A queue-dependent 2-cutoff heuristic for scheduling of routine and urgent tasks

A queue-dependent 2-cutoff heuristic for scheduling of routine and urgent tasks | 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 A queue-dependent 2-cutoff heuristic for scheduling of routine and urgent tasks Refael Hassin, Jiesen Wang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7374243/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 presence of urgent customers, whose service cannot be delayed, is common in clinics, maintenance systems, government departments, etc. As a result, service slots are often reserved for such customers, and if the number of arrivals exceeds the reserved capacity, costly overtime work may be incurred. In contrast, routine customers can be appointed to a later day. The system manager must decide how many routine customers to serve today and how many to postpone, given the current number of unserved routine customers. We characterize the optimal strategy that minimizes the expected waiting and overtime costs, and introduce a 2-cutoff heuristic that closely approximates the optimal policy. In addition, we examine a special case with no urgent customers and propose alternative solution methods for this simpler setting. scheduling patients urgent tasks cutoff heuristic 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-7374243","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":525531621,"identity":"fc1cb82d-1383-4128-9fde-5608db90cbd2","order_by":0,"name":"Refael Hassin","email":"","orcid":"","institution":"Tel Aviv University","correspondingAuthor":false,"prefix":"","firstName":"Refael","middleName":"","lastName":"Hassin","suffix":""},{"id":525531622,"identity":"962c81f6-2c05-4c72-aee0-08cdcb8affde","order_by":1,"name":"Jiesen Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4ElEQVRIiWNgGAWjYBACxmY4k/kAkJCQIUULWwJICw8pFvIYgEmC6pjbmQ9/+LjjsLw5/5rPr27UWPAwsB8+ugG/w9jSJGeeOWy4c8bbbdY5x4AO40lLu4FfC48ZM2/bbcYNN85uM85hA2qR4DEjoIX/8+e/bbftN9w488w45x9RWngYpBnbbiduON/D/Di3jSgtbGaSvW3/kzfcYDNjzu2T4GEj5BfD/sOPP/xsS7PdcP7w48853+rk+NkPH8OvpQHGkkhgkwDRbPiUg4A8nMV/gPkDIdWjYBSMglEwMgEAjpVLICBgW9QAAAAASUVORK5CYII=","orcid":"","institution":"Tel Aviv University","correspondingAuthor":true,"prefix":"","firstName":"Jiesen","middleName":"","lastName":"Wang","suffix":""}],"badges":[],"createdAt":"2025-08-14 13:23:08","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7374243/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7374243/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":93739844,"identity":"5790c7a5-e175-4bfc-b5ed-e0ab7814a16d","added_by":"auto","created_at":"2025-10-17 04:44:29","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":895404,"visible":true,"origin":"","legend":"","description":"","filename":"CapacityAllocationRafiJiesen.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7374243/v1/833578d405ed110096ac5ca2.pdf"},{"id":93739843,"identity":"0569790b-78c3-4c5b-a826-0867ff59e272","added_by":"auto","created_at":"2025-10-17 04:44:29","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":3336,"visible":true,"origin":"","legend":"","description":"","filename":"a2f5ed085a6049318f37d0dd08283b0e.json","url":"https://assets-eu.researchsquare.com/files/rs-7374243/v1/111ac0f63f63ac2ee78102c3.json"},{"id":93740115,"identity":"da20a5e2-6eff-4205-b038-54ea13edce9d","added_by":"auto","created_at":"2025-10-17 04:52:30","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":804420,"visible":true,"origin":"","legend":"","description":"","filename":"CapacityAllocationRafiJiesen.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7374243/v1_covered_7bf18d3b-f0c1-4311-97c8-78dea7307a90.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A queue-dependent 2-cutoff heuristic for scheduling of routine and urgent tasks","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":"scheduling patients, urgent tasks, cutoff heuristic","lastPublishedDoi":"10.21203/rs.3.rs-7374243/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7374243/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The presence of urgent customers, whose service cannot be delayed, is common in clinics, maintenance systems, government departments, etc. As a result, service slots are often reserved for such customers, and if the number of arrivals exceeds the reserved capacity, costly overtime work may be incurred. In contrast, routine customers can be appointed to a later day. The system manager must decide how many routine customers to serve today and how many to postpone, given the current number of unserved routine customers. We characterize the optimal strategy that minimizes the expected waiting and overtime costs, and introduce a 2-cutoff heuristic that closely approximates the optimal policy. In addition, we examine a special case with no urgent customers and propose alternative solution methods for this simpler setting.","manuscriptTitle":"A queue-dependent 2-cutoff heuristic for scheduling of routine and urgent tasks","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-17 04:44:24","doi":"10.21203/rs.3.rs-7374243/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":"b65f07fb-3269-493b-8ae6-4727f28ed1a0","owner":[],"postedDate":"October 17th, 2025","published":true,"recentEditorialEvents":[{"type":"decision","content":"Revision requested","date":"2026-05-12T19:59:14+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-05-12T20:09:52+00:00","versionOfRecord":[],"versionCreatedAt":"2025-10-17 04:44:24","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7374243","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7374243","identity":"rs-7374243","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}