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1. Coordinated Inventory Stocking and Assortment Customization

   https://doi.org/10.1287/opre.2022.0651  

   Bai, Yicheng; El_Housni, Omar; Rusmevichientong, Paat; Topaloglu, Huseyin (February 2025, Operations Research)

   Jointly Making Inventory Stocking and Assortment Offering Decisions Making the product assortment offer decisions for a customer requires keeping a balance between offering an assortment that will satisfy the current customer and reserving the products with scarce inventories for the customers who will arrive in the future. Therefore, whereas the assortment offer decisions should depend on the current inventories of the products, the stocking decisions should anticipate how the offered assortments will deplete the inventories, thereby creating a natural interaction between inventory stocking and assortment offer decisions. In “Coordinated Inventory Stocking and Assortment Customization,” Bai, El Housni, Rusmevichientong, and Topaloglu develop models that jointly make the assortment offer and inventory stocking decisions. Their models allocate the limited stocking capacity to the inventories for different products, while taking into consideration the assortment offer decisions that will be made for the customers arriving over a selling horizon. 

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2. Offline Feature-Based Pricing Under Censored Demand: A Causal Inference Approach

   https://doi.org/10.1287/msom.2024.1061  

   Tang, Jingwen; Qi, Zhengling; Fang, Ethan; Shi, Cong (March 2025, Manufacturing & Service Operations Management)

   Problem definition: We study a feature-based pricing problem with demand censoring in an offline, data-driven setting. In this problem, a firm is endowed with a finite amount of inventory and faces a random demand that is dependent on the offered price and the features (from products, customers, or both). Any unsatisfied demand that exceeds the inventory level is lost and unobservable. The firm does not know the demand function but has access to an offline data set consisting of quadruplets of historical features, inventory, price, and potentially censored sales quantity. Our objective is to use the offline data set to find the optimal feature-based pricing rule so as to maximize the expected profit. Methodology/results: Through the lens of causal inference, we propose a novel data-driven algorithm that is motivated by survival analysis and doubly robust estimation. We derive a finite sample regret bound to justify the proposed offline learning algorithm and prove its robustness. Numerical experiments demonstrate the robust performance of our proposed algorithm in accurately estimating optimal prices on both training and testing data. Managerial implications: The work provides practitioners with an innovative modeling and algorithmic framework for the feature-based pricing problem with demand censoring through the lens of causal inference. Our numerical experiments underscore the value of considering demand censoring in the context of feature-based pricing. Funding: The research of E. Fang is partially supported by the National Science Foundation [Grants NSF DMS-2346292, NSF DMS-2434666] and the Whitehead Scholarship. The research of C. Shi is partially supported by the Amazon Research Award. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2024.1061 . 

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3. Private Optimal Inventory Policy Learning for Feature-Based Newsvendor with Unknown Demand

   https://doi.org/10.1287/mnsc.2023.01268  

   Zhao, Tuoyi; Zhou, Wen-Xin; Wang, Lan (October 2024, Management Science)

   The data-driven newsvendor problem with features has recently emerged as a significant area of research, driven by the proliferation of data across various sectors such as retail, supply chains, e-commerce, and healthcare. Given the sensitive nature of customer or organizational data often used in feature-based analysis, it is crucial to ensure individual privacy to uphold trust and confidence. Despite its importance, privacy preservation in the context of inventory planning remains unexplored. A key challenge is the nonsmoothness of the newsvendor loss function, which sets it apart from existing work on privacy-preserving algorithms in other settings. This paper introduces a novel approach to estimating a privacy-preserving optimal inventory policy within the f-differential privacy framework, an extension of the classical [Formula: see text]-differential privacy with several appealing properties. We develop a clipped noisy gradient descent algorithm based on convolution smoothing for optimal inventory estimation to simultaneously address three main challenges: (i) unknown demand distribution and nonsmooth loss function, (ii) provable privacy guarantees for individual-level data, and (iii) desirable statistical precision. We derive finite-sample high-probability bounds for optimal policy parameter estimation and regret analysis. By leveraging the structure of the newsvendor problem, we attain a faster excess population risk bound compared with that obtained from an indiscriminate application of existing results for general nonsmooth convex loss. Our bound aligns with that for strongly convex and smooth loss function. Our numerical experiments demonstrate that the proposed new method can achieve desirable privacy protection with a marginal increase in cost. This paper was accepted by J. George Shanthikumar, data science. Funding: This work was supported by the National Science Foundation [Grants DMS-2113409 and DMS 2401268 to W.-X. Zhou, and FRGMS-1952373 to L. Wang]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.01268 . 

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4. Optimal Policy for Dynamic Assortment Planning Under Multinomial Logit Models

   https://doi.org/10.1287/moor.2021.1133  

   Chen, Xi; Wang, Yining; Zhou, Yuan (May 2021, Mathematics of Operations Research)

   null (Ed.)

   We study the dynamic assortment planning problem, where for each arriving customer, the seller offers an assortment of substitutable products and the customer makes the purchase among offered products according to an uncapacitated multinomial logit (MNL) model. Because all the utility parameters of the MNL model are unknown, the seller needs to simultaneously learn customers’ choice behavior and make dynamic decisions on assortments based on the current knowledge. The goal of the seller is to maximize the expected revenue, or, equivalently, to minimize the expected regret. Although dynamic assortment planning problem has received an increasing attention in revenue management, most existing policies require the estimation of mean utility for each product and the final regret usually involves the number of products [Formula: see text]. The optimal regret of the dynamic assortment planning problem under the most basic and popular choice model—the MNL model—is still open. By carefully analyzing a revenue potential function, we develop a trisection-based policy combined with adaptive confidence bound construction, which achieves an item-independent regret bound of [Formula: see text], where [Formula: see text] is the length of selling horizon. We further establish the matching lower bound result to show the optimality of our policy. There are two major advantages of the proposed policy. First, the regret of all our policies has no dependence on [Formula: see text]. Second, our policies are almost assumption-free: there is no assumption on mean utility nor any “separability” condition on the expected revenues for different assortments. We also extend our trisection search algorithm to capacitated MNL models and obtain the optimal regret [Formula: see text] (up to logrithmic factors) without any assumption on the mean utility parameters of items. 

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5. Maximum Load Assortment Optimization: Approximation Algorithms and Adaptivity Gaps

   https://doi.org/10.1287/opre.2023.0495  

   El_Housni, Omar; Ibn_Brahim, Marouane; Segev, Danny (April 2025, Operations Research)

   Motivated by modern-day applications such as attended home delivery and preference-based group scheduling, where decision makers wish to steer a large number of customers toward choosing the exact same alternative, we introduce a novel class of assortment optimization problems, referred to as maximum load assortment optimization. In such settings, given a universe of substitutable products, we are facing a stream of customers, each choosing between either selecting a product out of an offered assortment or opting to leave without making a selection. Assuming that these decisions are governed by the multinomial logit choice model, we define the random load of any underlying product as the total number of customers who select it. Our objective is to offer an assortment of products to each customer so that the expected maximum load across all products is maximized. We consider both static and dynamic formulations of the maximum load assortment optimization problem. In the static setting, a single offer set is carried throughout the entire process of customer arrivals, whereas in the dynamic setting, the decision maker offers a personalized assortment to each customer, based on the entire information available at that time. As can only be expected, both formulations present a wide range of computational challenges and analytical questions. The main contribution of this paper resides in proposing efficient algorithmic approaches for computing near-optimal static and dynamic assortment policies. In particular, we develop a polynomial time approximation scheme for the static problem formulation. Additionally, we demonstrate that an elegant policy utilizing weight-ordered assortments yields a 1/2 approximation. Concurrently, we prove that such policies are sufficiently strong to provide a 1/4 approximation with respect to the dynamic formulation, establishing a constant factor bound on its adaptivity gap. Finally, we design an adaptive policy whose expected maximum load is within factor 1-\epsilon of optimal, admitting a quasi-polynomial time implementation. 

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