Rene Caldentey - Academia.edu (original) (raw)

Papers by Rene Caldentey

Operations Research, Oct 1, 2009

A retailer is endowed with a finite inventory of a non-perishable product. Demand for this produc... more A retailer is endowed with a finite inventory of a non-perishable product. Demand for this product is driven by a price-sensitive Poisson process that depends on an unknown parameter which is a proxy for the market size. The retailer has a prior belief on the value of this parameter which he updates as time and available information (prices and sales) evolves. The retailer's objective is to maximize the discounted long-term average profits of his operation using dynamic pricing policies. We consider two cases. In the first case, the retailer is constrained to sell the entire initial stock of the non-perishable product before a different assortment is considered. In the second case, the retailer is able to stop selling the non-perishable product at any time and switch to a different menu of products. For both cases, we formulate the retailer's problem as a (Poisson) intensity control problem and derive structural properties of an optimal solution and suggest a simple and efficient approximated solution. We use numerical computations, together with asymptotic analysis, to evaluate the performance of our proposed policy.

arXiv (Cornell University), Feb 13, 2021

We consider a decision maker who must choose an action in order to maximize a reward function tha... more We consider a decision maker who must choose an action in order to maximize a reward function that depends on the action that she selects as well as 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. First, it reveals that the problems of (i) selecting the optimal sequence of experiments to use and (ii) deciding the optimal time when to stop experimenting decouple and can be solved independently. Second, it shows that an optimal experimentation policy is one that chooses the experiment that maximizes the instantaneous volatility of the belief process. Third, the diffusion approximation provides a more mathematically malleable formulation that we can solve in closed form and suggests efficient heuristics for the non-asympototic regime. 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.

Social Science Research Network, 2003

We consider the problem of dynamically hedging the profits of a corporation when these profits ar... more We consider the problem of dynamically hedging the profits of a corporation when these profits are correlated with returns in the financial markets. In particular, we consider the general problem of simultaneously optimizing over both the operating policy and the hedging strategy of the corporation. We discuss how different informational assumptions give rise to different types of hedging and solution techniques. Finally, we solve some problems commonly encountered in operations management to demonstrate the methodology.

Operations Research, 2022

We consider a multi-class multi-server queueing system and study the problem of designing an opti... more We consider a multi-class multi-server queueing system and study the problem of designing an optimal matching topology (or service compatibility structure) between customer classes and servers under a FCFS-ALIS service discipline. Specifically, we are interested in finding matching topologies that optimize-in a Pareto efficiency sense-the trade-off between two competing objectives: (i) minimizing customers' waiting time delays and (ii) maximizing matching rewards generated by pairing customers and servers. Our analysis of the problem is divided in three main parts. First, under heavy-traffic conditions, we show that any bipartite matching system can be partitioned into a collection of complete resource pooling (CRP) subsystems, which are interconnected by means of a direct acyclic graph (DAG). We show that this DAG together with the aggregate service capacity on each CRP component fully determine the vector of steady-state waiting times. In particular, we show that the average (scaled) steady-state delay across all customer classes is asymptotically equal to the number of CRP components divided by the total system capacity. Second, since computing matching rewards under a FCFS-ALIS service discipline is computationally infeasible as the number of customer classes and servers grow large, we propose a quadratic programming (QP) formulation to approximate matching rewards. We show that the QP formulation is exact for a number of instances of the problem and provides a very good approximation in general. Extensive numerical experiments show that in over 98% of problem instances the relative error between the exact rewards and the QP approximate rewards is less than 2%. Lastly, combining our characterization of average delays in terms of the number of CRP components and the quadratic programming formulation to compute matching rewards, we propose a mixed-integer linear program (MILP) that can be used to find the set of matching topologies that define the Pareto frontier of reward-delay pairs.

Social Science Research Network, 2005

Operations Research, Oct 1, 2006

Motivated by recent electronic marketplaces, we consider a single-product make-to-stock manufactu... more Motivated by recent electronic marketplaces, we consider a single-product make-to-stock manufacturing system that uses two alternative selling channels: long-term contracts and a spot market of electronic orders. At time 0, the risk-averse manufacturer selects the long-term contract price, at which point buyers choose one of the two channels. The resulting long-term contract demand is a deterministic fluid, while the spot-market demand is modeled as a stochastic renewal process. An exponential reflected random walk model is used to model the spot-market price, which is correlated with the spot-market demand process. The manufacturer accepts or rejects each electronic order, and long-term contracts and accepted electronic orders are backordered if necessary. The manufacturer's control problem is to select the optimal longterm contract price as well as the optimal production (i.e., busy/idle) and electronic-order admission policies to maximize revenue minus inventory holding and backorder costs. Under heavy-traffic conditions, the problem is approximated by a diffusion-control problem, and analytical approximations are used to derive a policy that is simple, and reasonably accurate and robust.

Operations Research, Feb 1, 2017

We consider the pricing problem faced by a monopolist who sells a product to a population of cons... more We consider the pricing problem faced by a monopolist who sells a product to a population of consumers over a finite time horizon. Customers are heterogeneous along two dimensions: (i) willingness-to-pay for the product and (ii) arrival time during the selling season. We assume that the seller knows only the support of the customers' valuations and do not make any other distributional assumptions about customers' willingness-to-pay or arrival times. We consider a robust formulation of the seller's pricing problem which is based on the minimization of her worst-case regret, a framework first proposed by Bergemann and Schlag (2008) in the context of static pricing. We consider two distinct cases of customers' purchasing behavior: myopic and strategic customers. For both of these cases, we characterize optimal price paths. For myopic customers, the regret is determined by the price at a critical time. Depending on the problem parameters, this critical time will be either the end of the selling season or it will be a time that equalizes the worstcase regret generated by undercharging customers and the worst-case regret generated by customers waiting for the price to fall. The optimal pricing strategy is not unique except at the critical time. For strategic consumers, we develop a robust mechanism design approach to compute an optimal policy. Depending on the problem parameters, the optimal policy might lead some consumers to wait until the end of the selling season and might price others out of the market. Under strategic customers, the optimal price equalizes the regrets generated by different customer types that arrive at the beginning of the selling season. We show that a seller that does not know if the customers are myopic should price as if they are strategic. We also show there is no benefit under myopic consumers to having a selling season longer than a certain uniform bound, but that the same is not true with strategic consumers.

Management Science, Aug 1, 2022

A decision maker (DM) must choose an action in order to maximize a reward function that depends o... more A decision maker (DM) must choose an action in order to maximize a reward function that depends on the DM’s action as well as on an unknown parameter Θ. The DM can delay taking the action in order to experiment and gather additional information on Θ. We model the problem using a Bayesian sequential experimentation framework and use dynamic programming and diffusion-asymptotic analysis to solve it. For that, we consider environments in which 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 regimes, 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. First, it reveals that the problems of (i) selecting the optimal sequence of experiments to use and (ii) deciding the optimal time when to stop experimenting decouple and can be solved independently. Second, it shows that an optimal experimentation policy is one that chooses the experiment that maximizes the instantaneous volatility of the belief process. Third, the diffusion approximation provides a more mathematically malleable formulation that we can solve in closed form and suggests efficient heuristics for the nonasympototic regime. 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 crowd voting 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. This paper was accepted by Omar Besbes, revenue management and market analytics.

RePEc: Research Papers in Economics, 1999

W e model an isolated portion of a competitive supply chain as a M/M/1 make-tostock queue. The re... more W e model an isolated portion of a competitive supply chain as a M/M/1 make-tostock queue. The retailer carries finished goods inventory to service a Poisson demand process, and specifies a policy for replenishing his inventory from an upstream supplier. The supplier chooses the service rate, i.e., the capacity of his manufacturing facility, which behaves as a single-server queue with exponential service times. Demand is backlogged and both agents share the backorder cost. In addition, a linear inventory holding cost is charged to the retailer, and a linear cost for building production capacity is incurred by the supplier. The inventory level, demand rate, and cost parameters are common knowledge to both agents. Under the continuous-state approximation where the M/M/1 queue has an exponential rather than geometric steady-state distribution, we characterize the optimal centralized and Nash solutions, and show that a contract with linear transfer payments replicates a cost-sharing agreement and coordinates the system. We also compare the total system costs, the agents' decision variables, and the customer service levels of the centralized versus Nash versus Stackelberg solutions.

Social Science Research Network, 2022

IEEE Engineering Management Review, 2016

I n this paper, we examine the research and results of dynamic pricing policies and their relatio... more I n this paper, we examine the research and results of dynamic pricing policies and their relation to revenue management. The survey is based on a generic revenue management problem in which a perishable and nonrenewable set of resources satisfy stochastic pricesensitive demand processes over a finite period of time. In this class of problems, the owner (or the seller) of these resources uses them to produce and offer a menu of final products to the end customers. Within this context, we formulate the stochastic control problem of capacity that the seller faces: How to dynamically set the menu and the quantity of products and their corresponding prices to maximize the total revenue over the selling horizon.

Manufacturing & Service Operations Management

Problem definition: We study the use of nonmonetary incentives based on reciprocity to facilitate... more Problem definition: We study the use of nonmonetary incentives based on reciprocity to facilitate capacity sharing between two service providers that have limited and substitutable service capacity. Academic/practical relevance: We propose a parsimonious game theory framework, in which two firms dynamically choose whether to accept each other’s customers without the capability to perfectly monitor each other’s capacity utilization state. Methodology: We solve the continuous-time imperfect-monitoring game by focusing on a class of public strategy, in which firms’ real-time capacity-sharing decision depends on an intuitive and easy-to-implement accounting device, namely the current net number of transferred customers. We refer to such an equilibrium as a trading-favors equilibrium. We characterize the condition in which capacity sharing takes place in such an equilibrium. Results: We find that some degree of efficiency loss (as compared with a central planner’s solution) is necessary ...

Why use call centers —- resource pooling Queues are a function of variability, Scaling will stay ... more Why use call centers —- resource pooling Queues are a function of variability, Scaling will stay with same queue length Double the size will half the waiting time System of size n will be n times faster Many servers reduce variability in waiting time Sojourn = Wait + Service long service is not a problem, we want short wait Gideon Weiss, University of Haifa, FCFS-ALIS parallel skill based service, ©2014 4 Multi-type customers, skill based parallel servers Pooled servers may not have all the skills – quality suffers Skill based service may lose pooling advantage Solution: some overlap Bipartite Compatibility Graph

Social Science Research Network, Apr 1, 2004

arXiv (Cornell University), Mar 30, 2023

This paper examines the performance of multi-class multi-server bipartite queueing systems under ... more 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 Afèche et al. (2022), we generalize the model by allowing the vector of arrival rates to approach the heavytraffic 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.

SSRN Electronic Journal

We model an isolated portion of a competitive supply chain as a M/M/1 make-to-stock queue. The re... more We model an isolated portion of a competitive supply chain as a M/M/1 make-to-stock queue. The retailer carries finished goods inventory to service a Poisson demand process, and specifies a policy for replenishing his inventory from an upstream supplier. The supplier chooses the service rate, i.e., capacity, of his manufacturing facility, which behaves as a single-server queue with exponential service times. Demand is backlogged and both agents share the backorder cost. In addition, a linear inventory holding cost is charged to the retailer, and a linear cost for building production capacity is incurred by the supplier. The inventory level, demand rate and cost parameters are common knowledge to both agents. Under the continuous state approximation that the M/M/1 queue has an exponential rather than geometric steady-state distribution, we characterize the optimal centralized and Nash solutions, and show that a contract with linear transfer payments based on backorder, inventory and ...