Vivek F. Farias

A Nonparametric Approach to Modeling Choice with Limited Data

Choice models today are ubiquitous across a range of applications in operations and marketing. Real-world implementations of many of these models face the formidable stumbling block of simply identifying the “right” model of choice to use. Because models of choice are inherently high-dimensional objects, the typical approach to dealing with this problem is positing, a priori, a parametric model that one believes adequately captures choice behavior. This approach can be substantially suboptimal in scenarios where one cares about using the choice model learned to make fine-grained predictions; one must contend with the risks of mis-specification and overfitting/underfitting. Thus motivated, we visit the following problem: For a “generic” model of consumer choice namely, distributions over preference lists and a limited amount of data on how consumers actually make decisions such as marginal information about these distributions, how may one predict revenues from offering a particular assortment of choices? An outcome of our investigation is a nonparametric approach in which the data automatically select the right choice model for revenue predictions. The approach is practical. Using a data set consisting of automobile sales transaction data from a major U.S. automaker, our method demonstrates a 20% improvement in prediction accuracy over state-of-the-art benchmark models; this improvement can translate into a 10% increase in revenues from optimizing the offer set. We also address a number of theoretical issues, among them a qualitative examination of the choice models implicitly learned by the approach. We believe that this paper takes a step toward “automating” the crucial task of choice model selection. This paper was accepted by Yossi Aviv, operations management.

Dynamic Pricing with a Prior on Market Response

We study a problem of dynamic pricing faced by a vendor with limited inventory, uncertain about demand, and aiming to maximize expected discounted revenue over an infinite time horizon. The vendor learns from purchase data, so his strategy must take into account the impact of price on both revenue and future observations. We focus on a model in which customers arrive according to a Poisson process of uncertain rate, each with an independent, identically distributed reservation price. Upon arrival, a customer purchases a unit of inventory if and only if his reservation price equals or exceeds the vendors prevailing price. We propose a simple heuristic approach to pricing in this context, which we refer to as decay balancing. Computational results demonstrate that decay balancing offers significant revenue gains over recently studied certainty equivalent and greedy heuristics. We also establish that changes in inventory and uncertainty in the arrival rate bear appropriate directional impacts on decay balancing prices in contrast to these alternatives, and we derive worst-case bounds on performance loss. We extend the three aforementioned heuristics to address a model involving multiple customer segments and stores, and provide experimental results demonstrating similar relative merits in this context.

On the Efficiency-Fairness Trade-off

This paper deals with a basic issue: How does one approach the problem of designing the “right” objective for a given resource allocation problem? The notion of what is right can be fairly nebulous; we consider two issues that we see as key: efficiency and fairness. We approach the problem of designing objectives that account for the natural tension between efficiency and fairness in the context of a framework that captures a number of resource allocation problems of interest to managers. More precisely, we consider a rich family of objectives that have been well studied in the literature for their fairness properties. We deal with the problem of selecting the appropriate objective from this family. We characterize the trade-off achieved between efficiency and fairness as one selects different objectives and develop several concrete managerial prescriptions for the selection problem based on this trade-off. Finally, we demonstrate the value of our framework in a case study that considers air traffic management. This paper was accepted by Yossi Aviv, operations management.

Tetris: A Study of Randomized Constraint Sampling

Approximate Dynamic Programming is a means of synthesizing nearoptimal policies for large scale stochastic control problems. We examine here the LP approach to approximate Dynamic Programming [98] which requires the solution of a linear program with a tractable number of variables but a potentially large number of constraints. Randomized constraint sampling is one means of dealing with such a program and results from [99] suggest that in fact, such a scheme is capable of producing good solutions to the linear program that arises in the context of approximate Dynamic Programming. We present here a summary of those results, and a case study wherein the technique is used to produce a controller for the game of Tetris. The case study highlights several practical issues concerning the applicability of the constraint sampling approach. We also demonstrate a controller that matches - and in some ways outperforms - controllers produced by other state of the art techniques for large-scale stochastic control.

Fairness, Efficiency, and Flexibility in Organ Allocation for Kidney Transplantation

We propose a scalable, data-driven method for designing national policies for the allocation of deceased donor kidneys to patients on a waiting list in a fair and efficient way. We focus on policies that have the same form as the one currently used in the United States. In particular, we consider policies that are based on a point system that ranks patients according to some priority criteria, e.g., waiting time, medical urgency, etc., or a combination thereof. Rather than making specific assumptions about fairness principles or priority criteria, our method offers the designer the flexibility to select his desired criteria and fairness constraints from a broad class of allowable constraints. The method then designs a point system that is based on the selected priority criteria and approximately maximizes medical efficiency---i.e., life-year gains from transplant---while simultaneously enforcing selected fairness constraints. Among the several case studies we present employing our method, one case study designs a point system that has the same form, uses the same criteria, and satisfies the same fairness constraints as the point system that was recently proposed by U.S. policy makers. In addition, the point system we design delivers an 8% increase in extra life-year gains. We evaluate the performance of all policies under consideration using the same statistical and simulation tools and data as the U.S. policy makers use. Other case studies perform a sensitivity analysis for instance, demonstrating that the increase in extra life-year gains by relaxing certain fairness constraints can be as high as 30% and also pursue the design of policies targeted specifically at remedying criticisms leveled at the recent point system proposed by U.S. policy makers.

Optimizing Intensive Care Unit Discharge Decisions with Patient Readmissions

This work examines the impact of discharge decisions under uncertainty in a capacity-constrained high-risk setting: the intensive care unit ICU. New arrivals to an ICU are typically very high-priority patients and, should the ICU be full upon their arrival, discharging a patient currently residing in the ICU may be required to accommodate a newly admitted patient. Patients so discharged risk physiologic deterioration, which might ultimately require readmission; models of these risks are currently unavailable to providers. These readmissions in turn impose an additional load on the capacity-limited ICU resources. We study the impact of several different ICU discharge strategies on patient mortality and total readmission load. We focus on discharge rules that prioritize patients based on some measure of criticality assuming the availability of a model of readmission risk. We use empirical data from over 5,000 actual ICU patient flows to calibrate our model. The empirical study suggests that a predictive model of the readmission risks associated with discharge decisions, in tandem with simple index policies of the type proposed, can provide very meaningful throughput gains in actual ICUs while at the same time maintaining, or even improving upon, mortality rates. We explicitly provide a discharge policy that accomplishes this. In addition to our empirical work, we conduct a rigorous performance analysis for the family of discharge policies we consider. We show that our policy is optimal in certain regimes, and is otherwise guaranteed to incur readmission related costs no larger than a factor of

Pathwise Optimization for Optimal Stopping Problems

\hat{\rho}+1

Model Predictive Control for Dynamic Resource Allocation

of an optimal discharge strategy, where

Approximate Dynamic Programming via a Smoothed Linear Program

\hat{\rho}

Simple Policies for Dynamic Pricing with Imperfect Forecasts

is a certain natural measure of system utilization.