arXiv subjects

Yi-Chun Akchen

Publications and source records attributed to Yi-Chun Akchen.

4 recordsLinked to original sources

arXiv2026

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

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.

math.OC↗

arXiv2023

Column-Randomized Linear Programs: Performance Guarantees and Applications

We propose a randomized method for solving linear programs with a large number of columns but a relatively small number of constraints. Since enumerating all the columns is usually unrealistic, such linear programs are commonly solved by column generation, which is often still computationally challenging due to the intractability of the subproblem in many applications. Instead of iteratively introducing one column at a time as in column generation, our proposed method involves sampling a collection of columns according to a user-specified randomization scheme and solving the linear program consisting of the sampled columns. While similar methods for solving large-scale linear programs by sampling columns (or, equivalently, sampling constraints in the dual) have been proposed in the literature, in this paper we derive an upper bound on the optimality gap that holds with high probability. This bound converges at a rate $1 / \sqrt{K}$, where $K$ is the number of sampled columns, to the optimality gap of a linear program related to the sampling distribution. We analyze the gap of this latter linear program, which we dub the distributional counterpart, and derive conditions under which this gap will be small. Finally, we numerically demonstrate the effectiveness of the proposed method in the cutting-stock problem and in nonparametric choice model estimation.

math.OC↗

arXiv2023

Consider or Choose? The Role and Power of Consideration Sets

Consideration sets play a crucial role in discrete choice modeling, where customers often form consideration sets in the first stage and then use a second-stage choice mechanism to select the product with the highest utility. While many recent studies aim to improve choice models by incorporating more sophisticated second-stage choice mechanisms, this paper takes a step back and goes into the opposite extreme. We simplify the second-stage choice mechanism to its most basic form and instead focus on modeling customer choice by emphasizing the role and power of the first-stage consideration set formation. To this end, we study a model that is parameterized solely by a distribution over consideration sets with a bounded rationality interpretation. Intriguingly, we show that this model is characterized by the axiom of symmetric demand cannibalization, enabling complete statistical identification. The latter finding highlights the critical role of consideration sets in the identifiability of two-stage choice models. We also examine the model's implications for assortment planning, proving that the optimal assortment is revenue-ordered within each partition block created by consideration sets. Despite this compelling structure, we establish that the assortment problem under this model is NP-hard even to approximate, highlighting how consideration sets contribute to nontractability, even under the simplest uniform second-stage choice mechanism. Finally, using real-world data, we show that the model achieves prediction performance comparable to other advanced choice models. Given the simplicity of the model's second-stage phase, this result showcases the enormous power of first-stage consideration set formation in capturing customers' decision-making processes.

econ.EM↗

arXiv2021

Assortment Optimization under the Decision Forest Model

We study the problem of finding the optimal assortment that maximizes expected revenue under the decision forest model, a recently proposed nonparametric choice model that is capable of representing any discrete choice model and in particular, can be used to represent non-rational customer behavior. This problem is of practical importance because it allows a firm to tailor its product offerings to profitably exploit deviations from rational customer behavior, but at the same time is challenging due to the extremely general nature of the decision forest model. We approach this problem from a mixed-integer optimization perspective and present two different formulations. We theoretically compare the two formulations in strength, and analyze when they are integral in the special case of a single tree. We further propose a methodology for solving the two formulations at a large-scale based on Benders decomposition, and show that the Benders subproblem can be solved efficiently by primal-dual greedy algorithms when the master solution is fractional for one of the formulations, and in closed form when the master solution is binary for both formulations. Using synthetically generated instances, we demonstrate the practical tractability of our formulations and our Benders decomposition approach, and their edge over heuristic approaches. In a case study based on a real-world transaction data, we demonstrate that our proposed approach can factor the behavioral anomalies observed in consumer choice into assortment decision and create higher revenue.

math.OC↗