Integrated Production Scheduling and Multi-trip Vehicle Routing in Mobile 3D Printing: A Two-Phase Genetic Algorithm–MILP Approach

Integrated Production Scheduling and Multi-trip Vehicle Routing in Mobile 3D Printing: A Two-Phase Genetic Algorithm–MILP Approach | 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 Integrated Production Scheduling and Multi-trip Vehicle Routing in Mobile 3D Printing: A Two-Phase Genetic Algorithm–MILP Approach Vilém Heinz, Mohammad Rohaninejad, Zdeněk Hanzálek, Behdin Vahedi-Nouri This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9622053/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 This paper studies a novel integrated optimization problem that arises in mobile additive manufacturing, where production and delivery are performed simultaneously by 3D printing vehicles. It extends existing Mobile Production Vehicle Routing Problem formulations by incorporating realistic manufacturing constraints, including area-based batch capacity, material compatibility, sequence-dependent setup times, and the possibility of job rejection and depot refilling. To address the high computational complexity, several heuristic methods were initially tested, with a tailored genetic algorithm (GA) being described in detail, as it clearly outperformed the others. A parameter study on key GA parameters was carried out. It identified the best configuration, with an average deviation of 0.06% to the best solution—eight times lower than the next best. Computational experiments show that GA consistently produces high-quality solutions in approximately 1–2 minutes, outperforming or matching the MILP solutions obtained with a 1-hour time limit, while also using significantly fewer computational resources. These results indicate that GA alone is an effective candidate for generating high-quality solutions. Furthermore, a hybrid approach (MILP ws ) is proposed, using GA solutions as a warm start of the MILP solver. This significantly improves model scalability for larger instances, where MILP ws achieves solutions more than a third closer to the lower bound (22.2% vs 34.8% gap) for instances of 20 customers, compared to the standalone MILP. In general, the results demonstrate that integrating production and routing in mobile manufacturing while incorporating an extended set of manufacturing constraints is computationally tractable. JEL Classification: C61 , C63 , L60 , R41 , D24 , O33 MSC Classification: 90C11 , 90B06 , 90B35 , 90C59 , 90C90 , 90C27 , 68W50 Operations Research Mobile additive manufacturing Integrated production and distribution Vehicle routing problem Batch scheduling Genetic algorithm Warm start 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. 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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-9622053","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":635015505,"identity":"ccd63273-e328-4826-bcdc-7fbaf10b7b05","order_by":0,"name":"Vilém 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4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper studies a novel integrated optimization problem that arises in mobile additive manufacturing, where production and delivery are performed simultaneously by 3D printing vehicles. It extends existing Mobile Production Vehicle Routing Problem formulations by incorporating realistic manufacturing constraints, including area-based batch capacity, material compatibility, sequence-dependent setup times, and the possibility of job rejection and depot refilling.\u003c/p\u003e\n\u003cp\u003eTo address the high computational complexity, several heuristic methods were initially tested, with a tailored genetic algorithm (GA) being described in detail, as it clearly outperformed the others. A parameter study on key GA parameters was carried out. It identified the best configuration, with an average deviation of 0.06% to the best solution—eight times lower than the next best. Computational experiments show that GA consistently produces high-quality solutions in approximately 1–2 minutes, outperforming or matching the MILP solutions obtained with a 1-hour time limit, while also using significantly fewer computational resources. These results indicate that GA alone is an effective candidate for generating high-quality solutions.\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFurthermore, a hybrid approach (MILP\u003csub\u003ews\u003c/sub\u003e) is proposed, using GA solutions as a warm start of the MILP solver. This significantly improves model scalability for larger instances, where MILP\u003csub\u003ews\u003c/sub\u003e achieves solutions more than a third closer to the lower bound (22.2% vs 34.8% gap) for instances of 20 customers, compared to the standalone MILP. In general, the results demonstrate that integrating production and routing in mobile manufacturing while incorporating an extended set of manufacturing constraints is computationally tractable.\u003c/p\u003e\n\u003cp\u003eJEL Classification: C61 , C63 , L60 , R41 , D24 , O33\u003c/p\u003e\n\u003cp\u003eMSC Classification: 90C11 , 90B06 , 90B35 , 90C59 , 90C90 , 90C27 , 68W50\u003c/p\u003e","manuscriptTitle":"Integrated Production Scheduling and Multi-trip Vehicle Routing in Mobile 3D Printing: A Two-Phase Genetic Algorithm–MILP Approach","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-07 06:57:04","doi":"10.21203/rs.3.rs-9622053/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":"45d2b16d-e651-4dd4-9dc6-0949238f6ca6","owner":[],"postedDate":"May 7th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":67585019,"name":"Operations Research"}],"tags":[],"updatedAt":"2026-05-07T06:57:04+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-07 06:57:04","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9622053","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9622053","identity":"rs-9622053","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}