Faculty & Research

John R. Birge

Jerry W. and Carol L. Levin Distinguished Service Professor of Operations Management

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5807 South Woodlawn Avenue
Chicago, IL 60637

John R. Birge studies mathematical modeling of systems under uncertainty, especially for maximizing operational and financial goals using the methodologies of stochastic programming and large-scale optimization. He was first drawn to this area by a need to use mathematics in a useful and practical way. "My research has shown how special problem structure can allow for efficient solution of complex problems of decision making under uncertainty," Birge explains. This research has been supported by the National Science Foundation, the Ford Motor Company, General Motors Corporation, the National Institute of Justice, the Office of Naval Research, the Electric Power Research Institute, and Volkswagen of America. He has published widely and is the recipient of the Best Paper Award from the Japan Society for Industrial and Applied Mathematics, the Institute for Operations Research and the Management Sciences Fellows Award, the Institute of Industrial Engineers Medallion Award and was elected to the National Academy of Engineering.

A former dean of the Robert R. McCormick School of Engineering and Applied Sciences at Northwestern University, he has worked as a consultant for a variety of firms including the University of Michigan Hospitals, Deutsche Bank, Allstate Insurance Company, and Morgan Stanley, and he uses cases from these experiences in his teaching.

Birge earned a bachelor's degree in mathematics from Princeton University in 1977 and a master's degree and a PhD in operations research from Stanford University in 1979 and 1980, respectively. He joined the Chicago Booth faculty in 2004.

He is a member of the Institute for Operations Research and the Management Sciences, the Mathematical Programming Society, the Mathematical Association of America, and Sigma Xi. He also speaks French, Russian, German, and English.

Outside of academia, Birge enjoys running, reading, and travel.


2016 - 2017 Course Schedule

Number Name Quarter
36600 Workshop in Operations/Management Science 2017 (Winter)
36909 Stochastic Optimization I 2016 (Fall)
36910 Stochastic Optimization II 2017 (Winter)
40108 Revenue Management 2017 (Spring)

Other Interests

Running, reading, travel.


Research Activities

Methods and models for optimal decision making under uncertainty; emphasis on relationships between operations and finance.

With C.H. Rosa, "Incorporating investment uncertainty into greenhouse policy models," The Energy Journal (1996).

"Option methods for incorporating risk into linear planning models," Manufacturing and Services Operations Management (2000).

With C. Supatgiat and R.Q. Zhang, "Equilibrium value in a competitive power exchange market," Computational Economics (2001).

With J.W. Yen, "A Stochastic Programming Approach to the Airline Crew Scheduling Problem," Transportation Science (2006).

With S. Yang, "A Model for Tax Advantages of Portfolios with Many Assets," Journal of Banking & Finance(2007).

For a listing of research publications, please visit the university library listing page.

REVISION: Inverse Optimization for the Recovery of Market Structure from Market Outcomes: An Application to the MISO Electricity Market
Date Posted: May  18, 2017
We propose an inverse optimization based methodology to determine market structure from commodity and transportation prices. The methods are appropriate for locational marginal price based electricity markets where prices are shadow prices in the centralized optimization used to clear the market. We apply the inverse optimization methodology to outcome data from the Midcontinent ISO electricity market (MISO) and, under noise-free assumptions, recover parameters of transmission and related constraints that are not revealed to market participants but explain the price variation. We demonstrate and evaluate analytical uses of the recovered structure including reconstruction of the pricing mechanism and investigations of locational market power through the transmission constrained residual demand derivative. Prices generated from the reconstructed mechanism are highly correlated to actual MISO prices under a wide variety of market conditions. In a case study, the residual demand ...

REVISION: Risk Sensitive Asset Management and Cascading Defaults
Date Posted: Feb  22, 2017
We consider an optimal risk-sensitive portfolio allocation problem accounting for the possibility of cascading defaults. Default events have an impact on the distress state of the surviving stocks in the portfolio. We study the recursive system of non-Lipschitz quasi-linear parabolic HJB-PDEs associated with the value function of the control problem in the different default states of the economy. We show the existence of a classical solution to this system via super-sub solution techniques and give an explicit characterization of the optimal feedback strategy in terms of the value function. We prove a verification theorem establishing the uniqueness of the solution. A numerical analysis indicates that the investor accounts for contagion effects when making investment decisions, reduces his risk exposure as he becomes more sensitive to risk, and that his strategy depends non-monotonically on the aggregate risk level.

REVISION: Trade Credit, Risk Sharing, and Inventory Financing Portfolios
Date Posted: Feb  08, 2017
As an integrated part of a supply contract, trade credit has intrinsic connections with supply chain coordination and inventory management. Using a model that explicitly captures the interaction of firms' operations decisions, financial constraints, and multiple financing channels (bank loans and trade credit), this paper attempts to better understand the risk-sharing role of trade credit -- that is, how trade credit enhances supply chain efficiency by allowing the retailer to partially share the demand risk with the supplier. Within this role, in equilibrium, trade credit is an indispensable external source for inventory financing, even when the supplier is at a disadvantageous position in managing default relative to a bank. Specifically, the equilibrium trade credit contract is net terms when the retailer's financial status is relatively strong. Accordingly, trade credit is the only external source that the retailer uses to finance inventory. By contrast, if the retailer's cash ...

REVISION: When Customers Anticipate Liquidation Sales: Managing Operations under Financial Distress
Date Posted: Jan  16, 2017
The presence of strategic customers may force an already financially distressed firm into a death spiral: Sensing the firm's financial difficulty, customers may wait strategically for deep discounts in liquidation sales. In turn, such waiting lowers the firm's profitability and increases the firm's bankruptcy risk. Using a two-period model to capture these dynamics, this paper identifies customers' strategic waiting behavior as a source of a firm's cost of financial distress. We also find that customers' anticipation of bankruptcy can be self-fullling: When customers anticipate a high bankruptcy probability, they prefer to delay their purchases, making the firm more likely to go bankrupt than when customers anticipate a low probability of bankruptcy. Such behavior has important operational and financial implications. First, the firm acts more conservatively when either facing more severe financial distress or a large share of strategic customers. As its financial situation ...

New: Online Appendix to 'When Customers Anticipate Liquidation Sales: Managing Operations Under Financial Distress'
Date Posted: Jan  12, 2017
This is the online appendix for When Customers Anticipate Liquidation Sales: Managing Operations under Financial Distress. The full paper is available here: http://ssrn.com/abstract=2652994.

New: Optimal Dynamic Product Development and Launch For a Network of Customers
Date Posted: Nov  16, 2016
We consider a firm that dynamically chooses its effort to develop a product for a network of customers represented by a connected graph. The product’s technological development is governed by a stochastic process dependent on the firm’s efforts. In addition to dynamically choosing its development effort, the firm chooses when to launch or abandon the product. If the firm launches the product, the firm also chooses a selling price, a promotional price and a target customer to offer promotion. Once the target customer adopts the product, the product diffuses over the customer network based on the topology of the graph and the selling price. The product provides local network benefits to its adopters. The expected local network benefit of adoption is proportional to the number of neighbor customers that have already adopted the product. In a continuous-time setting, we explicitly solve the firm’s jointly-optimal development, launch and post-launch strategies for any connected network. ...

REVISION: How Inventory Is (Should Be) Financed: Trade Credit in Supply Chains with Demand Uncertainty and Costs of Financial Distress
Date Posted: Sep  07, 2016
A new substantially revised version of this paper under the title of "Trade Credit, Risk Sharing, and Inventory Financing Portfolios" is available for download at: http://ssrn.com/abstract=2746645. As an integrated part of a supply contract, trade credit has intrinsic connections with supply chain contracting and inventory management. Using a model that explicitly captures the interaction of firms’ operations decisions and financial risks, this paper attempts to develop a deeper understanding of trade credit from an operational perspective. Revolving around the question of what role trade credit plays in channel coordination and inventory financing, we demonstrate that with demand uncertainty, trade credit enhances supply chain efficiency by serving as a risk-sharing mechanism. When offering trade credit, the supplier balances its impact on operational profit and costs of financial distress. Facing a trade credit contract, the retailer ...

REVISION: Dynamic Selling Mechanisms for Product Differentiation and Learning
Date Posted: Aug  08, 2016
We consider a firm that designs a menu of vertically differentiated products for a population of customers with heterogeneous quality sensitivities. The firm faces an uncertainty about production costs, and we formulate this uncertainty as a belief distribution on a set of cost models. Over a time horizon of T periods, the firm can dynamically adjust its menu and make noisy observations on the underlying cost model through customers’ purchasing decisions. We characterize how optimal product differentiation depends on the “informativeness” of quality choices, formally measured by a contrast-to-noise ratio defined on the firm’s feasible quality set. We prove that, if there exist informative quality choices, then the optimal product differentiation policy improves the product quality to accelerate information accumulation and exercises the most extreme experimentation on less quality-sensitive customers. We design a minimum quality standard (MQS) policy that mimics the aforementioned ...

New: Quality Management Using Data Analytics: An Application to Pharmaceutical Regulation
Date Posted: Jan  03, 2016
The U.S. government regulates consumer products through its various federal agencies. One such agency is the Food and Drug Administration (FDA) that governs the approval and safe public use of pharmaceutical products. If a drug is found unsafe, the FDA can issue a recall or a black box warning (BBW). This regulatory decision directly affects an operational decision: providers' production technology, affecting their treatment choices. Existing methods for monitoring drug safety are geared towards identifying unknown adverse drug reactions (ADRs) and suffer from several shortcomings such as reliance on limited data. There is a lack of data-driven approaches to evaluate a drug's association with a specific ADR. We propose a data-driven approach that fills this gap. We demonstrate the workings of our approach using a controversial BBW on a diabetes drug that warned prescribers of an increased risk of heart attack and cardiovascular mortality with the drug. Our findings, based on a large ...

REVISION: Response-Adaptive Designs for Clinical Trials: Simultaneous Learning from Multiple Patients
Date Posted: Jan  01, 2016
Clinical trials have traditionally followed a fixed design, in which randomization probabilities of patients to various treatments remains fixed throughout the trial and specified in the protocol. The primary goal of this static design is to learn about the efficacy of treatments. Response-adaptive designs, on the other hand, allow clinicians to use the learning about treatment effectiveness to dynamically adjust randomization probabilities of patients to various treatments as the trial progresses. An ideal adaptive design is one where patients are treated as effectively as possible without sacrificing the potential learning or compromising the integrity of the trial. We propose such a design, termed Jointly Adaptive, that uses forward-looking algorithms to fully exploit learning from multiple patients simultaneously. Compared to the best existing implementable adaptive design that employs a multiarmed bandit framework in a setting where multiple patients arrive sequentially, we show ...

REVISION: Supply Chain Network Structure and Firm Returns
Date Posted: Nov  06, 2015
The complexity and opacity of the network of interconnections among firms and their supply chains inhibits understanding of the impact of management decisions concerning the boundaries of the firm and the number and intensity of its relationships with suppliers and customers. Using recently available data on the relationships of public US firms, this paper investigates the effects of supply chain connections on firm performance as reflected in stock returns. The paper finds that supply chain structure is closely related to firm returns at two levels, a first-order effect from direct connections and a second-order impact from systemic exposures through the network. For the first order effect, using a cross-sectional data set of the supply chain network and monthly returns, we show that a firm’s return can be explained by its concurrent supplier returns, concurrent customer returns, own momentum, and supplier momentum, whereas customer momentum has little impact. A long-short equity ...

New: Strategic Commitment to a Production Schedule with Supply and Demand Uncertainty: Renewable Energy in Day-Ahead Electricity Markets
Date Posted: Oct  20, 2015
Motivated by the increase in variable renewable energy (such as wind and solar) generation, we study a day-ahead electricity market that consists of finitely many competing firms, each facing supply uncertainty. Each firm commits to a price-contingent production schedule in the day-ahead market, and chooses its actual production quantity after the day-ahead market is cleared and the firm’s available supply is realized. If a firm produces less than its cleared production commitment, the firm pays an undersupply penalty in proportion to its underproduction. We investigate two cases regarding overproduction: each firm either receives a credit or pays a penalty in proportion to its overproduction. Using differential equations theory, we explicitly characterize the firms’ committed production schedules and actual production strategies in equilibrium with and without subsidies. The purpose of an undersupply penalty is to improve system reliability by motivating each firm to commit to a ...

New: Local Discontinuous Galerkin Method for Portfolio Optimization with Transaction Costs
Date Posted: Oct  15, 2015
We study the continuous time portfolio selection problem over a finite horizon for an investor who maximizes the expected utility of terminal wealth and faces transaction costs. The portfolio consists of a risk-free asset, and a risky asset whose price is modeled as a geometric Brownian motion. The problem can be formulated as a stochastic singular control or an impulse control problem depending on whether the transaction costs are of proportional or fixed type. Due to the intractability of the problem, modelers resort to numerical methods to obtain approximations of solutions to the problem. In this paper we propose a stable and high-order computational scheme to solve this problem, which is capable of handling any form of transaction costs. Specifically, we implement the Local Discontinuous Galerkin (LDG) Finite Element Method (FEM) to solve the resulting convection-diffusion Partial Differential Equation (PDE), and obtain error estimates for the LDG method. Moreover, we prove the ...

REVISION: The Supply Chain Effects of Bankruptcy
Date Posted: Jan  09, 2015
This paper examines how a firm's financial distress and the legal environment regarding the ease of bankruptcy reorganization can alter product market competition and supplier-buyer relationships. We identify three effects, predation, bail-out, and abetment, that can change firms' behavior from their actions in the absence of financial distress. The predation effect increases competition before potential bankruptcy as the non-distressed competitor behaves as if it has some first-mover advantage, which could benefit a supplier with price control. The bailout effect reflects the supplier's incentive to grant the distressed firm concessions to preserve competition, improving supply chain efficiency and providing support for the exclusivity rule in Chapter 11 of the United States Bankruptcy Code when the supplier and the distressed firm are financially linked. The abetment effect is that the supplier may deliberately abet the competitor's predation, leading to increased operational ...

REVISION: A Model for Tax Advantages of Portfolios with Many Assets
Date Posted: Jan  08, 2015
Taxable portfolios present challenges for optimization models with even a limited number of assets. Holding many assets, however, has a distinct tax advantage over holding few assets. In this paper, we develop a model that takes an extreme view of a portfolio as a continuum of assets to gain the broadest possible advantage from holding many assets. We find the optimal strategy for trading in this portfolio in the absence of transaction costs and develop bounding approximations on the optimal value. We compare the results in a simulation study to a portfolio consisting only of a market index and show that the multi-asset portfolio's tax advantage can lead either to significant consumption or bequest increases.

New: Robustness of Renewable Energy Support Schemes Facing Uncertainty and Regulatory Ambiguity
Date Posted: Sep  13, 2014
Renewable portfolio standards, feed-in-tariffs, and market premia are widely used policy instruments to promote investments in renewable energy sources. Regulators continuously evaluate these instruments along the main electricity policy objectives of affordability, reliability, and sustainability. We develop a quantitative approach to assess these policies and their robustness to exogenous changes along these dimensions using a long-term dynamic capacity investment model. We compare their robustness in the light of uncertain renewable feed-in and ambiguous future regulation. We implement the robustness analysis employing different risk measures and find that renewable portfolio standards deliver most robust results, while feed-in-tariffs achieve target renewable buildup rates at least cost.

New: Index Tracking and Enhanced Indexation Using a Parametric Approach
Date Posted: Jun  19, 2014
Based on the work of Brandt et al. (2009), we formulate an index tracking and enhanced indexation model using a parametric approach. The portfolio weights are modeled as functions of assets characteristics and similarity measures of the assets with the index to track. This approach permits handling nonlinear and nonconvex objectives functions that are difficult to incorporate in existing index tracking and enhanced indexation models. Additionally, this approach gives the investor more information about the portfolio holdings since the optimization is performed over portfolio strategies. Finally, an empirical implementation and an analysis of selected characteristics are presented for the S&P500 index.

REVISION: Portfolio Optimization Under Generalized Hyperbolic Skewed t Distribution and Exponential Utility
Date Posted: Jun  14, 2014
In this paper, we show that if asset returns follow a generalized hyperbolic skewed t distribution, the investor has exponential utility function and a riskless asset is available, the optimal portfolio weights can be found either in closed-form or using a successive approximation scheme. We also derive lower bounds for the certainty equivalent return generated by the optimal portfolios. Finally, we present a study of the performance of mean-variance analysis and Taylor's series expected utility expansion (up to the fourth moment) to compute optimal portfolios in this framework.

New: Assessing the Long-Term Effects of Bank Policies
Date Posted: May  28, 2014
Current risk management frameworks are not suitable for testing the long-term implications of balance sheet policies. The current established methodologies, such as interest rate gap analysis or Credit Value-at-Risk are short-term and do not give a clear picture of the long-term risk of a bank. Backtesting is also difficult, given that the data is limited, thus not producing risk measures for long-term policies. Therefore, simulation is the best option for assessing the long-term implications of regulatory and management choices. In a previous note, we developed a scenario generation tool for simulating the long-term behavior of balance sheets of banks. In this note, we use this framework to quantify the long-term impact on risk and return of the leverage ratio, the core deposit ratio, operating costs and interest rates. As Basel III is being implemented, our tests confirm the benefits of holding a cushion of capital above the leverage ratio limit of 3%, a policy similar to the one ...

New: The Structural Impact of Renewable Portfolio Standards and Feed-in-Tariffs on Electricity Markets
Date Posted: Apr  01, 2014
Renewable energy sources (RES) capacity has grown globally at a rapid rate benefiting from multiple support schemes such as renewable portfolio standards (RPS), feed-in-tariffs (FIT), and market premia (MP). While research concentrated on comparing the effectiveness of these policy instruments in driving RES investment, the focus is increasingly shifting towards assessments of the structural impact of these schemes on electricity markets. RES support schemes are continuously being assessed on how they help achieve the three main objectives of electricity policy, i.e., the affordability, reliability, and sustainability of electricity supply. In this work, we quantitatively compare RPS, FIT and MP schemes in these three dimensions by assessing their future impact on electricity prices, on generation portfolios and security of supply as well as on carbon emissions. We simulate the impact of all three support schemes using a long-term capacity expansion model with an hourly granularity ...

REVISION: Long-Term Bank Balance Sheet Management: Estimation and Simulation of Risk-Factors
Date Posted: Aug  01, 2012
We propose a dynamic framework which encompasses the main risks in balance sheets of banks in an integrated fashion. Our contributions are fourfold: 1) solving a simple one-period model that describes the optimal bank policy under credit risk; 2) estimating the long-term stochastic processes underlying the risk factors in the balance sheet, taking into account the credit and interest rate cycles; 3) simulating several scenarios for interest rates and charge-offs; and 4) describing the ...

REVISION: Trade Credit in Supply Chains: Multiple Creditors and Priority Rules
Date Posted: Jun  10, 2012
Priority rules determine the order of repayment when the debtor cannot repay all of his debt. In this paper, we study how different priority rules influence trade credit usage and supply chain efficiency when multiple creditors are present. We find that with only demand risk, when the wholesale price is exogenous, trade credit with high priority can lead to high chain efficiency, yet trade credit with low priority allows more retailers to obtain trade credit and suppliers to gain higher profits.

New: Firm Profitability, Inventory Volatility, and Capital Structure
Date Posted: Aug  23, 2011
Traditional theories of capital structure imply a consistent relationship between firm profitability and firm leverage. Empirical data, however, suggest that the relationship is not monotonic. In the cross-section of firms, non-profitable firms become significantly more leveraged as losses decrease; profitable firms become significantly less leveraged as profits increase until a point where the most profitable firms have again significantly greater leverage as profits increase. In this paper, ...

REVISION: Index Tracking and Enhanced Indexation Using a Parametric Approach
Date Posted: Nov  03, 2009
Based on the work of Brandt, Santa-Clara and Valkanov (2009), we formulate an index tracking and enhanced indexation model using a parametric approach. The portfolio weights are modeled as functions of assets characteristics and similarity measures of the assets with the index to track. This approach permits to handle non-linear and non-convex objectives functions that are common in index tracking and enhanced indexation. An empirical implementation and analysis of the characteristics are ...

REVISION: Optimal Investment and Production Across Markets with Stochastic Exchange Rates
Date Posted: Jun  18, 2009
All multinational firms face foreign exchange fluctuations, which can create unstable cash flows and even bankruptcy. Managers of these firms face critical questions over how to reduce the risk due to income and expenses in multiple currencies. Traditional financial risk controls include futures and options, but firms also can use operational controls, such as foreign production capacity. In this paper, we study these alternatives for a simplified single-product firm operating in a home ...

New: Discrete-Time Optimization of Consumption and Investment Decisions Given Intolerance for a Decline i
Date Posted: Feb  19, 2008
We extend Samuelson's (1969) discrete-time dynamic consumption and investment optimization problem to the case where the investor is intolerant of any decline in her standard of living. This constraint represents a strong form of habit formation such that the consumption rate is non-decreasing over time. To achieve this objective, the investor first guarantees a consumption perpetuity at the current consumption rate and then allocates the remaining wealth under a state-dependent, adjusted ...

Equity Valuation, Production, and Financial Planning: A Stochastic Programming Approach
Date Posted: Jan  23, 2005
Most of the operations management literature assumes that the firm can always finance production decisions at an optimal level or borrow at a constant interest rate; however, operational decisions are constrained by limited capital and often critically depend on external financing. This paper proposes an integrated corporate planning model, which extends the forecasting-based discount dividend pricing method into an optimization-based valuation framework to make production and financial ...

Operational Decisions, Capital Structure, and Managerial Compensation: A News Vendor Perspective
Date Posted: Jan  23, 2005
While firm growth critically depends on financing ability and access to external capital, the operations management literature seldom considers the effects of financial constraints on the firms' operational decisions. Another critical assumption in traditional operations models is that corporate managers always act in the firm owners' best interests. Managers are, however, agents of the owners of the company, whose interests are often not aligned with those of equity-holders or debt-holders; ...

Joint Production and Financing Decisions: Modeling and Analysis
Date Posted: Jan  23, 2005
This paper develops models to make production and financing decisions simultaneously in the presence of demand uncertainty and market imperfections. While the Modigliani and Miller propositions demonstrate that a firm's investment and financing decisions can be made independently in a perfect capital market, our models illustrate how a firm's production decisions are affected by the existence of financial constraints. We analyze the interactions between a firm's production and financing ...

Comparisons of Alternative Quasi-Monte Carlo Sequences for American Option Pricing
Date Posted: Dec  29, 2004
Quasi-Monte Carlo sequences have been shown to provide accurate option price approximations for a variety of options. In this paper, we apply quasi-Monte Carlo sequences in a duality approach to value American options. We compare the results using different low discrepancy sequences and estimate error bounds and computational effort. The results demonstrate the value of sequences using expansions of irrationals.

Error Bounds for Quasi-Monte Carlo Methods in Option Pricing
Date Posted: Dec  29, 2004
The classic error bounds for quasi-Monte Carlo approximation follow the Koksma-Hlawka inequality based on the assumption that the integrand has finite variation. Unfortunately, not all functions have this property. In particular, integrands for common applications in finance, such as option pricing, do not typically have bounded variation. In contrast to this lack of theoretical precision, quasi-Monte Carlo methods perform quite well empirically. This paper provides some theoretical ...