Houcai Shen

We study periodic-review inventory systems with minimum order quantity and positive lead times. The optimal policy is difficult to characterize due to the discontinuous action space. Consequently, the literature has focused on developing effective heuristics, among which the (s, t) policy is widely studied and has been shown to perform well in numerical experiments. In this paper, we establish three fundamental properties of (s, t) policies, including convexity and ergodicity. We expect that these properties will facilitate future research on (s, t) policies.

This paper studies the optimal policies for stochastic periodic-review inventory systems with general quantitydependent costs, where both fixed and unit costs decrease with the order quantity z. The cost structure is defined as (K 1 + c 1 z)1[0 < z < Q] + (K 2 + c 2 z)1[z ≥ Q], with K 1 ≥ K 2 and c 1 ≥ c 2. Managing inventory under this general nonlinear ordering cost has long been an open problem. Methodologically, we introduce a new technical property called (K, c, Q)increase. We show that the optimal policy is a state-dependent (s, S, X, Q) policy, which is also a (s, S)-type policy. Specifically, the finite-horizon policy exhibits characteristics of the (s, S) policy for higher and lower inventory levels. For medium inventory levels, we identify the corresponding critical points and the range of the optimal order quantities, which guide decisions on when to avoid ordering, when to place an order less than Q, or when to order more than Q. For the infinite-horizon case, we prove that the discount-optimal policy preserves the structure of the finite-horizon counterpart. We then focus on the c 1 = c 2 model, which considers only decreasing fixed costs. This special model not only satisfies the (K, c, Q)-increase property but also exhibits the bounded differences property, enabling us to derive more refined structural properties compared to the general model. Furthermore, its average-optimal policy maintains the discount-optimal structure through the vanishing discount approach. Regarding heuristic policies, we first analyze the performance of (s, S) policy in our model. Under bounded demand, we show that as Q grows sufficiently large, (s, S) policy becomes optimal for the finite-horizon problem and achieves asymptotic optimality for the infinite-horizon case. We propose the (s 1 , s 2 , Q) policy as another heuristic, which demonstrates effective performance across a large number of instances in numerical experiments.

Artificial intelligence (AI) is increasingly integrated into medical decision-making, yet its liability implications remain complex, particularly when physicians differ in diagnostic skills and their quality is unobservable. This paper develops a principal-agent model in which a social planner designs medical liability to regulate a physician with private quality information who chooses between a standard treatment, a personalized judgment-based treatment, or following an imperfect AI recommendation. Our analysis yields several novel insights. First, we show that the optimal mechanism under asymmetric information is surprisingly simple: a uniform, one-size-fits-all liability level for all physician types who deviate from the standard of care. Despite physician heterogeneity, this simple policy often achieves the full-information first-best outcome, particularly when standard care is reliable or AI is highly accurate. Second, the relationship between AI accuracy and optimal liability is non-monotonic. Contrary to common intuition, better AI does not always imply more relaxed liability. As AI accuracy increases, the optimal liability either decreases monotonically or follows an inverted-U pattern, depending on the uncertainty of the standard treatment. Third, asymmetric information does not universally reduce social welfare. Welfare loss arises only when standard care is unreliable and AI accuracy is too low; even then, its magnitude follows an inverted U-shape, initially increasing as AI complicates the regulatory problem, but declining as more accurate AI helps mitigate it. Finally, we find that information asymmetry is a double-edged sword in the presence of AI, and greater transparency does not benefit all stakeholders equally.

This paper proposes a joint optimization approach for the production decision-making and inventory allocation in a fault-prone machine Make-to-Stock System, considering both production-side uncertainties and demand-side uncertainties, these factors often cause operational inefficiencies, higher costs and lower customer satisfaction, thus highlighting the need to integrate maintenance strategies into production-inventory management. A model based on Markov decision theory is presented to more accurately reflect real-world production processes, utilizing a preventive repair maintenance strategy, which focuses on repairing the machine only when it fails, as opposed to traditional fixed-cycle or fixed-threshold maintenance strategies. To tackle the complex structure of the optimal control strategy, the paper employs a numerical algorithm for updating the optimal strategy. Computational experiments are conducted to explain the properties of the optimal control strategies and emphasize the importance of considering a maintenance factor in the system. The study highlights the significance of effective production inventory system management, with the conclusion that the optimal control strategy is a machine-state-dependent threshold strategy.

Motivated by the perishable inventory system of JD in Shanghai, we establish a two-echelon perishable One-Warehouse Multi-Retailer (OWMR) inventory system. A key challenge in such systems lies in determining optimal allocations with unknown demand distributions faced by each retailer. Unlike most existing studies that rely on prior assumptions about underlying distribution, we propose a data-driven distribution-free prescriptive analysis framework—Constrained Local Learning (CLL) model framework leveraging historical dataset to estimate unknown demand distribution accurately. This novel framework uses integrated machine learning methods to prescribe ordering quantity for each retailer directly from historical demand and numerous features (covariates) without having to make assumptions about the underlying distribution. To demonstrate the effectiveness of our framework, we theoretically analyze its properties, including asymptotic optimality, convexity and establish performance guarantee. We design a tractable WFS-OPT algorithm for solving the model framework and numerically compare the performance of different weight functions under varying scenarios. Compared to the benchmark SAA method, the Kernel Method performs most prominently, achieving up to an approximately 3% reduction in general cost across all test cases, while also improving computational efficiency by up to 80%. We also provide extensive practical insights into our approach.

The double‐ended matching queueing model has wide applicability across various real‐life scenarios. In this paper, we analyze fluid models of bilateral matching queues with time‐varying arrivals. The model contains fluid contents with general patience time distributions in a task queue and a worker queue, aiming to approximate the characteristics of bilateral queueing systems. We first prove the existence and uniqueness of the solution to the fluid model. When the arrival rates of both tasks and workers are constant, we determine the steady‐state queue lengths and abandonment proportions for both sides of the queueing system. Furthermore, we demonstrate that the solution converges to an equilibrium state starting from any initial state. For situations involving time‐varying arrival rates, satisfactory results from numerical experiments validate the reliability of the fluid model in describing the queueing system. Finally, we explore the matching problems within bilateral queueing systems and provide tailored solutions for various scenarios.

This study explores optimal pricing in dual-channel retailing with return insurance, considering price differentiation across channels, consumer heterogeneity, and return behavior. Three prevalent return insurance scenarios are examined: (i) no return insurance (Scenario N), (ii) retailer's free return insurance (Scenario R) and (iii) consumers' purchasing return insurance (Scenario C). Findings first suggest that when a retailer offers free return insurance, it should set higher prices online compared to offline. Conversely, if no free return insurance is provided, lowering the online price can encourage more online sales. Interestingly, the impact of return insurance on pricing and demand is non-intuitive. When product value and consumers' return cost are high, the introduction of return insurance leads to price increases across both online and offline channels, and simultaneously boosts online demand. Finally, we also find that return insurance does not always improve profitability for the dual-channel retailer. The retailer only benefits from introducing return insurance if the product has high value and consumers face substantial return costs. The study highlights the role of return insurance as an important tool for dual-channel retailers when combined with strategic pricing.