"","firstName":"Xu","middleName":"","lastName":"Cheng","suffix":""},{"id":622304048,"identity":"301fec01-808a-4ded-af1a-40ccaef1ef52","order_by":2,"name":"Yu Cao","email":"","orcid":"","institution":"Liaoning Petrochemical University","correspondingAuthor":false,"prefix":"","firstName":"Yu","middleName":"","lastName":"Cao","suffix":""}],"badges":[],"createdAt":"2026-03-26 14:53:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9235581/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9235581/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106845116,"identity":"f58a3399-6bea-4db3-a913-8fda72fa3af6","added_by":"auto","created_at":"2026-04-14 04:40:41","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":654037,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9235581/v1_covered_72b0b2b9-faa0-4092-86e9-492bdc1118b6.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Integrated Continuous Berth Allocation and Time-Invariant Specific Quay Crane Assignment: A Mixed-Integer Model and a Greedy Genetic Algorithm","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"continuous berth allocation, specific quay crane assignment, container terminal, mixed-integer programming, greedy genetic algorithm","lastPublishedDoi":"10.21203/rs.3.rs-9235581/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9235581/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eEfficient coordination of berth and quay crane resources is essential for improving the operational performance of container terminals under increasing vessel traffic and limited shoreline capacity. This paper studies an integrated optimization problem that combines continuous berth allocation with specific quay crane assignment. Unlike studies that determine only the number of quay cranes assigned to each vessel, the present work explicitly determines the identities of assigned quay cranes while considering practical operational constraints, including continuous berth positions, ship-specific crane quantity limits, contiguous crane assignment, vessel non-overlap, and crane non-crossing requirements.\u003c/p\u003e \u003cp\u003eA mixed-integer programming model is formulated with the objective of minimizing the total time that vessels spend in port. Since exact optimization becomes computationally expensive as the problem size increases, a greedy genetic algorithm (GGA) is developed to obtain high-quality feasible solutions within limited computational time. The proposed algorithm combines greedy initialization with a feasibility-repair procedure for offspring generated during crossover and mutation, thereby improving feasibility maintenance during the evolutionary search process.\u003c/p\u003e \u003cp\u003eComputational experiments are conducted using real operational data collected from a container port in Liaoning, China, together with synthetic instances of different scales. The results indicate that the proposed method provides better average solution quality and higher stability than a standard genetic algorithm while maintaining competitive computational efficiency. 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