Optimizing scheduling and bunkering decision for tramp shipping fleet under stochastic demand and bunker prices

Optimizing scheduling and bunkering decision for tramp shipping fleet under stochastic demand and bunker prices | 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 Research Article Optimizing scheduling and bunkering decision for tramp shipping fleet under stochastic demand and bunker prices Jun Gao, Junfeng Zhang, Lei Xu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6774071/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The operational decisions faced by tramp shipping fleet operators are crucial, particularly in the current volatile global economic and trade environment. Navigating through uncertain market conditions poses a significant challenge for operators striving to optimize the operational decisions of their tramp shipping fleets. This paper delves into the tramp shipping fleet scheduling and bunkering problem, incorporating stochastic demand and bunker prices, with the objective of maximizing operational revenue while adhering to specified service levels for shippers. We introduce the service level for shippers as the probability of demand being served and formulate our research problem as a stochastic mixed-integer programming model with a service level constraint. To address this model, we transform it into a multi-objective reachability problem, defining operational revenue and service level requirements while setting a total operational revenue target. Concurrently, we propose a Debt Related Tramp Shipping Fleet Scheduling and Bunkering (DRTSFSB) algorithm framework to guide fleet scheduling and bunkering decisions in each scenario. The numerical experiments conducted conclusively demonstrate that the proposed approach significantly reduces computation time while maintaining comparable performance to the Sample Average Approximation (SAA) method. This underscores the superiority of our approach in addressing operational decision problems for tramp shipping fleets under stochastic conditions. Tramp shipping fleet Ship scheduling and bunkering Stochastic demand and bunker prices Service level Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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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-6774071","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":488057237,"identity":"1f979bba-4f75-4b24-8123-d9c37185c208","order_by":0,"name":"Jun Gao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1ElEQVRIiWNgGAWjYJACAwYGGxkGZh4Qm5loLWk8pGkBgsNA9cRqkXc/fKCYd8d5HoPjvAcfMFRYJzawnz2AV4vhmbQEY94zt3kMDvMlGzCcSU9s4MlLwK+lIcfAmLcNpIXHTIKx7XBigwSPAX4t/W9AWs6BtJj/YPxHhBZ5CbAtB8C2MDA2EKHFQOJZguHctmQeSaBfJBKOpRu38eQQsKU/+ZjB2zY7Ob7zZw9++FBjLdvPfoaALQcY2BAqEoCYDa96kC0NDMwPCCkaBaNgFIyCEQ4AzhM+4WthJ9AAAAAASUVORK5CYII=","orcid":"","institution":"Liaoning University of International Business and Economics","correspondingAuthor":true,"prefix":"","firstName":"Jun","middleName":"","lastName":"Gao","suffix":""},{"id":488057238,"identity":"97d4e953-8656-4fa1-babf-46496d98626f","order_by":1,"name":"Junfeng Zhang","email":"","orcid":"","institution":"Liaoning University of International Business and Economics","correspondingAuthor":false,"prefix":"","firstName":"Junfeng","middleName":"","lastName":"Zhang","suffix":""},{"id":488057239,"identity":"340e21b6-9358-4a2c-ba90-3f9d438629d7","order_by":2,"name":"Lei Xu","email":"","orcid":"","institution":"Liaoning University of International Business and Economics","correspondingAuthor":false,"prefix":"","firstName":"Lei","middleName":"","lastName":"Xu","suffix":""}],"badges":[],"createdAt":"2025-05-29 07:53:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6774071/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6774071/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":99318046,"identity":"9700515f-ddc1-4ab4-b4c6-6b0c866fcfa6","added_by":"auto","created_at":"2025-12-31 16:31:17","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":720219,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6774071/v1_covered_a3f3bdfe-cd2e-4b24-9be3-254ace933ec8.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Optimizing scheduling and bunkering decision for tramp shipping fleet under stochastic demand and bunker prices","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Tramp shipping fleet, Ship scheduling and bunkering, Stochastic demand and bunker prices, Service level","lastPublishedDoi":"10.21203/rs.3.rs-6774071/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6774071/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe operational decisions faced by tramp shipping fleet operators are crucial, particularly in the current volatile global economic and trade environment. Navigating through uncertain market conditions poses a significant challenge for operators striving to optimize the operational decisions of their tramp shipping fleets. This paper delves into the tramp shipping fleet scheduling and bunkering problem, incorporating stochastic demand and bunker prices, with the objective of maximizing operational revenue while adhering to specified service levels for shippers. We introduce the service level for shippers as the probability of demand being served and formulate our research problem as a stochastic mixed-integer programming model with a service level constraint. To address this model, we transform it into a multi-objective reachability problem, defining operational revenue and service level requirements while setting a total operational revenue target. Concurrently, we propose a Debt Related Tramp Shipping Fleet Scheduling and Bunkering (DRTSFSB) algorithm framework to guide fleet scheduling and bunkering decisions in each scenario. The numerical experiments conducted conclusively demonstrate that the proposed approach significantly reduces computation time while maintaining comparable performance to the Sample Average Approximation (SAA) method. 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