Nikolaos Trichakis

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.

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.

Dynamic Network Utility Maximization with Delivery Contracts

We consider a multi-period variation on the network utility maximization problem that includes delivery constraints. We allow the flow utilities, link capacities and routing matrices to vary over time, and we introduce the concept of delivery contracts, which couple the flow rates across time. We describe a distributed algorithm, based on dual decomposition, that solves this problem when all data is known ahead of time. We briefly describe a heuristic, based on model predictive control, for approximately solving a variation on the problem, in which the data are not known ahead of time. The formulation and algorithms are illustrated with numerical examples.

Is Operating Flexibility Harmful under Debt

We study the inefficiencies stemming from a firm’s operating flexibility under debt. We find that flexibility in replenishing or liquidating inventory, by providing risk-shifting incentives, could lead to borrowing costs that erase more than one-third of the firm’s value. In this context, we examine the effectiveness of practical and widely used covenants in restoring firm value by limiting such risk-shifting behavior. We find that simple financial covenants can fully restore value for a firm that possesses a midseason inventory liquidation option. In the presence of added flexibility in replenishing or partially liquidating inventory, financial covenants fail, but simple borrowing base covenants successfully restore firm value. Explicitly characterizing optimal covenant tightness for all these cases, we find that better market conditions, such as lower inventory depreciation rate, higher gross margins, or increased product demand, are typically associated with tighter covenants. Our results suggest that ...

Accept or Decline? An Analytics-based Decision Tool for Kidney Offer Evaluation

Background When a deceased-donor kidney is offered to a waitlisted candidate, the decision to accept or decline the organ relies primarily upon a practitioner’s experience and intuition. Such decisions must achieve a delicate balance between estimating the immediate benefit of transplantation and the potential for future higher-quality offers. However, the current experience-based paradigm lacks scientific rigor and is subject to the inaccuracies that plague anecdotal decision-making. Methods A data-driven analytics-based model was developed to predict whether a patient will receive an offer for a deceased-donor kidney at Kidney Donor Profile Index thresholds of 0.2, 0.4, and 0.6, and at timeframes of 3, 6, and 12 months. The model accounted for Organ Procurement Organization, blood group, wait time, DR antigens, and prior offer history to provide accurate and personalized predictions. Performance was evaluated on data sets spanning various lengths of time to understand the adaptability of the method. Results Using United Network for Organ Sharing match-run data from March 2007 to June 2013, out-of-sample area under the receiver operating characteristic curve was approximately 0.87 for all Kidney Donor Profile Index thresholds and timeframes considered for the 10 most populous Organ Procurement Organizations. As more data becomes available, area under the receiver operating characteristic curve values increase and subsequently level off. Conclusions The development of a data-driven analytics-based model may assist transplant practitioners and candidates during the complex decision of whether to accept or forgo a current kidney offer in anticipation of a future high-quality offer. The latter holds promise to facilitate timely transplantation and optimize the efficiency of allocation.

Fairness and Efficiency in Multiportfolio Optimization

We deal with the problem faced by a portfolio manager in charge of multiple accounts. We argue that because of market impact costs, this setting differs in several subtle ways from the classical single account case, with the key distinction being that the performance of each individual account typically depends on the trading strategies of other accounts, as well. We propose a novel, tractable approach for jointly optimizing the trading activities of all accounts and also splitting the associated market impact costs between the accounts. Our approach allows the manager to balance the conflicting objectives of maximizing the aggregate gains from joint optimization and distributing them across the accounts in an equitable way. We perform numerical studies that suggest that our approach outperforms existing methods employed in the industry or discussed in the literature.

Robust Multiclass Queuing Theory for Wait Time Estimation in Resource Allocation Systems

In this paper, we study systems that allocate different types of scarce resources to heterogeneous allocatees based on predetermined priority rules—the U.S. deceased-donor kidney allocation system or the public housing program. We tackle the problem of estimating the wait time of an allocatee who possesses incomplete system information with regard, for example, to his relative priority, other allocatees’ preferences, and resource availability. We model such systems as multiclass, multiserver queuing systems that are potentially unstable or in transient regime. We propose a novel robust optimization solution methodology that builds on the assignment problem. For first-come, first-served systems, our approach yields a mixed-integer programming formulation. For the important case where there is a hierarchy in the resource types, we strengthen our formulation through a drastic variable reduction and also propose a highly scalable heuristic, involving only the solution of a convex optimization problem (usually...

Designing Response Supply Chain against Bioattacks

Bioattacks, i.e., the intentional release of pathogens or biotoxins against humans to cause serious illness and death, pose a significant threat to public health and safety due to the availability of pathogens worldwide, scale of impact, and short treatment time window. In this paper, we focus on the problem of prepositioning inventory of medical countermeasures (MCM) to defend against such bioattacks. We introduce a two-stage robust optimization model that considers the policymaker’s static inventory decision, attacker’s move, and policymaker’s adjustable shipment decision, so as to minimize inventory and life loss costs, subject to population survivability targets. We consider a heuristic solution approach that limits the adjustable decisions to be affine, which allows us to cast the problem as a tractable linear optimization problem. We prove that, under mild assumptions, the heuristic is in fact optimal. Experimental evidence suggests that the heuristic’s performance remains near-optimal for general settings as well. We illustrate how our model can serve as a decision support tool for policy making. In particular, we perform a thorough case study on how to preposition MCM inventory in the United States to guard against anthrax attacks. We calibrate our model using data from multiple sources, including publications of the National Academies of Sciences and the U.S. Census. We find that, for example, if U.S. policymakers want to ensure a 95% survivability target for anthrax attacks that simultaneously affect at most two cities (in the same or different states), the minimum annual inventory budget required is approximately

The Price of Fairness

330 million. We also discuss how our model can be applied in other contexts as well, e.g., to analyze safety-stock placement in supply-chain networks to hedge against disruptions.