Rene Caldentey

New: Designing Sparse Graphs for Stochastic Matching with an Application to Middle-Mile Transportation Management
Date Posted:Tue, 07 Jun 2022 06:11:25 -0500
Given an input graph Gin =(V,E_in), we consider the problem of designing a sparse subgraph G = (V, E) with E ? E_in that supports a large matching after some nodes in V are randomly deleted. We study three families of sparse graph designs (namely, Clusters, Rings, and Erdos-Rényi graphs) and show both theoretically and numerically that their performance is close to the optimal one achieved by a complete graph. Our interest in the stochastic sparse graph design problem is primarily motivated by a collaboration with a leading e-commerce retailer in the context of its middle-mile delivery operations. We test our theoretical results using real data from our industry partner and conclude that adding a little flexibility to the routing network can significantly reduce transportation costs.

REVISION: Order Smoothing and Information Sharing under Endogenous Inventory Cost Parameters
Date Posted:Fri, 07 Jan 2022 15:30:26 -0600
We consider a two-tier inventory management system with one retailer and one supplier. The
retailer serves a demand driven by a stationary moving average process (of possibly innite order) and places periodic inventory replenishment orders to the supplier. In this setting, we study the interplay between information sharing and order smoothing under the assumption that rms' inventory cost parameters (e.g., per unit holding and backordering costs) are functions of two forms of supply chain variability: (i) on-hand inventory variability and (ii) replenishment order variability. We show that there is a natural tension between these two sources of variability and characterize a "Pareto frontier" between them by identifying optimal inventory replenishment strategies that trade-o one type of variability for the other in a cost efficient way. For the case in which the retailer is able to share her complete demand history, we provide a full characterization of the efficient frontier, as ...

REVISION: Diffusion Approximations for a Class of Sequential Experimentation Problems
Date Posted:Mon, 11 Oct 2021 04:53:24 -0500
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 “Theta”. The decision maker can delay taking the action in order to experiment and gather additional information on “Theta”. 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 ...

REVISION: Diffusion Approximations for a Class of Sequential Experimentation Problems
Date Posted:Mon, 20 Sep 2021 06:51:15 -0500
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 “Theta”. The decision maker can delay taking the action in order to experiment and gather additional information on “Theta”. 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 ...

REVISION: Diffusion Approximations for a Class of Sequential Testing Problems
Date Posted:Fri, 18 Jun 2021 03:44:55 -0500
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 “Theta”. The decision maker can delay taking the action in order to experiment and gather additional information on “Theta”. 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 ...

REVISION: Robust Learning of Consumer Preferences
Date Posted:Mon, 05 Apr 2021 11:21:11 -0500
This paper studies a class of ranking and selection problems faced by a company that wants to identify the most preferred product out of a finite set of alternatives when consumer preferences are a priori unknown. The only information available is that consumer preferences satisfy two key properties: (i) they are consistent with some unknown true ranking of the alternatives and (ii) they are strict, namely, no two products are equally preferred. To learn the unknown ranking, the company is able to sample consumer preferences by sequentially showing different subsets of products to different consumers and asking them to report their top preference within the displayed set. The objective of the company is to design a display policy that minimizes the expected number of samples needed to identify the top-ranked product with high probability. We prove an instance-specific lower bound on the sample complexity of any policy that identifies the top-ranked version within a given ...

REVISION: Diffusion Approximations for a Class of Sequential Testing Problems
Date Posted:Sat, 06 Feb 2021 09:49:58 -0600
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 “Theta”. The decision maker can delay taking the action in order to experiment and gather additional information on “Theta”. 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 ...

REVISION: Order Smoothing and Information Sharing under Endogenous Inventory Cost Parameters
Date Posted:Fri, 14 Aug 2020 04:15:56 -0500
We consider a two-tier inventory management system with one retailer and one supplier. The
retailer serves a demand driven by a stationary moving average process (of possibly innite order) and places periodic inventory replenishment orders to the supplier. In this setting, we study the interplay between information sharing and order smoothing under the assumption that rms' inventory cost parameters (e.g., per unit holding and backordering costs) are functions of two forms of supply chain variability: (i) on-hand inventory variability and (ii) replenishment order variability. We show that there is a natural tension between these two sources of variability and characterize a \Pareto frontier" between them by identifying optimal inventory replenishment strategies that trade-o one type of variability for the other in a cost efficient way. For the case in which the retailer is able to share her complete demand history, we provide a full characterization of the efficient frontier, as ...

REVISION: Robust Learning of Consumer Preferences
Date Posted:Mon, 10 Feb 2020 04:39:03 -0600
This paper studies a class of ranking and selection problems faced by a company that wants to identify the most preferred product out of a finite set of alternatives when consumer preferences are a priori unknown. The only information available is that consumer preferences satisfy two key properties: (i) they are consistent with some unknown true ranking of the alternatives and (ii) they are strict, namely, no two products are equally preferred. To learn the unknown ranking, the company is able to sample consumer preferences by sequentially showing different subsets of products to different consumers and asking them to report their top preference within the displayed set. The objective of the company is to design a display policy that minimizes the expected number of samples needed to identify the top-ranked product with high probability. We prove an instance-specific lower bound on the sample complexity of any policy that identifies the top-ranked version within a given ...

REVISION: Diffusion Approximations for a Class of Sequential Testing Problems
Date Posted:Tue, 12 Nov 2019 12:10:42 -0600
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 "Theta". The decision maker can delay taking the action in order to experiment and gather additional information on "Theta". We model the decision maker's problem using a Bayesian sequential experimentation framework and use dynamic programming and asymptotic analysis to solve it. In particular, we consider environments in which the average number of experiments that can be conducted per unit of time is large but the informativeness of each individual experiment is low. Under these conditions, 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 ...

REVISION: On the Optimal Design of a Bipartite Matching Queueing System
Date Posted:Mon, 11 Nov 2019 04:07:23 -0600
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 ...

REVISION: On the Optimal Design of a Bipartite Matching Queueing System
Date Posted:Sat, 23 Mar 2019 16:32:54 -0500
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 ...

REVISION: Inventory Policies and Information Sharing: An Efficient Frontier Approach
Date Posted:Mon, 04 Mar 2019 06:03:24 -0600
We consider a two-tier inventory management system with one retailer and one supplier. The retailer serves a demand driven by a stationary moving average process (of possibly infinite order) and places periodic inventory replenishment orders to the supplier. In this setting, we study the value of information sharing and its impact on the retailer’s optimal ordering strategy. We argue that information sharing affects performance through two key cost drivers: (i) on-hand inventory variability and (ii) replenishment order variability. We characterize a “Pareto frontier” between these two sources of variability by identifying optimal inventory replenishment strategies that trade-off one type of variability for the other in a cost efficient way. For the case in which the retailer is able to share her complete demand history, we provide a full characterization of the efficient frontier, as well as of an optimal replenishment policy. On the other hand, when the retailer is not able (or ...

REVISION: Learning Customer Preferences from Personalized Assortments
Date Posted:Tue, 07 Aug 2018 02:58:24 -0500
A company wishes to identify the most popular version of a product from a menu of alternative options. Unaware of customers' true preferences, the company relies on a feedback system that allows potential buyers to provide feedback on their preferred versions. Under a general ranking-based choice model framework, we study how to dynamically individualize the set of versions shown to each customer for them to provide feedback on. This allows the company to identify the top-ranked version with a fixed probabilistic confidence level using a minimal amount of feedback. We prove an instance-specific lower bound on the sample complexity and propose a sampling policy (Myopic Tracking Policy), which is both asymptotically optimal and intuitive to implement. Our methodology draws on previous work in the sequential design of experiments and best arm identification. We illustrate our methodology using a special class of choice models based on Luce's (1959) attraction model and provide a simple ...

New: Crowdvoting the Timing of New Product Introduction
Date Posted:Wed, 27 Jan 2016 12:09:44 -0600
Launching new products into the marketplace is a complex and risky endeavor that companies must continuously undertake. As a result, it is not uncommon to witness major rms discontinuing a product shortly after its introduction. In this paper, we consider a seller who has the ability to first test the market and gather demand information before deciding whether or not to launch a new product. In particular, we consider the case in which the seller sets up an online voting system that potential customers can use to provide feedback about their willingness to buy the new product. This voting system has the potential of offering a win-win situation whereby a consumer who votes hopes to influence the seller's final assortment, while at the same time these votes and their pace benefit the seller as they provide valuable information to better forecast demand. We investigate the optimal design of such a crowdvoting system and its implications on the seller's commercialization strategy.

REVISION: Intertemporal Pricing under Minimax Regret
Date Posted:Wed, 29 Apr 2015 02:09:34 -0500
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 ...

REVISION: Intertemporal Pricing Without Priors
Date Posted:Thu, 21 Nov 2013 13:12:50 -0600
We consider the pricing problem faced by a monopolist who sells a product to a population of consumers over a discrete number of periods. 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. In this setting, we consider a robust formulation of the seller's pricing problem which is based on the minimization of her worst-case regret. This regret is defined as the difference between her payoff under full demand information and her realized payoff. We consider two distinct cases of customers' purchasing behavior: myopic and strategic customers. For each of these demand models, we characterize the optimal pricing strategy and corresponding minimum regret. We show that an optimal pricing strategy is not (necessarily) ...

New: Online Auction and List Price Revenue Management
Date Posted:Wed, 29 Oct 2008 00:47:45 -0500
We analyze a revenue management problem in which a seller facing a Poisson arriving stream of customers operates an online multiunit auction. Customers have an alternative list price channel where to get the product from. We consider two variants of this problem: In the first one, the list price is an external channel run by another firm. In the second variant, the seller manages simultaneously both the auction and the list price channels. Each consumer, trying to maximize his own surplus, ...

An Overview of Pricing Models for Revenue Management
Date Posted:Thu, 24 Apr 2008 05:10:28 -0500
In 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 non-renewable set of resources satisfy stochastic price-sensitive 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 ...

Optimal Control and Hedging of Operations in the Presence of Financial Markets
Date Posted:Thu, 24 Apr 2008 05:09:26 -0500
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 ...

New: Insider Trading With Stochastic Valuation
Date Posted:Tue, 15 May 2007 20:55:09 -0500
This paper studies a model of strategic trading with asymmetric information of an asset whose value follows a Brownian motion. An insider continuously observes a signal that tracks the evolution of the asset fundamental value. At a random time a public announcement reveals the current value of the asset to all the traders. The equilibrium has two regimes separated by an endogenously determined time T. In [0,T), the insider gradually transfers her information to the market and the market's ...

Dynamic Pricing for Non-Perishable Products with Demand Learning
Date Posted:Sun, 26 Feb 2006 18:12:31 -0600
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, theta; a proxy for the market size. If theta is high then the retailer can take advantage of a large market charging premium prices, but if theta is small then price markdowns can be applied to encourage sales. The retailer has a prior belief on the value of theta which he updates as time and available ...