Optimising Elective Theatre Lists: Machine Learning and Mathematical Optimisation for Patient Scheduling

Optimising Elective Theatre Lists: Machine Learning and Mathematical Optimisation for Patient Scheduling | 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 Optimising Elective Theatre Lists: Machine Learning and Mathematical Optimisation for Patient Scheduling Madhu Sudan Sapkota, Michael Kampouridis, Hugo Herrera, Faiyaz Doctor, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9140578/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 Current elective surgical scheduling often depends on planners’ judgement and local rules of thumb. While machine learning and optimisation have advanced rapidly and show clear promise for improving such decisions, they are still not widely used in routine theatre list planning. This study introduces an integrated approach to elective surgical scheduling that reflects the uncertainty and day-to-day pressures of real theatre planning. It uses pre-trained machine learning model(s) to predict how long operations are likely to take, and a statistical component to capture how variable those durations can be. Together, these estimates feed into the scheduling problem so that the lists can be built to be more reliable and less prone to disruption. To solve the core scheduling problem, two optimisation methodologies are employed: (1) an Integer Linear Programming (ILP) solver for exact mathematical optimisation, and (2) a custom-developed meta-heuristic algorithm designed for scalability and flexibility in complex scheduling environments. Evaluating both methods across different operational conditions enables decision-makers to select the most suitable approach based on usability, solution quality, and runtime requirements (e.g., exact optimal schedules when time permits versus fast, scalable schedules when responsiveness is critical). The ultimate model(s) are designed in line with an NHS Trust setting— scheduling patients from the waiting list while taking into account the Trust's objectives in optimal resource allocation and patient satisfaction. The proposed approaches demonstrate the potential for improved scheduling efficiency, better resource utilisation, and enhanced patient satisfaction, highlighting the value of integrating AI-driven techniques in healthcare operations. Health Economics & Outcomes Research Surgery Scheduling Meta-heuristic Integer Linear Programming Simulated-Annealing Full Text Additional Declarations The authors declare no competing interests. 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-9140578","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":607100088,"identity":"22475cd5-5302-4035-8b14-8b04c5a873b7","order_by":0,"name":"Madhu Sudan Sapkota","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABDUlEQVRIiWNgGAWjYHACMwjFAyIM/ssBScYDDAwJRGlhbGCoYDZmYGBmIEXLGebEBkJadNsPb3vMw1Anb85z+PiDn21s6f0S+QcOfKhIY+Bv78aqz+xMWrkxD8Nhw529bYmNvW08uTNnJDMcnHEmh0HizNkNWLUcyDGT5mE4wLjhPI9hA2+bRO6GG8kMh3nbKhgMgGysWs6/AWmpswdpafzbZpBuQFDLDbAtzIkbzvYYNvOcSUiAasnBo+VZmeQcg8PJO3uOJc6WqThgOLPnsQHQL2k8OP1yPnmbxJuKOtvtPMkHPr4xOCDPz5748MGHimQ5/vZerFogwACMUAEPbuUIXaNgFIyCUTAKsAMAJERm4LDdAn4AAAAASUVORK5CYII=","orcid":"https://orcid.org/0009-0002-6487-5749","institution":"ESNEFT, Colchester UK","correspondingAuthor":true,"prefix":"","firstName":"Madhu","middleName":"Sudan","lastName":"Sapkota","suffix":""},{"id":607100089,"identity":"67ebf1f6-4d96-4ca8-a96c-8ca8f1222d46","order_by":1,"name":"Michael Kampouridis","email":"","orcid":"","institution":"University of Essex, Colchester, UK","correspondingAuthor":false,"prefix":"","firstName":"Michael","middleName":"","lastName":"Kampouridis","suffix":""},{"id":607100090,"identity":"3dca15d8-b9c0-4a7e-a631-b0ab79b4fbb8","order_by":2,"name":"Hugo Herrera","email":"","orcid":"","institution":"ESNEFT, Colchester UK","correspondingAuthor":false,"prefix":"","firstName":"Hugo","middleName":"","lastName":"Herrera","suffix":""},{"id":607100091,"identity":"96c24e06-b52b-416c-88d0-86c38ffe756e","order_by":3,"name":"Faiyaz Doctor","email":"","orcid":"","institution":"University of Essex, Colchester, UK","correspondingAuthor":false,"prefix":"","firstName":"Faiyaz","middleName":"","lastName":"Doctor","suffix":""},{"id":607100092,"identity":"cb2de697-79d3-4540-95e6-047a219560d2","order_by":4,"name":"Xinan Yang","email":"","orcid":"","institution":"University of Essex, Colchester, UK","correspondingAuthor":false,"prefix":"","firstName":"Xinan","middleName":"","lastName":"Yang","suffix":""}],"badges":[],"createdAt":"2026-03-16 17:08:45","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9140578/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9140578/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104808712,"identity":"fe121589-9e6f-417f-9157-818f22a83b22","added_by":"auto","created_at":"2026-03-17 12:39:35","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1389073,"visible":true,"origin":"","legend":"","description":"","filename":"OptimalSchedulingmodelSN4.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9140578/v1_covered_daae1b05-af82-48f1-a57d-a97b5b15e2c8.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eOptimising Elective Theatre Lists: Machine Learning and Mathematical Optimisation for Patient Scheduling\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"University of Essex","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":"Surgery Scheduling, Meta-heuristic, Integer Linear Programming, Simulated-Annealing","lastPublishedDoi":"10.21203/rs.3.rs-9140578/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9140578/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCurrent elective surgical scheduling often depends on planners’ judgement and local rules of thumb. While machine learning and optimisation have advanced rapidly and show clear promise for improving such decisions, they are still not widely used in routine theatre list planning.\u003c/p\u003e\n\u003cp\u003eThis study introduces an integrated approach to elective surgical scheduling that reflects the uncertainty and day-to-day pressures of real theatre planning. It uses pre-trained machine learning model(s) to predict how long operations are likely to take, and a statistical component to capture how variable those durations can be. Together, these estimates feed into the scheduling problem so that the lists can be built to be more reliable and less prone to disruption.\u003c/p\u003e\n\u003cp\u003eTo solve the core scheduling problem, two optimisation methodologies are employed: (1) an Integer Linear Programming (ILP) solver for exact mathematical optimisation, and (2) a custom-developed meta-heuristic algorithm designed for scalability and flexibility in complex scheduling environments. Evaluating both methods across different operational conditions enables decision-makers to select the most suitable approach based on usability, solution quality, and runtime requirements (e.g., exact optimal schedules when time permits versus fast, scalable schedules when responsiveness is critical).\u003c/p\u003e\n\u003cp\u003eThe ultimate model(s) are designed in line with an NHS Trust setting— \u0026nbsp;scheduling patients from the waiting list while taking into account the Trust's objectives in optimal resource allocation and patient satisfaction. The proposed approaches demonstrate the potential for improved scheduling efficiency, better resource utilisation, and enhanced patient satisfaction, highlighting the value of integrating AI-driven techniques in healthcare operations.\u003c/p\u003e","manuscriptTitle":"Optimising Elective Theatre Lists: Machine Learning and Mathematical Optimisation for Patient Scheduling","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-17 11:59:13","doi":"10.21203/rs.3.rs-9140578/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"eb687f3a-77c8-4272-b478-12cdf2a5479c","owner":[],"postedDate":"March 17th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":64650893,"name":"Health Economics \u0026 Outcomes Research"}],"tags":[],"updatedAt":"2026-03-17T11:59:13+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-17 11:59:13","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9140578","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9140578","identity":"rs-9140578","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}