arXiv subjects

Rene Caldentey

Publications and source records attributed to Rene Caldentey.

5 recordsLinked to original sources

arXiv2026

Binomial Smoothing for Inventory and Information Control in Supply Chains

In many decentralized supply chains, upstream firms do not observe market demand directly and instead infer downstream conditions from the order stream. A retailer's replenishment policy therefore plays a dual role: it governs inventory replenishment and shapes the information available for upstream forecasting. This creates a fundamental trade-off. Smoother orders improve upstream predictability, but delaying the response to demand can increase downstream inventory costs. We study how a retailer should optimally smooth demand in a two-tier supply chain with one retailer and one manufacturer when the manufacturer forecasts future orders from the retailer's order history. We propose Binomial Smoothing, a class of replenishment policies that implements delayed demand response by spreading each unit of demand over a finite horizon using binomial weights. The class is interpretable, easy to calibrate, and analytically tractable. Under weakly stationary Gaussian demand satisfying mild regularity conditions, we show that, for any fixed smoothing horizon, the Binomial policy minimizes the manufacturer's forecast error among all policies with the same degree of smoothing. It remains invertible, so the manufacturer can recover demand history from observed orders. More generally, Binomial Smoothing achieves a constant-factor approximation guarantee relative to an optimal policy. Our results yield a broader insight: replenishment policies should be designed not merely to reduce order variance, as in the traditional bullwhip measure, but to reduce the unpredictable component of orders. Carefully designed smoothing can improve supply-chain performance and partially substitute for information sharing, providing a concrete mechanism for coordination without collaboration.

stat.AP↗

arXiv2026

Intertemporal Demand Allocation for Inventory Control in Online Marketplaces

Online marketplaces increasingly do more than simply match buyers and sellers: they route orders across competing sellers and, in many categories, offer ancillary fulfillment services that make seller inventory a source of platform revenue. We investigate how a platform can use intertemporal demand allocation to influence sellers' inventory choices without directly controlling stock. We develop a model in which the platform observes aggregate demand, allocates orders across sellers over time, and sellers choose between two fulfillment options, fulfill-by-merchant (FBM) and fulfill-by-platform (FBP), while replenishing inventory under state-dependent base-stock policies. The key mechanism we study is informational: by changing the predictability of each seller's sales stream, the platform changes sellers' safety-stock needs even when average demand shares remain unchanged. We focus on nondiscriminatory allocation policies that give sellers the same demand share and forecast risk. Within this class, uniform splitting minimizes forecast uncertainty, whereas any higher level of uncertainty can be implemented using simple low-memory allocation rules. Moreover, increasing uncertainty above the uniform benchmark requires routing rules that prevent sellers from inferring aggregate demand from their own sales histories. These results reduce the platform's problem to choosing a level of forecast uncertainty that trades off adoption of platform fulfillment against the inventory held by adopters. Our analysis identifies demand allocation as a powerful operational and informational design lever in digital marketplaces.

cs.MA↗

arXiv2026

Designing Information Delays in Supply Chains

This paper studies how a downstream retailer in a decentralized two-tier supply chain can implicitly transmit demand information to an upstream supplier through the structure of its order stream in the absence of an explicit information-sharing mechanism. We distinguish our work from prior work by introducing the notion of information delay and by linking optimal implicit information sharing to the group delay of the retailer's ordering transfer function. We show that pure delay is strictly suboptimal, while fractional-delay mechanisms can reshape the order autocorrelation to improve supplier forecastability and reduce system-wide inventory costs. Using Hardy-space factorization, we develop a tractable family of invertible ARMA policies that approximates the theoretically optimal (but non-rational) limiting filter derived by Caldentey et al. (2025) and preserves its informational delay properties. This construction yields sharp guidance on how policy complexity, as measured by the degrees of the ARMA policies, impacts supply chain costs. We further extend the analysis to memory-constrained suppliers and characterize how the complexity of the retailer's policy should scale with the supplier's finite forecasting window, highlighting when, perhaps counterintuitively, increasing policy complexity can become counterproductive.

math.OC↗

arXiv2023

Heavy Traffic Analysis of Multi-Class Bipartite Queueing Systems Under FCFS

This paper examines the performance of multi-class multi-server bipartite queueing systems under a FCFS-ALIS service discipline, where each arriving customer is only compatible with a subset of servers. We analyze the system under conventional heavy-traffic conditions, where the traffic intensity approaches one from below. Building upon the formulation and results of Afeche et al. 2021, we generalize the model by allowing the vector of arrival rates to approach the heavy-traffic limit from an arbitrary direction. We characterize the steady-state waiting times of the various customer classes and demonstrate that a much wider range of waiting time outcomes is achievable. Furthermore, we establish that the matching probabilities, i.e., the probabilities of different customer classes being served by different servers, do not depend on the direction along which the system approaches heavy traffic. We also investigate the design of compatibility between customer classes and servers, finding that a service provider who has complete control over the matching can design a delay-minimizing menu by considering only the limiting arrival rates. When some constraints on the compatibility structure exist, the direction of convergence to heavy-traffic affects which menu minimizes delay. Additionally, we discover that the bipartite matching queueing system exhibits a form of Braess's paradox, where adding more connectivity to an existing system can lead to higher average waiting times, despite the fact that neither customers nor servers act strategically.

math.PR↗

arXiv2021

Diffusion Approximations for a Class of Sequential Testing Problems

We consider a decision maker who must choose an action in order to maximize a reward function that depends also on an unknown parameter Θ. The decision maker can delay taking the action in order to experiment and gather additional information on Θ. We model the decision maker's problem using a Bayesian sequential experimentation framework and use dynamic programming and diffusion-asymptotic analysis to solve it. For that, we scale our problem in a way that both the average number of experiments that is conducted per unit of time is large and the informativeness of each individual experiment is low. Under such regime, we derive a diffusion approximation for the sequential experimentation problem, which provides a number of important insights about the nature of the problem and its solution. Our solution method also shows that the complexity of the problem grows only quadratically with the cardinality of the set of actions from which the decision maker can choose. We illustrate our methodology and results using a concrete application in the context of assortment selection and new product introduction. Specifically, we study the problem of a seller who wants to select an optimal assortment of products to launch into the marketplace and is uncertain about consumers' preferences. Motivated by emerging practices in e-commerce, we assume that the seller is able to use a crowdvoting system to learn these preferences before a final assortment decision is made. In this context, we undertake an extensive numerical analysis to assess the value of learning and demonstrate the effectiveness and robustness of the heuristics derived from the diffusion approximation.

stat.ML↗