The Newsvendor problem is a fundamental model in inventory management (Rossi, 2021) that accommodates both known (Dvoretzky et al., 1952a) and unknown (Dvoretzky et al., 1952b) demand distributions. Since its inception (Edgewort, 1888), it has been widely applied in inventory control and policy-making (Arrow et al., 1951), as well as various real-world situations (Choi, 2012; Chen et al., 2016). Its simplicity stems from considering a single product for sale, for which the optimal initial stock level must be determined to satisfy forecasted demand over a given period without restocking. The interplay among purchasing cost, selling price, and stock ordered at the beginning of the period determines the inventory management policies (Whitin, 1952; Rosenblatt, 1954; Petruzzi and Dada, 1999). The model has been extensively studied for single stock-keeping units (SKUs). Electronic marketplaces introduce an extra complication to the problem, as they need to manage a large number of SKUs at distribution centers alongside highly variable demand received through electronic platforms.

We study nonstationary newsvendor problems under nonparametric demand models and general distributional measures of nonstationarity, addressing the practical challenges of unknown degree of nonstationarity and demand censoring. We propose a novel distributional-detection-and-restart framework for learning in nonstationary environments, and instantiate it through two efficient algorithms for the uncensored and censored demand settings. The algorithms are fully adaptive, requiring no prior knowledge of the degree and type of nonstationarity, and offer a flexible yet powerful approach to handling both abrupt and gradual changes in nonstationary environments. We establish a comprehensive optimality theory for our algorithms by deriving matching regret upper and lower bounds under both general and refined structural conditions with nontrivial proof techniques that are of independent interest. Numerical experiments using real-world datasets, including nurse staffing data for emergency departments and COVID-19 test demand data, showcase the algorithms' superior and robust empirical performance. While motivated by the newsvendor problem, the distributional-detection-and-restart framework applies broadly to a wide class of nonstationary stochastic optimization problems. Managerially, our framework provides a practical, easy-to-deploy, and theoretically grounded solution for decision-making under nonstationarity.

The last few years have witnessed rapid growth in the on-demand delivery market, with many start-ups entering the field. However, not all of these start-ups have succeeded due to various reasons, among others, not being able to establish a large enough customer base. In this paper, we address this problem that many on-demand transportation start-ups face: how to establish themselves in a new market. When starting, such companies often have limited fleet resources to serve demand across a city. Depending on the use of the fleet, varying service quality is observed in different areas of the city, and in turn, the service quality impacts the respective growth of demand in each area. Thus, operational fulfillment decisions drive the longer-term demand development. To integrate strategic demand development into real-time fulfillment operations, we propose a two-step approach. First, we derive analytical insights into optimal allocation decisions for a stylized problem. Second, we use these insights to shape the training data of a reinforcement learning strategy for operational real-time fulfillment. Our experiments demonstrate that combining operational efficiency with long-term strategic planning is highly advantageous. Further, we show that the careful shaping of training data is essential for the successful development of demand.

In this paper, we investigate the performance of Thompson Sampling (TS) for online learning with censored feedback, focusing primarily on the classic repeated newsvendor model--a foundational framework in inventory management--and demonstrating how our techniques can be naturally extended to a broader class of problems. We model demand using a Weibull distribution and initialize TS with a Gamma prior to dynamically adjust order quantities. Our analysis establishes optimal (up to logarithmic factors) frequentist regret bounds for TS without imposing restrictive prior assumptions. More importantly, it yields novel and highly interpretable insights on how TS addresses the exploration-exploitation trade-off in the repeated newsvendor setting. Specifically, our results show that when past order quantities are sufficiently large to overcome censoring, TS accurately estimates the unknown demand parameters, leading to near-optimal ordering decisions. Conversely, when past orders are relatively small, TS automatically increases future order quantities to gather additional demand information. Extensive numerical simulations further demonstrate that TS outperforms more conservative and widely-used approaches such as online convex optimization, upper confidence bounds, and myopic Bayesian dynamic programming. This study also lays the foundation for exploring general online learning problems with censored feedback.

-- In this paper, we propose a novel reinforcement learning algorithm for inventory management of newly launched products with no historical demand information. The algorithm follows the classic Dyna-Q structure, balancing the model-free and model-based approaches, while accelerating the training process of Dyna-Q and mitigating the model discrepancy generated by the model-based feedback. Based on the idea of transfer learning, warm-start information from the demand data of existing similar products can be incorporated into the algorithm to further stabilize the early-stage training and reduce the variance of the estimated optimal policy. Our approach is validated through a case study of bakery inventory management with real data. The adjusted Dyna-Q shows up to a 23.7% reduction in average daily cost compared with Q-learning, and up to a 77.5% reduction in training time within the same horizon compared with classic Dyna-Q . By using transfer learning, it can be found that the adjusted Dyna-Q has the lowest total cost, lowest variance in total cost, and relatively low shortage percentages among all the benchmarking algorithms under a 30-day testing. I. INTRODUCTION Inventory management is crucial for supply chain operations, overseeing and controlling the order, storage, and usage of goods in business [1]. In inventory management, the cold-start setting refers to predicting demand and formulating appropriate inventory strategies when new products are introduced or new market demands arise due to the lack of historical data [2].

We study a censored variant of the data-driven newsvendor problem, where the decision-maker must select an ordering quantity that minimizes expected overage and underage costs based only on offline censored sales data, rather than historical demand realizations. Our goal is to understand how the degree of historical demand censoring affects the performance of any learning algorithm for this problem. To isolate this impact, we adopt a distributionally robust optimization framework, evaluating policies according to their worst-case regret over an ambiguity set of distributions. This set is defined by the largest historical order quantity (the observable boundary of the dataset), and contains all distributions matching the true demand distribution up to this boundary, while allowing them to be arbitrary afterwards. We demonstrate a spectrum of achievability under demand censoring by deriving a natural necessary and sufficient condition under which vanishing regret is an achievable goal. In regimes in which it is not, we exactly characterize the information loss due to censoring: an insurmountable lower bound on the performance of any policy, even when the decision-maker has access to infinitely many demand samples. We then leverage these sharp characterizations to propose a natural robust algorithm that adapts to the historical level of demand censoring. We derive finite-sample guarantees for this algorithm across all possible censoring regimes and show its near-optimality with matching lower bounds (up to polylogarithmic factors). We moreover demonstrate its robust performance via extensive numerical experiments on both synthetic and real-world datasets.

We consider data-driven inventory and pricing decisions in the feature-based newsvendor problem, where demand is influenced by both price and contextual features and is modeled without any structural assumptions. The unknown demand distribution results in a challenging conditional stochastic optimization problem, further complicated by decision-dependent uncertainty and the integration of features. Inspired by recent advances in deep generative learning, we propose a novel approach leveraging conditional deep generative models (cDGMs) to address these challenges. cDGMs learn the demand distribution and generate probabilistic demand forecasts conditioned on price and features. This generative approach enables accurate profit estimation and supports the design of algorithms for two key objectives: (1) optimizing inventory for arbitrary prices, and (2) jointly determining optimal pricing and inventory levels. We provide theoretical guarantees for our approach, including the consistency of profit estimation and convergence of our decisions to the optimal solution. Extensive simulations-ranging from simple to complex scenarios, including one involving textual features-and a real-world case study demonstrate the effectiveness of our approach. Our method opens a new paradigm in management science and operations research, is adaptable to extensions of the newsvendor and pricing problems, and holds potential for solving other conditional stochastic optimization problems.

Deploying deep reinforcement learning (DRL) in real-world inventory management presents challenges, including dynamic environments and uncertain problem parameters, e.g. demand and lead time distributions. These challenges highlight a research gap, suggesting a need for a unifying framework to model and solve sequential decision-making under parameter uncertainty. We address this by exploring an underexplored area of DRL for inventory management: training generally capable agents (GCAs) under zero-shot generalization (ZSG). Here, GCAs are advanced DRL policies designed to handle a broad range of sampled problem instances with diverse inventory challenges. ZSG refers to the ability to successfully apply learned policies to unseen instances with unknown parameters without retraining. We propose a unifying Super-Markov Decision Process formulation and the Train, then Estimate and Decide (TED) framework to train and deploy a GCA tailored to inventory management applications. The TED framework consists of three phases: training a GCA on varied problem instances, continuously estimating problem parameters during deployment, and making decisions based on these estimates. Applied to periodic review inventory problems with lost sales, cyclic demand patterns, and stochastic lead times, our trained agent, the Generally Capable Lost Sales Network (GC-LSN) consistently outperforms well-known traditional policies when problem parameters are known. Moreover, under conditions where demand and/or lead time distributions are initially unknown and must be estimated, we benchmark against online learning methods that provide worst-case performance guarantees. Our GC-LSN policy, paired with the Kaplan-Meier estimator, is demonstrated to complement these methods by providing superior empirical performance.

We study the regret performance of Sample Average Approximation (SAA) for data-driven newsvendor problems with general convex inventory costs. In literature, the optimality of SAA has not been fully established under both \alpha-global strong convexity and (\alpha,\beta)-local strong convexity (\alpha-strongly convex within the \beta-neighborhood of the optimal quantity) conditions. This paper closes the gaps between regret upper and lower bounds for both conditions. Under the (\alpha,\beta)-local strong convexity condition, we prove the optimal regret bound of \Theta(\log T/\alpha + 1/ (\alpha\beta)) for SAA. This upper bound result demonstrates that the regret performance of SAA is only influenced by \alpha and not by \beta in the long run, enhancing our understanding about how local properties affect the long-term regret performance of decision-making strategies. Under the \alpha-global strong convexity condition, we demonstrate that the worst-case regret of any data-driven method is lower bounded by \Omega(\log T/\alpha), which is the first lower bound result that matches the existing upper bound with respect to both parameter \alpha and time horizon T. Along the way, we propose to analyze the SAA regret via a new gradient approximation technique, as well as a new class of smooth inverted-hat-shaped hard problem instances that might be of independent interest for the lower bounds of broader data-driven problems.

This paper discusses the revenue management (RM) problem to maximize revenue by pricing items or services. One challenge in this problem is that the demand distribution is unknown and varies over time in real applications such as airline and retail industries. In particular, the time-varying demand has not been well studied under scenarios of unknown demand due to the difficulty of jointly managing the remaining inventory and estimating the demand. To tackle this challenge, we first introduce an episodic generalization of the RM problem motivated by typical application scenarios. We then propose a computationally efficient algorithm based on posterior sampling, which effectively optimizes prices by solving linear programming. We derive a Bayesian regret upper bound of this algorithm for general models where demand parameters can be correlated between time periods, while also deriving a regret lower bound for generic algorithms. Our empirical study shows that the proposed algorithm performs better than other benchmark algorithms and comparably to the optimal policy in hindsight. We also propose a heuristic modification of the proposed algorithm, which further efficiently learns the pricing policy in the experiments.