A Multi-Scenario Bi-objective Optimization Model for Robotic Parcel Sorting System

A Multi-Scenario Bi-objective Optimization Model for Robotic Parcel Sorting System | 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 Multi-Scenario Bi-objective Optimization Model for Robotic Parcel Sorting System Bilal Ahmadi, Iwan Vanany, Ratna Sari Dewi, Muhammad Khakim Habibi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8930324/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract This study contributes to the robotic-based sorting system, specifically in the parcel industry, due to the lack of multi-objective consideration that prior studies neglected. This study examines a robotic parcel-sorting system with two loading stations and a fleet of robots that sorts parcels to their respective collection points. The parcel-to-station, robot-to-station, and parcel-to-robot assignment decisions are considered. A mixed-integer programming model with two important yet conflicting objective functions, namely the makespan and fleet size of robots, is proposed. To regulate workload balance of parcel assignments between stations and robots, we evaluate two scenarios regarding to the number of parcels to be processed: Scenario 1 with lower limit only and Scenario 2 with both lower and upper limit. The ε-constraint method with a branch-and-cut algorithm and lazy constraint procedure is used to generate solutions using the Gurobi solver. The results show that the model can produce optimum non-dominated solutions that govern the Pareto front for all scenarios. Furthermore, in most cases, Scenario 2 outperformed Scenario 1 in terms of hypervolume values. bi-objective optimization ε-constraint method robotic parcel sorting workload balancing Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 13 Apr, 2026 Reviewers invited by journal 24 Feb, 2026 Editor assigned by journal 23 Feb, 2026 Submission checks completed at journal 23 Feb, 2026 First submitted to journal 20 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. 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-8930324","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":596197410,"identity":"d2bec52e-955b-47cb-96c4-e2d2985706ab","order_by":0,"name":"Bilal Ahmadi","email":"","orcid":"","institution":"Institut Teknologi Sepuluh Nopember","correspondingAuthor":false,"prefix":"","firstName":"Bilal","middleName":"","lastName":"Ahmadi","suffix":""},{"id":596197411,"identity":"b8adcf15-d012-41e4-a235-66f89c002376","order_by":1,"name":"Iwan Vanany","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3ElEQVRIiWNgGAWjYPACGx4GBsYGCJuZwYAYLWkgLY0NpGg5DCJg1hDQYnD87MHPhW3nZfgZmNsf/mCwk2dgZ96AX8uZvGTpmW23eSQbGBubeRiSDRuY2QrwapFsyDGQ5gVqMTgA1AL0SAIDMw9+h0n2vzH+zdt2jsceqKXxB0M9YS38EjlmQFsOAJUBQ4yH4TAxWt6YWfOcS+aROMzYOJvH4LhhGyG/sPHnGN/mKbOz529vf/DxR0W1PD//YfwhBgaMbAygGGQAxwgbYfUg8Ic4ZaNgFIyCUTBCAQD9mTf2tSNvhwAAAABJRU5ErkJggg==","orcid":"","institution":"Institut Teknologi Sepuluh Nopember","correspondingAuthor":true,"prefix":"","firstName":"Iwan","middleName":"","lastName":"Vanany","suffix":""},{"id":596197412,"identity":"80d968f5-ef10-4710-85d4-f229471198fa","order_by":2,"name":"Ratna Sari Dewi","email":"","orcid":"","institution":"Institut Teknologi Sepuluh Nopember","correspondingAuthor":false,"prefix":"","firstName":"Ratna","middleName":"Sari","lastName":"Dewi","suffix":""},{"id":596197413,"identity":"abbf9b12-7ac8-46a3-a845-fbcf4f73b235","order_by":3,"name":"Muhammad Khakim Habibi","email":"","orcid":"","institution":"Rennes School of Business","correspondingAuthor":false,"prefix":"","firstName":"Muhammad","middleName":"Khakim","lastName":"Habibi","suffix":""}],"badges":[],"createdAt":"2026-02-21 03:53:29","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8930324/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8930324/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":103478480,"identity":"f9e50ba1-e367-456b-8c4a-2d901480e0a1","added_by":"auto","created_at":"2026-02-26 07:27:17","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":945991,"visible":true,"origin":"","legend":"","description":"","filename":"ManuscriptRPSS.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8930324/v1_covered_d26b8aa3-be6b-4991-89d3-422e3c0ff535.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Multi-Scenario Bi-objective Optimization Model for Robotic Parcel Sorting System","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"journal-of-king-saud-university-engineering-sciences","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Journal of King Saud University – Engineering Sciences](https://link.springer.com/journal/44444)","snPcode":"44444","submissionUrl":"https://submission.springernature.com/new-submission/44444/3","title":"Journal of King Saud University – Engineering Sciences","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Open","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"bi-objective optimization, ε-constraint method, robotic parcel sorting, workload balancing","lastPublishedDoi":"10.21203/rs.3.rs-8930324/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8930324/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This study contributes to the robotic-based sorting system, specifically in the parcel industry, due to the lack of multi-objective consideration that prior studies neglected. 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