An Optimization Model for the University School Bus Routing Problem

An Optimization Model for the University School Bus Routing Problem | 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 Case Report An Optimization Model for the University School Bus Routing Problem Marco Antonio Sánchez Carmona, J.R. Marcial-Romero, Lourdes Loza-Hernandez, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8843865/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 12 You are reading this latest preprint version Abstract Passenger transport, and particularly student transport, tends to become saturated due to on one side the growing increase and distribution of the student population, and the other the few available buses. This article proposes the use of clustering processes through the Density-Based Spatial Clustering of Applications with Noise algorithm, alongside cluster quality assessment metrics, to establish suitable bus stops. Additionally, a convex hull is employed to determine the subset of bus stops from which the transport routes will start, called terminals. Based on the elements identified through clustering and the convex hull, the parameters and dataset required for an Integer Linear Programming model were defined. In order to generate appropriate transport routes for each available bus, the model incorporates constraints based on the Vehicle Routing Problem. Furthermore, decision variables and constraints were defined to transport the maximum number of students to their designated destinations by means of the Maximum Flow Problem, resulting in a multi-objective function aimed at finding routes with minimum cost and maximum student flow per bus, and also incorporating departure times. The transport service at the Autonomous University of the State of Mexico was used as a case study to test the proposal. The model was solved using the COIN-OR Branch and Cut solver, which enabled the determination of optimal routes for each bus, successfully transporting the highest possible number of students to their respective destinations at minimal (time) cost, and ensuring that all routes start and end at appropriate times, in accordance with student entry schedules. SBRP Max Flow VRP Integer Linear Programming Clustering DBSCAN Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 19 Mar, 2026 Reviewers agreed at journal 09 Mar, 2026 Reviews received at journal 09 Mar, 2026 Reviewers agreed at journal 07 Mar, 2026 Reviews received at journal 06 Mar, 2026 Reviewers agreed at journal 24 Feb, 2026 Reviewers agreed at journal 20 Feb, 2026 Reviewers invited by journal 20 Feb, 2026 Editor invited by journal 18 Feb, 2026 Editor assigned by journal 13 Feb, 2026 Submission checks completed at journal 13 Feb, 2026 First submitted to journal 10 Feb, 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. 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-8843865","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Case Report","associatedPublications":[],"authors":[{"id":594503948,"identity":"9eb0112b-17f6-4762-adcf-8bd3da1be576","order_by":0,"name":"Marco Antonio Sánchez Carmona","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA30lEQVRIiWNgGAWjYPCCAyCC8QHJWpgNSNbCJkGUWt324w8/F9TckZNvP/ysmqfGJppfIoF1Mw8eLWZncoylZxx7ZszYk2Z2m+dYWu7MngNsN2fg03Igh0Gat+FwYrMEA1AL2+HcDccb2G58wKfl/PPHv4Fa6tsk2L8V8/z7n7v/MAPbjQR8Wm4kmIFsSeCR4DFj5m07kLuBnZAtN96YWfMcO2w4gyenWHJuX3LujDMH2/D75Xz649s8NYfl5duPb/zw5ptdbv+M5GO38YUYNsDYQKKGUTAKRsEoGAXoAADullI6Z/hZzgAAAABJRU5ErkJggg==","orcid":"","institution":"Universidad Autónoma del Estado de México","correspondingAuthor":true,"prefix":"","firstName":"Marco","middleName":"Antonio Sánchez","lastName":"Carmona","suffix":""},{"id":594503949,"identity":"b64ae344-b3c9-42c5-b67e-f35d8bcb331e","order_by":1,"name":"J.R. 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