ISyE Seminar Series: Jake Feldman
"Assortment and Inventory Optimization under the Consider–Fit–Then–Choose Model: Size-Based Substitution in Fashion and Grocery Retail"
Jake Feldman
Associate Professor in the SCOT group, Olin Business School
Washington University
About the Seminar:
Retailers in grocery, apparel, and footwear routinely offer products in multiple sizes, such as different package volumes or numerical shoe sizes. While these variants share common core attributes, the proliferation of size-based stock keeping units (SKUs) significantly increases operational complexity. Because stockouts occur at the size level, retailers must estimate demand at a finer granularity and coordinate assortment and inventory decisions across size variants. This often leads to imbalances, with excess inventory in some sizes and stockouts in others. A key challenge in such settings is that substitution behavior is highly structured. Customers have a preferred size and are willing to substitute only to nearby sizes, with utility decreasing as the deviation increases. This localized, one-dimensional substitution pattern differs fundamentally from classical models that treat products as unrelated alternatives, rendering standard discrete choice models inadequate. Motivated by these features, we develop an integrated framework for modeling and optimizing size-differentiated assortments and inventories. We introduce the Consider-Fit-Then-Choose (CFTC) model, which captures fit-driven substitution through a two-stage process. Customers first form a consideration set by selecting, for each base product, the closest available size within an acceptable deviation range. They then choose among these options according to a multinomial logit model with size-dependent disutility. We first study assortment optimization under the CFTC model and show the problem is NP-hard even with two sizes per base. Despite this, we develop a PTAS when size deviations are bounded. We then study inventory optimization under dynamic substitution and provide a polynomial-time (1/2 − ε)-approximation algorithm under mild assumptions. Our results provide a tractable framework for optimization under dynamic substitution beyond classical MNL models.
Related Abstract:
About the Speaker:
Jake Feldman is an Associate Professor in the SCOT group at Washington University’s Olin Business School. He holds a B.S. in Mathematics from Harvey Mudd College and a Ph.D. in Operations Research from Cornell University. His research has primarily focused on the development of approximation algorithms for pricing and assortment optimization problems of various kinds, ranging in applications from optimal product displays in recommender systems to the dynamic pricing of grocery items. He currently serves as Associate Editor at POMS, MSOM and OR.
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