A Simulation-Driven Hybrid SPN–Machine Learning Framework for Container Freight Rate Forecasting under Uncertainty

A Simulation-Driven Hybrid SPN–Machine Learning Framework for Container Freight Rate Forecasting under Uncertainty | 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 A Simulation-Driven Hybrid SPN–Machine Learning Framework for Container Freight Rate Forecasting under Uncertainty Shabnam Shahzadi, Fawaz Khaled Alarfaj This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8587911/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 In a market where the business environment is unstable and uncertain, forecasting container freight rates is crucial for effective supply chain planning, cost control, and risk avoidance. This paper proposes a hybrid forecasting model that predicts container freight rates more accurately by clearly considering operational uncertainty. The model integrates machine learning (ML) and stochastic petri nets (SPNs). The simulation covers key logistic operations, such as port congestion, vessel queues, capacity usage, and equipment availability. It uses monthly route-level data from the Ningbo Containerized Freight Index (NCFI). To learn complex Machine Learning models like Prophet, LSTM, Random Forest, and XGBoost, the stochastic operational states are transformed into structures features. These features are combined with historical market data. The model’s performance is measured by RMSE, MAE, MAPE, and í µí± 2. The results show that the hybrid SPN-ML model outperforms benchmark ML models. It produces fewer predication errors and offers greater explanatory power, especially during periods of market uncertainty. Simulations enhance the learning processes. Sensitivity analysis confirms a clear correction between forecast accuracy and the realism of the simulation layer. The results suggest combining machine learning with stochastic simulation improves predictive robustness, interpretability, and generalizability compared to models based solely on real data. The proposed methodology provides a practical basis for freight rate prediction amid uncertainty in global shipping markets. It offers a useful decision-making tool for carriers and shippers on the Ningbo-Middel East route. Physical sciences/Engineering Physical sciences/Mathematics and computing Maritime Logistics Ningbo Containerized Freight Index (NCFI) Port Congestion dynamics Time-Series Prediction Vessel Utilization Rate Uncertainty 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-8587911","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":578862459,"identity":"78233313-9868-45ad-a1e0-0c0cd37606b2","order_by":0,"name":"Shabnam Shahzadi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2klEQVRIiWNgGAWjYDACCQY2ECXHwAwkExgYGBuI1WJMupZEmErCWuRnNz97XFCzLX07O/vDDw8YbGQ3HGB+9gCfFoM7x8yNZxy7nbuzmcdYIoEhzXjDATZzA7xaJBLMpHnYbuduOMzDBvTL4cQNB3jYJPA6bEb6N2mef7fTDQ6zPwNq+U9YC8ONHDNp3rbbCQaHGcyAWg4Q1mJwI6fcmLfvtiHQYUC/GCQbzzzMZkbIYdse83y7LW9w/vjDjz8q7GT7jjc/w+8wNEuBmJkE9aNgFIyCUTAKsAMAuSlHDnOqMZ0AAAAASUVORK5CYII=","orcid":"","institution":"Ningbo China insitutute of Supply Chain Innovation","correspondingAuthor":true,"prefix":"","firstName":"Shabnam","middleName":"","lastName":"Shahzadi","suffix":""},{"id":578862460,"identity":"21e6d26f-f2d4-4d54-9951-6d014a9705a3","order_by":1,"name":"Fawaz Khaled Alarfaj","email":"","orcid":"","institution":"King Faisal University","correspondingAuthor":false,"prefix":"","firstName":"Fawaz","middleName":"Khaled","lastName":"Alarfaj","suffix":""}],"badges":[],"createdAt":"2026-01-13 06:23:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8587911/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8587911/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":101183223,"identity":"b054bcad-c5af-46ef-84ec-84af43d6bfa7","added_by":"auto","created_at":"2026-01-27 04:55:00","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":802132,"visible":true,"origin":"","legend":"","description":"","filename":"RevisedManuscriptammendments.docx","url":"https://assets-eu.researchsquare.com/files/rs-8587911/v1/2d88590b9eeeb83ddef61dc2.docx"},{"id":101183224,"identity":"7e36e949-c36a-4e49-b81c-537d0f3a88e1","added_by":"auto","created_at":"2026-01-27 04:55:01","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5290,"visible":true,"origin":"","legend":"","description":"","filename":"bb3de033883241bbaefd61183f4677de.json","url":"https://assets-eu.researchsquare.com/files/rs-8587911/v1/fb85a184e22b453f9e303ff7.json"},{"id":104433525,"identity":"879e2b13-dbaa-48b3-bc0a-09b69407701e","added_by":"auto","created_at":"2026-03-11 16:11:12","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":804734,"visible":true,"origin":"","legend":"","description":"","filename":"RevisedManuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8587911/v1_covered_77396983-8159-40a1-86b0-d71633125174.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Simulation-Driven Hybrid SPN–Machine Learning Framework for Container Freight Rate Forecasting under Uncertainty","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":"Maritime Logistics Ningbo Containerized Freight Index (NCFI), Port Congestion dynamics, Time-Series Prediction, Vessel Utilization Rate, Uncertainty","lastPublishedDoi":"10.21203/rs.3.rs-8587911/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8587911/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In a market where the business environment is unstable and uncertain, forecasting container freight rates is crucial for effective supply chain planning, cost control, and risk avoidance. 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