Do You Have My Size In Stock? Assortment and Inventory Optimization Under the Consider-Fit-Then-Choose Choice Model

[2608.15172] Do You Have My Size In Stock? Assortment and Inventory Optimization Under the Consider-Fit-Then-Choose Choice Model Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Optimization and Control arXiv:2608.15172 (math) [Submitted on 15 Aug 2026] Title: Do You Have My Size In Stock? Assortment and Inventory Optimization Under the Consider-Fit-Then-Choose Choice Model Authors: Yi-Chun Akchen , Kaan Cakiroglu , Felipe Caro , Jacob Feldman View a PDF of the paper titled Do You Have My Size In Stock? Assortment and Inventory Optimization Under the Consider-Fit-Then-Choose Choice Model, by Yi-Chun Akchen and 3 other authors View PDF HTML (experimental) Abstract: In apparel retail and other applications, when a customer's preferred size is unavailable, demand may shift to nearby sizes. This substitution creates new assortment and inventory optimization challenges by coupling product availability and demand across sizes. We introduce the consider-fit-then-choose (CFTC) model to capture such size-dependent choice behavior. Products may be offered in multiple sizes, which affect customer preferences and consideration sets through fit, measured by distance from the customer's ideal size. We study assortment optimization and show-all inventory selection, in which the retailer chooses initial inventory and subsequently offers every in-stock product. We show that assortment optimization under the CFTC model is NP-hard and develop a PTAS when customers deviate by at most $O(1)$ sizes from their ideal size. Combined with the recent black-box framework of Fu et al. (2026), this yields a nearly $0.272$-approximation for show-all inventory selection. We next exploit the specific choice dynamics of the CFTC model. By stocking only every other size, we decouple demand across stocked sizes and reduce CFTC to a special class of mixed multinomial logit models that we prove satisfies the convex chain decomposition (CCD) property of Goyal et al. (2023). For the fluid problem, we develop a polynomial-time $(1/2-\epsilon)$-approximation under adjacent-size substitution and a mild condition on preference weights. For the stochastic problem, we establish an asymptotic $1/2$-approximation using a new coupling argument connecting the stochastic inventory process to its fluid counterpart. Numerical experiments calibrated using footwear data show small optimality gaps across a broad range of substitution patterns and problem settings. Subjects: Optimization and Control (math.OC) ; Data Structures and Algorithms (cs.DS) Cite as: arXiv:2608.15172 [math.OC] (or arXiv:2608.15172v1 [math.OC] for this version) https://doi.org/10.48550/arXiv.2608.15172 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Yi-Chun Akchen [ view email ] [v1] Sat, 15 Aug 2026 11:19:46 UTC (169 KB) Full-text links: Access Paper: View a PDF of the paper titled Do You Have My Size In Stock? Assortment and Inventory Optimization Under the Consider-Fit-Then-Choose Choice Model, by Yi-Chun Akchen and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2026-08 Change to browse by: cs cs.DS math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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