Cross-product quantity discounts without requiring a unified discount schedule

Cross-product quantity discounts without requiring a unified discount schedule | 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 Cross-product quantity discounts without requiring a unified discount schedule Liu, Zuofeng This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2580042/v4 This work is licensed under a CC BY 4.0 License Status: Posted Version 4 posted You are reading this latest preprint version Show more versions Abstract Existing cross-product quantity discounts require unifying quantity discount schedules. However, the range of products eligible for a unified schedule is quite limited, particularly those already configured with different schedules, which severely restricts the scope of cross-product quantity discounts. To address this issue, we propose a general algorithm for reasonably computing discounts across any product combination while allowing each product to retain its individual schedule. Our approach is grounded in the observation that, in any quantification process, defining equivalent units is a fundamental prerequisite. By further analyzing the existing quantity discount methods and relevant research, we reveal the three-step methodology that any cross-product quantity discount must follow: (1) defining equivalent units in the context of quantity discounts; (2) establishing rules that allow products to possess such equivalent units; and (3) computing discounts based on these equivalences. Consequently, we uncover a fundamental theoretical gap: the definition of equivalent units in the context of quantity discounts remains unclear, and the corresponding rules remain underdeveloped. By delving into the underlying logic of quantity discounts, we deduce the definition of equivalent units; following the principles of rationality, necessity, and feasibility, we establish the rules and construct the algorithm. While this algorithm has not yet been applied in practice, we validate it through a series of typical simulation test cases, and the results fully comply with theoretical expectations. It paves the way for innovative business models, such as new group-buying, advanced loyalty management, and novel fission marketing, as discussed in this paper. Operations Research Econometrics Computational Mathematics Pricing Cross-product quantity discounts Product combination General algorithm Equivalent units Full Text Additional Declarations The authors declare no competing interests. Supplementary Files OnlineAppendixA.pdf Appendix A: Proof of uniqueness of CS4 method 1 under algorithm constraints OnlineAppendixB.pdf Appendix B: Simulation test design and test results in curves CPQDTestCaseGenerator.xlsx Test case generator Cite Share Download PDF Status: Posted Version 4 posted You are reading this latest preprint version Show more versions 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-2580042","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":373043494,"identity":"2f4938d8-145c-4847-9dfd-a8f83dec19b1","order_by":0,"name":"Liu, 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