Critical Chains and Its Randomness Study

Critical Chains and Its Randomness Study | 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Article Critical Chains and Its Randomness Study Xiaokang Han, Wenzhou Yan, Ting Liu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-522605/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 It has been widely accepted in the academic community that the Critical Chain Method (CCM) has significant advantages over the Critical Path Method (CPM) in solving the problem with resource constraints. However, this paper conducted a study on comparing the two methods of Critical Chain Method and Critical Path Method, and found that the only difference between those two methods lies in how to determine the priority of resources allocating, and on the assumption of not setting buffer zone, those two methods have no essential distinctions at all. By establishing the relationship between CCM and CPM, this paper also enriched and improved CCM to some extent, and pointed out that the buffer zone setting in CCM is merely subjective and short of scientificity. In the meantime, for the problem of unclear representation of critical chains, it proposed two ways of representing critical chains and related rules to follow. To verify the conclusion of this paper, further detailed case study of comparing CCM and CPM was performed. Affected by various uncertain factors, the project construction sequence is random, the total construction duration is random, and the critical chain is also random, so it is unable to determine how to direct construction. Aiming at the randomness of the critical chain, this article analyzed various uncertain factors of the critical chain, and on the basis of solving the critical chain sequence time, it proposed the approach to determine the completion probability of the total construction duration and control the construction of the critical chain to direct the construction, in the meantime, the inverse algorithm was adopted to determine of the construction duration under the condition of required completion probability. Computer Architecture and Engineering critical chain critical path method comparative study randomness duration optimization resource constraints Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Full Text Due to technical limitations, full-text HTML conversion of this manuscript could not be completed. However, the manuscript can be downloaded and accessed as a PDF. 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-522605","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":27888971,"identity":"343fa260-21b8-4fd0-b083-0988c8ff628e","order_by":0,"name":"Xiaokang Han","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvUlEQVRIiWNgGAWjYBACfv7mgw8/VPyX4ydai+SMY8nGEmeYjSUbiNVicCDHTIC3jTlxwwGibWk4YMYg2cbGuPl48gaGHxXbCGvhZ25Ie1BwjofZ7MyzAsaeM7eJsuW4gUSZBJvZjRwDZsY2IrQYHEhsk+BhM+AxnkG8lmQ2CZ62BAkDCWK1AAOZGRjIBwwkgH45SJRf+Pn7PwKj8kB9f3vyxgc/KojQggQSDA6QpB6shVQdo2AUjIJRMEIAAFRAQBwbA1eaAAAAAElFTkSuQmCC","orcid":"","institution":"Xi’an University of Architecture and Technology","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Xiaokang","middleName":"","lastName":"Han","suffix":""},{"id":27888972,"identity":"096891f3-ee9a-4c65-89f9-36d20d0ec2ae","order_by":1,"name":"Wenzhou Yan","email":"","orcid":"","institution":"Xi'an University of Architecture and Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Wenzhou","middleName":"","lastName":"Yan","suffix":""},{"id":27888973,"identity":"70d63f99-bfce-4584-a55e-8511558828f7","order_by":2,"name":"Ting Liu","email":"","orcid":"","institution":"Xi'an University of Architecture and Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Ting","middleName":"","lastName":"Liu","suffix":""}],"badges":[],"createdAt":"2021-05-13 06:59:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-522605/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-522605/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":9396446,"identity":"9aedb1b8-e77b-4b6b-afbd-0521acbdf422","added_by":"auto","created_at":"2021-05-20 16:32:05","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":22501,"visible":true,"origin":"","legend":"Directly mark out the changes in critical chains and related activity logic relationships on the network diagram","description":"","filename":"Fig1.png","url":"https://assets-eu.researchsquare.com/files/rs-522605/v1/c792e01b38f85a48ed30a379.png"},{"id":9396959,"identity":"e4cb25a9-6f39-4515-b39e-0efcab4e076b","added_by":"auto","created_at":"2021-05-20 16:41:05","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":58215,"visible":true,"origin":"","legend":"Critical chain representation","description":"","filename":"Fig2.png","url":"https://assets-eu.researchsquare.com/files/rs-522605/v1/2a6b598fc0f6689dc95690a6.png"},{"id":9396679,"identity":"3403b263-007d-4d93-8f54-3e3d10fc0b1e","added_by":"auto","created_at":"2021-05-20 16:35:06","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":38586,"visible":true,"origin":"","legend":"Critical chain representation","description":"","filename":"Fig3.png","url":"https://assets-eu.researchsquare.com/files/rs-522605/v1/37e027a078f879abe789c870.png"},{"id":9396825,"identity":"7eecf714-bd99-414d-98c2-84298823b816","added_by":"auto","created_at":"2021-05-20 16:38:05","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":16440,"visible":true,"origin":"","legend":"A comparative study of the Critical Chain Method and Critical Path Method","description":"","filename":"Fig4.png","url":"https://assets-eu.researchsquare.com/files/rs-522605/v1/b59c611694890856c802fe07.png"},{"id":9396675,"identity":"51a6b967-2183-49db-ab12-1ee3ef70679f","added_by":"auto","created_at":"2021-05-20 16:35:05","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":39313,"visible":true,"origin":"","legend":"Optimization principle diagram","description":"","filename":"Fig5.png","url":"https://assets-eu.researchsquare.com/files/rs-522605/v1/969d4c289ec93f034bad0618.png"},{"id":9396451,"identity":"b5bb6cfc-8f0f-4e15-a100-8d45bb5c65a7","added_by":"auto","created_at":"2021-05-20 16:32:05","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":24823,"visible":true,"origin":"","legend":"Schematic of the key chain based on CPM and CCM","description":"","filename":"Fig6.png","url":"https://assets-eu.researchsquare.com/files/rs-522605/v1/001d1816db554340fa22da33.png"},{"id":9396452,"identity":"26f65e85-b290-4ee6-9b66-8586cf1d7397","added_by":"auto","created_at":"2021-05-20 16:32:06","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":13287,"visible":true,"origin":"","legend":"Network for a case project","description":"","filename":"Fig7.png","url":"https://assets-eu.researchsquare.com/files/rs-522605/v1/2001b76ecd6957affc7bbdfd.png"},{"id":9396677,"identity":"0d5deaef-1e94-4b27-b9d5-587c5796c279","added_by":"auto","created_at":"2021-05-20 16:35:05","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":35577,"visible":true,"origin":"","legend":"Critical chain network for a project","description":"","filename":"Fig8.png","url":"https://assets-eu.researchsquare.com/files/rs-522605/v1/2711a534161752bcbd125dc9.png"},{"id":13635361,"identity":"3146be92-e568-4874-a2d6-d37dda406473","added_by":"auto","created_at":"2021-09-17 08:36:45","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":536737,"visible":true,"origin":"","legend":"","description":"","filename":"CriticalChainsandItsRandomnessStudy.pdf","url":"https://assets-eu.researchsquare.com/files/rs-522605/v1_covered.pdf"},{"id":9396960,"identity":"bf5d66fb-b97b-43c9-9fde-604f82974978","added_by":"auto","created_at":"2021-05-20 16:41:12","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":533085,"visible":true,"origin":"","legend":"","description":"","filename":"CriticalChainsandItsRandomnessStudy.pdf","url":"https://assets-eu.researchsquare.com/files/rs-522605/v1_covered.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Critical Chains and Its Randomness Study","fulltext":[{"header":"Full Text","content":"\u003cp\u003eDue to technical limitations, full-text HTML conversion of this manuscript could not be completed. However, the manuscript can be downloaded and accessed as a PDF.\u003c/p\u003e"}],"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":false,"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":"critical chain, critical path method, comparative study, randomness, duration optimization, resource constraints","lastPublishedDoi":"10.21203/rs.3.rs-522605/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-522605/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIt has been widely accepted in the academic community that the Critical Chain Method (CCM) has significant advantages over the Critical Path Method (CPM) in solving the problem with resource constraints. However, this paper conducted a study on comparing the two methods of Critical Chain Method and Critical Path Method, and found that the only difference between those two methods lies in how to determine the priority of resources allocating, and on the assumption of not setting buffer zone, those two methods have no essential distinctions at all. By establishing the relationship between CCM and CPM, this paper also enriched and improved CCM to some extent, and pointed out that the buffer zone setting in CCM is merely subjective and short of scientificity. In the meantime, for the problem of unclear representation of critical chains, it proposed two ways of representing critical chains and related rules to follow. To verify the conclusion of this paper, further detailed case study of comparing CCM and CPM was performed. Affected by various uncertain factors, the project construction sequence is random, the total construction duration is random, and the critical chain is also random, so it is unable to determine how to direct construction. Aiming at the randomness of the critical chain, this article analyzed various uncertain factors of the critical chain, and on the basis of solving the critical chain sequence time, it proposed the approach to determine the completion probability of the total construction duration and control the construction of the critical chain to direct the construction, in the meantime, the inverse algorithm was adopted to determine of the construction duration under the condition of required completion probability.\u003c/p\u003e","manuscriptTitle":"Critical Chains and Its Randomness Study","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2021-05-20 16:32:03","doi":"10.21203/rs.3.rs-522605/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":"534a33f4-853b-4cda-b7de-7e8afe8d5573","owner":[],"postedDate":"May 20th, 2021","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":4457383,"name":"Computer Architecture and Engineering"}],"tags":[],"updatedAt":"2021-05-21T05:14:04+00:00","versionOfRecord":[],"versionCreatedAt":"2021-05-20 16:32:03","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-522605","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-522605","identity":"rs-522605","version":["v1"]},"buildId":"WrCJVZZCHTDjtuVLN7oU0","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}