Inventory Order Scheduling Optimization: Capacity-Constrained Fulfillment Window Allocation in Perishable Subscription E-Commerce

Inventory Order Scheduling Optimization: Capacity-Constrained Fulfillment Window Allocation in Perishable Subscription E-Commerce | 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 Inventory Order Scheduling Optimization: Capacity-Constrained Fulfillment Window Allocation in Perishable Subscription E-Commerce arjun ravi pardasani This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9398688/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 We introduce the Capacity-Aware Perishable Fulfillment Scheduling (CAPFS) problem, a new class of combinatorial scheduling problem arising when subscription e-commerce orders must be assigned to weekday shipping slots under three simultaneous constraints: hard daily capacity limits at parallel fulfillment centers, customer-specific food-continuity deadlines derived from perishable on-hand inventory buffers, and order-type heterogeneity (trial versus regular) imposing asymmetric feasibility structures. We prove CAPFS is NP-hard by polynomial-time reduction from parallel machine scheduling with deadlines and weighted tardiness (Pm|r_j,d_j|ΣwjTj). We develop a MILP formulation with a multi-objective function covering capacity overload, aggregate stockout risk, and schedule lateness, alongside a polynomial O(n log n) Least-Slack Priority (LSP) heuristic with a provable structural safety property: early-order moves reduce both objectives simultaneously. Applied to 3,851 real meal-kit orders across two fulfillment centers in August 2020, the incumbent transit-time heuristic generates Tuesday overloads of 192–233% of capacity while Monday operates at 9–53% utilization — Jain Fairness Index 0.30–0.51 against a target of ≥0.90. The LSP heuristic achieves a 48.4% reduction in total capacity overload and 29.0% Other Economics Operations Research Perishable Subscription Fulfillment Capacity-Aware Scheduling (CAPFS) MILP Formulation Least-Slack Priority Available-to-Promise Earliest Deadline First Jain Fairness Index NP-Hardness Meal-Kit E-Commerce Fulfillment Window Allocation 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-9398688","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":621933396,"identity":"a1a04e57-a2aa-4ddc-aef4-0bf14351299d","order_by":0,"name":"arjun ravi pardasani","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABAElEQVRIiWNgGAWjYHCCBAh1AEQY2AAJxsYDpGhJA2lpIKSFAUkLw2EkNg7AP/vAM+nCHXb5fMePP/xcUHDebm37YaAtNTbRuLRInEtIk555Jtly5pkcY+kZBreTt51JBGo5lpbbgEvPGYY0ad42ZgODAzkM0jxALWYHgFoYGw7j1CIP0VJvYHD++ePfPAbnks3OP8SvxQCi5bCBwY0EM6AtB+zMbhCwxfAMQ7I175njBpI33phZ8xgkJ5jdANqSgMcvcmd4Em/z7qg24Duf/vg2zx87e7Pz6Q8ffKixwe19Bp4EYNwhuIlgdgJO5SDAfgBFiz1exaNgFIyCUTAiAQDbCGLy8fVeGQAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0009-0000-0961-2036","institution":"Northeastern Universiry","correspondingAuthor":true,"prefix":"","firstName":"arjun","middleName":"ravi","lastName":"pardasani","suffix":""}],"badges":[],"createdAt":"2026-04-13 04:48:41","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-9398688/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9398688/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106865292,"identity":"3ffcf719-c383-4746-b6c2-c1d7ddabd96f","added_by":"auto","created_at":"2026-04-14 08:58:24","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":239814,"visible":true,"origin":"","legend":"","description":"","filename":"CAPFSResearchPaper.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9398688/v1_covered_4d5c8bb1-bcd4-48a1-8725-d379a816cf7b.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eInventory Order Scheduling Optimization: Capacity-Constrained Fulfillment Window Allocation in Perishable Subscription E-Commerce\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"Perishable Subscription Fulfillment, Capacity-Aware Scheduling (CAPFS), MILP Formulation, Least-Slack Priority, Available-to-Promise, Earliest Deadline First, Jain Fairness Index, NP-Hardness, Meal-Kit E-Commerce, Fulfillment Window Allocation","lastPublishedDoi":"10.21203/rs.3.rs-9398688/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9398688/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe introduce the Capacity-Aware Perishable Fulfillment Scheduling (CAPFS) problem, a new class of combinatorial scheduling problem arising when subscription e-commerce orders must be assigned to weekday shipping slots under three simultaneous constraints: hard daily capacity limits at parallel fulfillment centers, customer-specific food-continuity deadlines derived from perishable on-hand inventory buffers, and order-type heterogeneity (trial versus regular) imposing asymmetric feasibility structures. We prove CAPFS is NP-hard by polynomial-time reduction from parallel machine scheduling with deadlines and weighted tardiness (Pm|r_j,d_j|ΣwjTj). We develop a MILP formulation with a multi-objective function covering capacity overload, aggregate stockout risk, and schedule lateness, alongside a polynomial O(n log n) Least-Slack Priority (LSP) heuristic with a provable structural safety property: early-order moves reduce both objectives simultaneously. Applied to 3,851 real meal-kit orders across two fulfillment centers in August 2020, the incumbent transit-time heuristic generates Tuesday overloads of 192–233% of capacity while Monday operates at 9–53% utilization — Jain Fairness Index 0.30–0.51 against a target of ≥0.90. 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