inventory managers

Abstract: Ski rental is one of the most fundamental online problems, where an agent repeatedly decides whether it should continue renting for a service, or buy it at a one-time fixed cost. In classic online analysis, an adversary may freely select any arbitrary time horizon $t$ after which the instance terminates, hence leading to strong competitive ratio lower bounds of 2 (deterministic) and $e/(e-1)$ (randomized). We consider a novel but natural model aiming at limiting the adversary's power without degrading its flexibility. A stochastic signal, containing no information apart from its arrival time, is transmitted to the algorithm at a time drawn from a known distribution scaled to $[0,t]$. This framework allows us to account for visible effects of the adversary's choice to the algorithm. Focusing as a first step on uniform distributions, we show that the best possible competitive ratios are approximately $1.478$ (deterministic) and $1.438$ (randomized). Surprisingly, simplistic deterministic strategies already achieve a performance of $1.489$.

Abstract: Deploying a new decision policy creates a cold-start problem for prediction models whose targets depend on the policy's actions: historical observations reflect earlier policies, while real observations under the new policy are not yet available. Simulation offers a way to address this gap by rolling out the target policy across counterfactual scenarios and using the resulting trajectories to learn how the system responds to those controls. The simulation-to-reality (Sim2Real) transfer of this simulator-trained model can then be backtested by evaluating it against real observations from past deployments. Using two real-world inventory-control deployments, we evaluate this process from three angles: simulator fidelity, zero-shot transfer to real behavior, and adaptation as real target-policy observations accumulate. The simulator-trained forecaster achieves lower point-estimate mean absolute percentage error (MAPE) than the same architecture trained on historical real data, reducing MAPE by 1.2-3.1 percentage points in Study 1 and 12.5-18.7 points in Study 2. After deployment, lightweight calibration using early real observations further reduces error by up to 2.5 percentage points. These results provide empirical evidence that simulator-generated counterfactual data can support cold-start forecasting under a new policy, and the resulting model can be further refined as real deployment data become available.

Abstract: Online Resource Allocation (ORA) is a fundamental framework for sequential decision-making problems under budget constraints. Classical ORA models typically assume that resources are monotonic, meaning that selecting actions can only decrease the available budget. In this work, we study a more general setting with replenishable budgets, in which actions may either consume or replenish resources over time. This extension is necessary to capture scenarios such as inventory systems or energy markets in which capacity can be actively recovered. We develop a dual-based algorithm that recovers best-of-both-worlds guarantees for standard ORA when the replenishment factor $β= 0$, and improves them when $β> 0$. In particular, our algorithm attains $\widetilde{\mathcal O}(\sqrt{T})$ regret in the stochastic setting and $\widetilde{\mathcal O}(\sqrt{T})$ $α$-regret in the adversarial setting, where $α$ depends on the per-round budget and on the replenishment factor of the void action. Moreover, the algorithm ensures strict satisfaction of the budget constraints.

Abstract: Future exogenous variables provide valuable information for forecasting endogenous time series. Existing covariate-aware methods primarily learn the direct influence of exogenous variables on endogenous variables. However, these effects can be complex and change with the pattern of the exogenous variables, making them difficult to capture. Beyond this perspective, we observe that a given exogenous pattern often co-occurs with only a small set of endogenous response patterns. These associations motivate a strategy that matches future and historical exogenous patterns and uses the corresponding endogenous patterns to enhance forecasting. However, in real-world forecasting scenarios with multiple exogenous variables, each exogenous variable provides a distinct dimension for matching, creating a dilemma for this strategy between precise matching and sufficient historical support. To bridge this gap, we propose XMatch (EXogenous MATCHing), a covariate-aware forecasting model that realizes the aforementioned strategy through a tree-structured matching process that adaptively adjusts the number of exogenous variables used as matching conditions. Specifically, we first introduce the ProtoTree Creator, which organizes historical correspondences between exogenous and endogenous patterns into a ProtoTree, whose deeper levels incorporate additional exogenous variables for matching. For forecasting, we then design the ProtoTree Matcher, which uses future exogenous variables to query the ProtoTree and adaptively determines how many exogenous variables to use for matching based on exogenous pattern similarity and historical support. Finally, the matched endogenous patterns are used as explicit historical evidence to enhance forecasting. Extensive experiments on 12 real-world datasets demonstrate that XMatch outperforms state-of-the-art baselines.

Abstract: We study fundamental information-theoretic limits of robust stochastic optimization when the distribution is known only through its exact moment sequence. We develop a unified framework that produces families of distinct distributions sharing all moments yet inducing radically different optimal decisions, thereby establishing strong impossibility results for a range of decision problems under moment ambiguity. Our approach gives two explicit constructions: a binary and an $N$-way construction showing that distributions with identical moment sequences can nevertheless exhibit arbitrarily different quantiles, order-statistics and threshold regions, forcing incompatible optimal actions. These families of distributions yield, in fact, strong impossibility results across several stochastic optimization problems. First, for the newsvendor problem, moment equivalence causes quantile ambiguity, inducing any fixed or randomized order quantity to fail arbitrarily badly. Second, for revenue maximization, no deterministic or randomized posted pricing scheme can secure a nontrivial approximation relative to the full-information benchmark. Third, for the secretary with cardinal observations setting, the worst-case robust value over all exact moment disclosures is exactly the classical $1/e$ finite-horizon value as opposed to the celebrated result of $0.58$ success probability with full-information by Gilbert and Mosteller (J. Am. Stat. Assoc., 1966). We also recover and expand upon the recent impossibility result of Correa et al. (STOC, 2026) for prophet inequalities with moment knowledge. Indeed, exact moment knowledge can yield at best a $Θ(1/\log n)$ competitive ratio, even when competing against relaxed benchmarks based on expected $r$-th order statistics or when the algorithm is allowed to select $r$ items.

Abstract: We study dynamic pricing problems under inter-temporal price constraints. We have resources with limited capacities. At each time period, we decide which products to make available and what prices to charge for the available products. The sale probability for a product depends on its price. If we make a sale for a product, then we collect a revenue reflecting the price and consume the capacities of a combination of resources. We work with two types of inter-temporal constraints. In price monotonicity, the prices charged for a product at different time periods have to be monotone. In promotion fatigue, we can discount a product at most once over each time interval of a fixed length. Computing the optimal policy is intractable. We use fluid approximations to construct policies. Traditionally, policies from fluid approximations make randomized decisions at each time period by following an optimal solution to the fluid approximation, but such randomized decisions easily violate price monotonicity or promotion fatigue constraints. We develop policies that sample price paths according to an optimal solution to the fluid approximation, while satisfying the inter-temporal constraints. Letting $c_{\min}$ be the smallest initial capacity of a resource and $L$ be the maximum number of resources used by a product, our policies have a performance guarantee of $\max\Big\{ \frac{1}{8L}, \, \frac{1}{2} - \sqrt{\frac{\log c_{\min}}{2 \,c_{\min}}} - \frac{L}{c_{\min}}\Big\}$. Thus, under large resource capacities, our policies are guaranteed to obtain at least half of the optimal total expected revenue. The latter performance guarantee is tight in the sense that no policy can, in general, obtain more than half of the optimal objective value of the fluid approximation even under large resource capacities. We unify our approach to open the path for extensions to other inter-temporal price constraints.

Abstract: Modern prediction-driven decision systems often rely on black-box predictors, but a point forecast alone does not provide the uncertainty scale required for robust downstream decision-making. We build a score-calibrated robustness framework that converts any fixed point predictor into a decision-relevant uncertainty representation through distribution-free conformal calibration. We use the conformal score, rather than a particular uncertainty set, as the primitive unit of robustness. The same score determines coverage-calibrated uncertainty sets for reliability-based robust optimization and normalizes target violations in a target-oriented formulation, Conformal Robust Satisficing. This formulation induces a conformal fragility measure that quantifies how rapidly performance deteriorates as the realized parameter departs from the forecast on the conformal score scale. For objective-uncertainty problems under standard convexity and duality conditions, we show that the reliability-based and target-oriented formulations parameterize the same score-calibrated robust decision frontier. This equivalence yields a data-driven mapping between reliability levels and acceptable targets and characterizes the marginal cost of robustness. Synthetic experiments validate the theoretical guarantees and illustrate the reliability-target correspondence. A real-data online-grocery case study demonstrates how the interface combines deep-learning demand forecasts with tractable inventory optimization, thereby improving reliability and reducing operational costs. Overall, our work shows that conformal scores endow fixed black-box predictors with an interpretable uncertainty scale for downstream decision-making while enabling reliability guarantees, acceptable-target selection, and fragility analysis within a unified framework.

Abstract: SabreAgent uses a language model at design time to construct two components for lost-sales inventory control: a product-specific seasonal prior and a validation-selected capped base-stock policy family. During operation, statistical forecasting and inventory optimization use these frozen artifacts to determine orders, with zero language-model calls. We evaluate the approach on the $1{,}320$ instances of InventoryBench. Under the benchmark's cost assumptions, the operations-research core draws on a zero-lead-time optimality result and a projected-inventory rule for positive deterministic lead times. The latter computes replenishment shortfalls by propagating inventory using sales along simulated demand paths. The seasonal prior adds forecast variants alongside the original forecaster, and the selected policy family handles stochastic lead times with order destruction. SabreAgent scores $0.6311$, compared with $0.5380$ for the strongest published baseline, and ranks first in all six benchmark cells. Ablations attribute most of the gain to the OR core. In the paired analysis, the seasonal component adds $1.79\%$ across the three real-data cells, and the search component adds $2.3\%$ across the two stochastic-lead-time cells. These results demonstrate how model-generated priors and policy structure can improve an OR controller through design-time use.

Abstract: We extend the analysis of strong aggregation to general compatibility graphs, focusing on item counts rather than positions, and exploring generalized greedy matching disciplines. We prove that under a condition of automorphism-based transition consistency, the associated Markov chain is strongly aggregable for an arbitrary graph with a non-trivial automorphism group. Furthermore, we extend our analysis to non-greedy matching disciplines, distinguishing scenarios where compatible items can or cannot coexist within the same state. This result is illustrated with a simple compatibility graph with a rich automorphism structure: the odd rings. For all scenarios, we investigate the strong aggregation properties of the resulting Markov chains. This work enhances the theoretical understanding of lumpability in stochastic matching models and provides a foundation for analyzing complex graph structures.

Abstract: A learner probes at most $k$ of $n$ arms each round, receives the maximum of their rewards in $[0,1]$, and competes with the best fixed arm. When does the probing advantage pay for learning? We determine two minimax laws. Under independent stochastic rewards with winner feedback (the maximum and a winning label), or on arbitrary fixed sequences given a single signed contrast between block maxima, the minimax regret has order $Φ_{n,k}(T)=\min\{\frac{n-k}{n}T,\frac{n-k}{k}\}$, $2\le k<n$. Under winner feedback, both arbitrary joint i.i.d. rewards and fixed sequences have minimax regret of order $R_{n,k}(T)=\frac{n-k}{n}\min\{T,\frac{n+T}{k},\sqrt{\frac{nT}{k}}\}$. Both laws have universal constants and anytime upper bounds. The first reduces regret to a pure coverage cost: same-round contrasts absorb the stability cost, and independence permits exact resampling whose gains fund sample advancement. The second adds a learning cost that becomes comparable to coverage at horizon $n$; beyond $nk$, numerical maxima improve over labels alone. The lower bound allows every adaptive action size.

Abstract: Demand forecasting is critical in modern industry, offering opportunities to reduce costs and gain competitive advantage through improved inventory management. However, forecasting becomes particularly challenging for products with intermittent demand, where demand occurs infrequently and time series contain many zero observations. Such dynamics are common across diverse sectors, such as industrial organizations, consumer goods, aviation, automotive, and electronics. Motivated by these challenges, this paper explores the potential of gradient boosting models to improve forecasting performance. We evaluate statistical, specialized, machine learning, and ensemble approaches across multiple datasets. The results show that specialized methods achieve the strongest performance among individual models, while gradient boosting on its own tends to underperform. However, combining a machine learning model with a specialized approach improves forecasting accuracy by up to 10%, demonstrating that even simple ensembles can outperform single models. Overall, the findings highlight the value of combining machine learning with domain-specific forecasting techniques for intermittent demand.