Journal Publications

• Multi-Product Dynamic Pricing with Reference Effects Under Logit Demand
  with Mengzi Amy Guo, ZJ Max Shen
  Manufacturing & Service Operations Management, 2025
  Abstract SSRN Journal
  

  We consider an infinite-horizon multi-product dynamic pricing problem with reference effects in a monopolistic setting, where the reference price is an exponentially weighted average of historical prices. In each period, the demand follows the multinomial logit (MNL) model, where the utility depends on both the current price and the reference price, and consumers can have product-differentiated sensitivities to the price and the reference price. We conduct thorough analyses of the myopic pricing policy, including its solution, long-run convergence behavior, and performance guarantee compared to the long-term discounted revenue of the optimal pricing policy. Furthermore, we establish the structural properties of the optimal pricing policy. When consumers are loss-neutral towards all products, we explicitly characterize the optimal pricing policy if it converges to a steady state, and based on our characterization we show that the steady state price can be computed efficiently by a binary search. Interestingly, we find that such a convergence behavior of the optimal pricing policy heavily relies on the upper bound of the admissible price range, and a low price upper bound facilitates the policy to converge. In contrast, when consumers are gain-seeking towards all products, we prove that the optimal pricing policy admits no steady state regardless of the price range. Nevertheless, if consumers are only gain-seeking towards certain but not all products, the optimal pricing policy can potentially be convergent. In addition, our numerical experiments show that loss-aversion over all products does not rule out price fluctuations. This finding is at odds with the classic belief on loss-averse consumers and hence, highlights the significance of accounting for cross-product effects through the MNL demand.

• Intertemporal Pricing via Nonparametric Estimation: Integrating Reference Effects and Consumer Heterogeneity
  with Junyu Cao, ZJ Max Shen
  Manufacturing & Service Operations Management, 2024
  Abstract SSRN Slides Code Data Journal
  ☆ MSOM Data-Driven Research Challenge Competition, Finalist
  

  We consider intertemporal pricing in the presence of reference effects and consumer heterogeneity. Our research question encompasses how to estimate heterogeneous consumer reference effects from data and how to efficiently compute the optimal pricing policy. Understanding reference effects is essential for designing pricing policies in modern retailing. Our work contributes to this area by incorporating consumer heterogeneity under arbitrary distributions. We propose a mixed logit demand model that allows arbitrary joint distributions of valuations, responsiveness to prices, and responsiveness to reference prices among consumers. We use a nonparametric estimation method to learn consumer heterogeneity from transaction data. Further, we formulate the pricing optimization as an infinite horizon dynamic programming problem and solve it by applying a modified policy iteration algorithm. Moreover, we investigate the structure of optimal pricing policies and prove the sub-optimality of constant pricing policies even when all consumers are loss-averse according to the classical definition. Our numerical studies show that our estimation and optimization framework improves the expected revenue of retailers via accounting for heterogeneity. We validate our model using real data from JD.com, a large E-commerce retailer, and find empirical evidence of consumer heterogeneity. In practice, ignoring consumer heterogeneity may lead to a significant loss of revenue. Furthermore, heterogeneous reference effect offers a strong motive for promotions and price fluctuations.

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Conference Proceedings

• Learning in Continuous State-Space MDPs for Network Inventory Management
  with Shunan Jiang, ZJ Max Shen
  International Conference on Artificial Intelligence and Statistics (AISTATS), 2026
  Abstract

  We consider online learning in infinite-horizon, average-cost Markov Decision Processes (MDPs) with multi-dimensional, continuous state spaces and censored feedback. Our model setting, motivated by network inventory management applications such as vehicle sharing, is characterized by complex, correlated state transitions and the absence of value function convexity, rendering standard analytical techniques for both MDPs and inventory control inapplicable. Our primary contribution is a integrated framework establishing and leveraging the Lipschitz property of the long-run average cost function. This insight allows us to analyze the problem through the lens of Lipschitz bandits, for which we design a provably efficient online learning algorithm that learns a near-optimal policy from censored demand data. We derive a high-probability regret bound of $O(T^{\frac{n}{n+1}} (\log T)^{\frac{1}{n+1}})$, where $n$ is the network size through new concentration inequalities for cumulative costs in MDPs with state-dependent transitions. Furthermore, we devise a matching lower bound for this learning problem, which captures the inherent dimensionality challenge.

• Out-of-distribution Robust Optimization
  with Zhongze Cai, Xiaocheng Li
  Conference on Uncertainty in Artificial Intelligence (UAI), 2025
  Abstract arXiv Proceeding
  

  In this paper, we consider the contextual robust optimization problem under an out-of-distribution setting. The contextual robust optimization problem considers a risk-sensitive objective function for an optimization problem with the presence of a context vector (also known as covariates or side information) capturing related information. While the existing works mainly consider the in-distribution setting, and the resultant robustness achieved is in an out-of-sample sense, our paper studies an out-of-distribution setting where there can be a difference between the test environment and the training environment where the data are collected. We propose methods that handle this out-of-distribution setting, and the key relies on a density ratio estimation for the distribution shift. We show that additional structures such as covariate shift and label shift are not only helpful in defending distribution shift but also necessary in avoiding non-trivial solutions compared to other principled methods such as distributionally robust optimization. We also illustrate how the covariates can be useful in this procedure. Numerical experiments generate more intuitions and demonstrate that the proposed methods can help avoid over-conservative solutions.

• Smoothness-Adaptive Dynamic Pricing with Nonparametric Demand Learning
  with Zeqi Ye
  International Conference on Artificial Intelligence and Statistics (AISTATS), 2024
  Abstract arXiv Slides Code Proceeding
  

  We study the dynamic pricing problem where the demand function is nonparametric and H\"older smooth, and we focus on adaptivity to the unknown H\"older smoothness parameter $\beta$ of the demand function. Traditionally the optimal dynamic pricing algorithm heavily relies on the knowledge of $\beta$ to achieve a minimax optimal regret of $\widetilde{O}(T^{\frac{\beta+1}{2\beta+1}})$. However, we highlight the challenge of adaptivity in this dynamic pricing problem by proving that no pricing policy can adaptively achieve this minimax optimal regret without knowledge of $\beta$. Motivated by the impossibility result, we propose a self-similarity condition to enable adaptivity. Importantly, we show that the self-similarity condition does not compromise the problem's inherent complexity since it preserves the regret lower bound $\Omega(T^{\frac{\beta+1}{2\beta+1}})$. Furthermore, we develop a smoothness-adaptive dynamic pricing algorithm and theoretically prove that the algorithm achieves this minimax optimal regret bound without the prior knowledge $\beta$.

  Quantum Computing Methods for Supply Chain Management
  with ZJ Max Shen, Junyu Liu
  IEEE/ACM Symposium on Edge Computing (SEC), 2022
  Abstract arXiv Proceeding
  

  Quantum computing is expected to have transformative influences on many domains, but its practical deployments on industry problems are underexplored. We focus on applying quantum computing to operations management problems in industry, and in particular, supply chain management. Many problems in supply chain management involve large state and action spaces and pose computational challenges on classic computers. We develop a quantized policy iteration algorithm to solve an inventory control problem and demonstrative its effectiveness. We also discuss in-depth the hardware requirements and potential challenges on implementing this quantum algorithm in the near term. Our simulations and experiments are powered by the IBM Qiskit and the qBraid system.

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Working Papers

• Designing Surprise Bags for Surplus Foods
  with Fan Zhou, Andrea Li, Joline Uichanco
  Abstract SSRN Too Good To Go Slides
  

  Too Good To Go (TGTG) has emerged as a global leader in reducing food waste by connecting consumers with retailers' surplus food through ``surprise bags.'' While TGTG provides both environmental and economic benefits, participating stores face significant operational challenges in determining the optimal number of bags to offer. Specifically, stores must decide on the number of surprise bags before knowing the actual surplus for the day. Additionally, key questions such as whether to include regular sale items in the bags and how to allocate food across bags are critical for balancing customer satisfaction and profitability. We explore these challenges and model the stores' decision-making process by stochastic dynamic programming. Our analysis reveals that the commonly adopted practice of evenly distributing surplus food across all surprise bags may not maximize consumer satisfaction, particularly when customer utility functions are non-concave. We propose an alternative---offering up to two types of bags---that achieves maximal consumer satisfaction while still remaining simple to implement. Determining the optimal number of bags and the total food volume to allocate at each period is a non-convex two-stage stochastic optimization problem. To address both the analytical and computational complexities, we propose two approximation policies that are computationally efficient with intuitive managerial insights and provable performance guarantees. Our findings provide practical guidance for stores in balancing revenue generation, customer satisfaction, and sustainability objectives, thereby enhancing the long-term viability of TGTG's mission to reduce food waste.

• A Nonparametric Maximum Likelihood Approach to Mixture of Regression
  with Adityanand Guntuboyina
  Abstract arXiv Slides Code
  ☆ IISA Best Student Paper – Theory/Methodology Track, Winner

  Mixture of regression models are useful for regression analysis in heterogeneous populations where a single regression model may not be appropriate for the entire population. We study the nonparametric maximum likelihood estimator (NPMLE) for fitting these models. The NPMLE is based on convex optimization and does not require prior specification of the number of mixture components. We establish existence of the NPMLE and prove finite-sample parametric (up to logarithmic multiplicative factors) Hellinger error bounds for the predicted density functions. We also provide an effective procedure for computing the NPMLE without ad-hoc discretization and prove a theoretical convergence rate under certain assumptions. Numerical experiments on simulated data for both discrete and non-discrete mixing distributions demonstrate the remarkable performance of our approach. We also illustrate the approach on two real data sets.

• Conformal Robust Optimization and Satisficing for Prescriptive Analytics with Black-Box Predictors
  with Lingjie Zhao, Wei Qi
  Abstract SSRN
  ☆ INFORMS Undergraduate Operations Research Prize, Finalist (Lingjie Zhao)
  

  We propose a unified conformal framework for robust decision-making in prescriptive analytics with black-box predictors. The framework addresses the challenge of leveraging predictive power of black-box predictors without sacrificing reliability in high-stakes optimization, whereas naively optimizing over point forecasts often yields fragile or infeasible decisions. It supports two complementary paradigms: Conformal Robust Optimization (CRO), which integrates any black-box predictor into a robust optimization model by constructing a data-driven uncertainty set calibrated to a user-specified coverage level, and Conformal Robust Satisficing (CRS), a target-oriented counterpart that minimizes fragility relative to a desired utility threshold. We prove that CRO and CRS are theoretically equivalent under mild convexity and duality conditions, establishing an explicit correspondence between the uncertainty set size and the satisficing target. We provide finite-sample analysis to show that the realized coverage concentrates the target coverage level at an O(n^{-1/2}) rate and that the CRO solution’s sub‐optimality gap is bounded by the diameter of the calibrated set. Extensive experiments on synthetic problems and a real-world perishable inventory management case study demonstrate the framework's effectiveness. Notably, CRO can significantly outperform baselines in objective value while guaranteeing out-of-sample coverage, whereas CRS demonstrates superior feasibility and optimality compared to distributionally robust satisficing benchmarks.

• Spatial Supply Repositioning with Censored Demand Data
  with Chunlin Sun, ZJ Max Shen
  Abstract SSRN Code
  ☆ CSAMSE Best Paper Competition, Second Place
  ☆ YinzOR Student Conference Flash Talk Competition, Winner

  We consider the vehicle repositioning problem for a one-way on-demand vehicle sharing service with a fixed number of rental units distributed across the network. Due to uncertainty in both customer arrivals and vehicle returns, the service provider needs to periodically reposition the vehicles to match the supply with the demand while minimizing the total costs of repositioning labor and lost sales. The repositioning problem is critical in the successful management of on-demand one-way vehicle sharing services, and it is challenging both analytically and computationally. The optimal repositioning policy under a general $n$-location network is intractable without knowing the optimal value function. We define the best base-stock repositioning policy as a generalization of the popular inventory control policy to the vehicle repositioning problem, and we establish its asymptotic optimality in two different limiting regimes under general network structures. We develop learning methods to dynamically reposition vehicles to find the best base-stock policy with censored demand. By establishing a tight concentration inequality, we show that the one-time learning algorithm achieves a regret of $\widetilde{\bigo}\left(T^{\frac{2}{3}}\right)$, which is independent of the number of locations in the network. We furthermore develop an online stochastic gradient descent algorithm using only censored demand and prove that it achieves a regret of $\widetilde{\bigo}\left(T^{\frac{1}{2}}\right)$ under a cost structure assumption. Crucially, our online algorithm is based on a novel decomposition of cumulative costs and linear programming reformulation of the offline problem. Numerical experiments illustrate the effective performance of our approaches.

• Supply Chain Forecast Sharing Under Asymmetric Forecast Preferences
  with Lin Zhao, Mengshi Lu, ZJ Max Shen, Kemal Guler
  Abstract SSRN
  

  Forecast sharing has been widely adopted to coordinate capacity planning in supply chains. However, the effectiveness of forecast sharing can be hindered by forecast inflation caused by the forecaster's asymmetric preferences toward underforecasts or overforecasts. In this paper, we study how suppliers can benefit from knowing the asymmetric preferences in forecasts shared by their customers. We employ a multi-period Bayesian repeated newsvendor model to depict the impact of forecast preferences on how a supplier updates its demand information and prepares its production capacity based on the shared forecast. We characterize the value of the forecast preference information, which is the increase in the supplier's expected profit through improved capacity planning enabled by considering asymmetric forecast preferences. We show that firms can benefit from the forecast preference information, and the benefit is more substantial under higher degrees of preference asymmetry, lower estimation error, and more profitable operations. We also show that it may not be optimal for the supplier to know the exact forecast preference. In the presence of estimation errors, the supplier may benefit from overestimating or underestimating the forecast preference. We further study the impact of the forecast preference information on the supplier's expected profit and derive a finite-sample bound on its regret. We apply the model in a numerical study with data from a real-world forecast sharing practice in a PC manufacturing supply chain. The results show that there exists significant forecast inflation in the shared forecasts. Furthermore, the preference toward overforecast is higher when the forecast horizon is shorter or when the product family's total demand is lower. Using forecast preferences reflected in the data set, we quantify the value of forecast preference information, which is shown to be significant and increasing in the manufacturer's estimation accuracy and the supplier's profitability.

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Ph.D. Dissertation

• Operations and Data Analytics in Platforms: Theory and Applications
  Hansheng Jiang
  University of California, Berkeley, 2023
  ☆ Supply Chain Analytics Institute Annual Conference Best Dissertation Competition, Second Place