J. Birge - Profile on Academia.edu (original) (raw)
Papers by J. Birge
Introduction to Stochastic Dynamic Programming
Journal of the American Statistical Association, 1986
The widely-used estimator of Berry, Levinsohn and Pakes (1995) produces estimates of consumer pre... more The widely-used estimator of Berry, Levinsohn and Pakes (1995) produces estimates of consumer preferences from a discrete-choice demand model with random coefficients, market-level demand shocks and endogenous prices. We derive numerical theory results characterizing the properties of the nested fixed point algorithm used to evaluate the objective function of BLP's estimator. We discuss problems with typical implementations, including cases that can lead to incorrect parameter estimates. As a solution, we recast estimation as a mathematical program with equilibrium constraints, which can be faster and which avoids the numerical issues associated with nested inner loops. The advantages are even more pronounced for forward-looking demand models where Bellman's equation must also be solved repeatedly. Several Monte Carlo and real-data experiments support our numerical concerns about the nested fixed point approach and the advantages of constrained optimization.
Journal of Global Optimization, 1996
Practical scheduling problems typically require decisions without full information about the outc... more Practical scheduling problems typically require decisions without full information about the outcomes of those decisions. Yields, resource availability, performance, demand, costs, and revenues may all
Operations Research Letters, 1988
In most scheduling problems discussed in the literature it is assumed that the machine (i.e. key ... more In most scheduling problems discussed in the literature it is assumed that the machine (i.e. key resource) is continuously available. Plainly, this i~ often unrealistic. Here we suggest assessing the effects of machine breakdowns by evaluating the strategy which is optimal when the machine is always available as a strategy for the breakdowns case. The results extend earlier ones of the authors and co-workers. alternating renewal process • Gittim • renewal function * stochastic scheduling
Transportation Science, 2006
Traditional methods model the billion-dollar airline crew scheduling problem as deterministic and... more Traditional methods model the billion-dollar airline crew scheduling problem as deterministic and do not explicitly include information on potential disruptions. Instead of modelling the crew scheduling problem as deterministic, we consider a stochastic crew scheduling model and devise a solution methodology for integrating disruptions in the evaluation of crew schedules. The goal is to use that information to find robust solutions that better withstand disruptions. Such an approach is important because we can proactively consider the effects of certain scheduling decisions. By identifying more robust schedules, cascading delay effects will be minimized. In this paper we describe our stochastic integer programming model for the airline crew scheduling problem and develop a branching algorithm to identify expensive flight connections and find alternative solutions. The branching algorithm uses the structure of the problem to branch simultaneously on multiple variables without invalidating the optimality of the algorithm. We present computational results demonstrating the effectiveness of our branching algorithm. where crew schedulers receive flight schedules several months in advance and assign crews their flights. (See
European Journal of Operational Research, 2005
This paper analyzes a finite buffer polling system with routing. Finite buffers are used to model... more This paper analyzes a finite buffer polling system with routing. Finite buffers are used to model the limited capacity of the system, and routing is used to represent the need for additional service. The most significant result of the analysis is the derivation of the generating function for queue length when buffer sizes are limited and a representation of the system workload. The queue lengths at polling instants are determined by solving a system of recursive equations, and an embedded Markov chain analysis and numerical inversion are used to derive the queue length distributions. This system may be used to represent production models with setups and lost sales or expediting.
SSRN Electronic Journal
Two salient features of most online platforms are that they do not dictate the transaction prices... more Two salient features of most online platforms are that they do not dictate the transaction prices, and use commissions/subscriptions for extracting revenues. We consider a platform that charges commission rates and subscription fees to sellers and buyers for facilitating transactions, but does not directly control the transaction prices, which are determined by the traders. Buyers and sellers are divided into types, and we represent the compatibility between different types using a bipartite network. Traders are heterogeneous in terms of their valuations, and different types have possibly different value distributions. The platform chooses commissions-subscriptions to maximize its revenues. We provide a convex optimization formulation to calculate the revenue-maximizing commissions/ subscriptions, and establish that, typically, different types should be charged different commissions/ subscriptions depending on their network positions. We establish lower and upper bounds on the platform's revenues in terms of the supply-demand imbalance across the network. Motivated by simpler schemes used in practice, we show that the revenue loss can be unbounded when all traders on the same side are charged the same commissions/subscriptions, and bound the revenue loss in terms of the supply-demand imbalance across the network. Charging only buyers or only sellers leads to a (bounded) revenue loss, even when different types on the same side can be charged differently. Under mild assumptions, we establish that a revenue-maximizing platform achieves at least 2/3 of the maximum achievable social welfare. Our results highlight the suboptimality of commonly used payment schemes, and showcase the importance of accounting for the compatibility between different user types.
Split Sampling: Expectations, Normalisation and Rare Events
In this paper we develop a methodology that we call split sampling methods to estimate high dimen... more In this paper we develop a methodology that we call split sampling methods to estimate high dimensional expectations and rare event probabilities. Split sampling uses an auxiliary variable MCMC simulation and expresses the expectation of interest as an integrated set of rare event probabilities. We derive our estimator from a Rao-Blackwellised estimate of a marginal auxiliary variable distribution. We illustrate our method with two applications. First, we compute a shortest network path rare event probability and compare our method to estimation to a cross entropy approach. Then, we compute a normalisation constant of a high dimensional mixture of Gaussians and compare our estimate to one based on nested sampling. We discuss the relationship between our method and other alternatives such as the product of conditional probability estimator and importance sampling. The methods developed here are available in the R package: SplitSampling.
While firm growth critically depends on financing ability and access to external capital, the ope... more 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; hence, managers may make major decisions that are suboptimal from the firm owners' point of view. This paper builds on a news vendor model to make optimal production decisions in the presence of financial constraints and managerial incentives. We explore the relationship * This work was supported in part by the National Science Foundation under Grant DMI-0100462. The second author is also grateful for the support of the University of Chicago Graduate School of Business. between operating conditions and financial leverage and observe that financial leverage can increase as margins reach either low or high extremes. We also provide some empirical support for this observation. We further extend our model to consider the effects of agency costs on the firm's production decision and debt choice by including performance-based bonuses in the manager's compensation. Our analyses show how managerial incentives may drive a manager to deviate from firm-optimal decisions and that low-margin producers face significant risk from this agency cost while high-margin producers face relatively low risk in using such compensation.
Various approximation schemes for stochastic optimization problems, involving either approximates... more Various approximation schemes for stochastic optimization problems, involving either approximates of the probability measures and/or approximates of the objective functional, are investigated. We discuss their potential implementation as part of general procedures for solving stochastic programs with recourse.
Journal of the Royal …, 1999
The achievable region approach seeks solutions to stochastic optimization problems by characteriz... more The achievable region approach seeks solutions to stochastic optimization problems by characterizing the space of all possible performances (the achievable region) of the system of interest and optimizing the overall system-wide performance objective over this space. ...
Exponential convergence of two-stage stochastic programming
IFAC Proceedings Volumes
Operations Research Letters
Operations Research, 2017
We argue that deterministic market clearing formulations introduce strong and arbitrary distortio... more We argue that deterministic market clearing formulations introduce strong and arbitrary distortions between day-ahead and expected real-time prices that bias economic incentives and block diversification. We extend and analyze the stochastic clearing formulation proposed by Pritchard et al. (2010) in which the social surplus function induces 1 penalties between day-ahead and real-time quantities. We prove that the formulation yields price distortions that are bounded by the bid prices, and we show that adding a similar penalty term to transmission flows ensures boundedness throughout the network. We prove that when the price distortions are zero, day-ahead quantities and flows converge to the medians of real-time counterparts. We demonstrate that convergence to expected value quantities can be induced by using a squared 2 penalty. The undesired effects of price distortions suggest that arguments based on social surplus alone are insufficient to fully appreciate the benefits of stochastic market settlements. We thus propose additional metrics to evaluate these benefits.
Local Discontinuous Galerkin Method for Portfolio Optimization with Transaction Costs
SSRN Electronic Journal, 2000
Inverse Optimization for the Recovery of Market Structure from Market Outcomes: An Application to the MISO Electricity Market
SSRN Electronic Journal, 2000
Adaptive Designs for Clinical Trials: Learning while Treating
On Some Dominance Results In Acheduling
Special Issue: Operational Research in Risk Management
Introduction to Stochastic Dynamic Programming
Journal of the American Statistical Association, 1986
The widely-used estimator of Berry, Levinsohn and Pakes (1995) produces estimates of consumer pre... more The widely-used estimator of Berry, Levinsohn and Pakes (1995) produces estimates of consumer preferences from a discrete-choice demand model with random coefficients, market-level demand shocks and endogenous prices. We derive numerical theory results characterizing the properties of the nested fixed point algorithm used to evaluate the objective function of BLP's estimator. We discuss problems with typical implementations, including cases that can lead to incorrect parameter estimates. As a solution, we recast estimation as a mathematical program with equilibrium constraints, which can be faster and which avoids the numerical issues associated with nested inner loops. The advantages are even more pronounced for forward-looking demand models where Bellman's equation must also be solved repeatedly. Several Monte Carlo and real-data experiments support our numerical concerns about the nested fixed point approach and the advantages of constrained optimization.
Journal of Global Optimization, 1996
Practical scheduling problems typically require decisions without full information about the outc... more Practical scheduling problems typically require decisions without full information about the outcomes of those decisions. Yields, resource availability, performance, demand, costs, and revenues may all
Operations Research Letters, 1988
In most scheduling problems discussed in the literature it is assumed that the machine (i.e. key ... more In most scheduling problems discussed in the literature it is assumed that the machine (i.e. key resource) is continuously available. Plainly, this i~ often unrealistic. Here we suggest assessing the effects of machine breakdowns by evaluating the strategy which is optimal when the machine is always available as a strategy for the breakdowns case. The results extend earlier ones of the authors and co-workers. alternating renewal process • Gittim • renewal function * stochastic scheduling
Transportation Science, 2006
Traditional methods model the billion-dollar airline crew scheduling problem as deterministic and... more Traditional methods model the billion-dollar airline crew scheduling problem as deterministic and do not explicitly include information on potential disruptions. Instead of modelling the crew scheduling problem as deterministic, we consider a stochastic crew scheduling model and devise a solution methodology for integrating disruptions in the evaluation of crew schedules. The goal is to use that information to find robust solutions that better withstand disruptions. Such an approach is important because we can proactively consider the effects of certain scheduling decisions. By identifying more robust schedules, cascading delay effects will be minimized. In this paper we describe our stochastic integer programming model for the airline crew scheduling problem and develop a branching algorithm to identify expensive flight connections and find alternative solutions. The branching algorithm uses the structure of the problem to branch simultaneously on multiple variables without invalidating the optimality of the algorithm. We present computational results demonstrating the effectiveness of our branching algorithm. where crew schedulers receive flight schedules several months in advance and assign crews their flights. (See
European Journal of Operational Research, 2005
This paper analyzes a finite buffer polling system with routing. Finite buffers are used to model... more This paper analyzes a finite buffer polling system with routing. Finite buffers are used to model the limited capacity of the system, and routing is used to represent the need for additional service. The most significant result of the analysis is the derivation of the generating function for queue length when buffer sizes are limited and a representation of the system workload. The queue lengths at polling instants are determined by solving a system of recursive equations, and an embedded Markov chain analysis and numerical inversion are used to derive the queue length distributions. This system may be used to represent production models with setups and lost sales or expediting.
SSRN Electronic Journal
Two salient features of most online platforms are that they do not dictate the transaction prices... more Two salient features of most online platforms are that they do not dictate the transaction prices, and use commissions/subscriptions for extracting revenues. We consider a platform that charges commission rates and subscription fees to sellers and buyers for facilitating transactions, but does not directly control the transaction prices, which are determined by the traders. Buyers and sellers are divided into types, and we represent the compatibility between different types using a bipartite network. Traders are heterogeneous in terms of their valuations, and different types have possibly different value distributions. The platform chooses commissions-subscriptions to maximize its revenues. We provide a convex optimization formulation to calculate the revenue-maximizing commissions/ subscriptions, and establish that, typically, different types should be charged different commissions/ subscriptions depending on their network positions. We establish lower and upper bounds on the platform's revenues in terms of the supply-demand imbalance across the network. Motivated by simpler schemes used in practice, we show that the revenue loss can be unbounded when all traders on the same side are charged the same commissions/subscriptions, and bound the revenue loss in terms of the supply-demand imbalance across the network. Charging only buyers or only sellers leads to a (bounded) revenue loss, even when different types on the same side can be charged differently. Under mild assumptions, we establish that a revenue-maximizing platform achieves at least 2/3 of the maximum achievable social welfare. Our results highlight the suboptimality of commonly used payment schemes, and showcase the importance of accounting for the compatibility between different user types.
Split Sampling: Expectations, Normalisation and Rare Events
In this paper we develop a methodology that we call split sampling methods to estimate high dimen... more In this paper we develop a methodology that we call split sampling methods to estimate high dimensional expectations and rare event probabilities. Split sampling uses an auxiliary variable MCMC simulation and expresses the expectation of interest as an integrated set of rare event probabilities. We derive our estimator from a Rao-Blackwellised estimate of a marginal auxiliary variable distribution. We illustrate our method with two applications. First, we compute a shortest network path rare event probability and compare our method to estimation to a cross entropy approach. Then, we compute a normalisation constant of a high dimensional mixture of Gaussians and compare our estimate to one based on nested sampling. We discuss the relationship between our method and other alternatives such as the product of conditional probability estimator and importance sampling. The methods developed here are available in the R package: SplitSampling.
While firm growth critically depends on financing ability and access to external capital, the ope... more 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; hence, managers may make major decisions that are suboptimal from the firm owners' point of view. This paper builds on a news vendor model to make optimal production decisions in the presence of financial constraints and managerial incentives. We explore the relationship * This work was supported in part by the National Science Foundation under Grant DMI-0100462. The second author is also grateful for the support of the University of Chicago Graduate School of Business. between operating conditions and financial leverage and observe that financial leverage can increase as margins reach either low or high extremes. We also provide some empirical support for this observation. We further extend our model to consider the effects of agency costs on the firm's production decision and debt choice by including performance-based bonuses in the manager's compensation. Our analyses show how managerial incentives may drive a manager to deviate from firm-optimal decisions and that low-margin producers face significant risk from this agency cost while high-margin producers face relatively low risk in using such compensation.
Various approximation schemes for stochastic optimization problems, involving either approximates... more Various approximation schemes for stochastic optimization problems, involving either approximates of the probability measures and/or approximates of the objective functional, are investigated. We discuss their potential implementation as part of general procedures for solving stochastic programs with recourse.
Journal of the Royal …, 1999
The achievable region approach seeks solutions to stochastic optimization problems by characteriz... more The achievable region approach seeks solutions to stochastic optimization problems by characterizing the space of all possible performances (the achievable region) of the system of interest and optimizing the overall system-wide performance objective over this space. ...
Exponential convergence of two-stage stochastic programming
IFAC Proceedings Volumes
Operations Research Letters
Operations Research, 2017
We argue that deterministic market clearing formulations introduce strong and arbitrary distortio... more We argue that deterministic market clearing formulations introduce strong and arbitrary distortions between day-ahead and expected real-time prices that bias economic incentives and block diversification. We extend and analyze the stochastic clearing formulation proposed by Pritchard et al. (2010) in which the social surplus function induces 1 penalties between day-ahead and real-time quantities. We prove that the formulation yields price distortions that are bounded by the bid prices, and we show that adding a similar penalty term to transmission flows ensures boundedness throughout the network. We prove that when the price distortions are zero, day-ahead quantities and flows converge to the medians of real-time counterparts. We demonstrate that convergence to expected value quantities can be induced by using a squared 2 penalty. The undesired effects of price distortions suggest that arguments based on social surplus alone are insufficient to fully appreciate the benefits of stochastic market settlements. We thus propose additional metrics to evaluate these benefits.
Local Discontinuous Galerkin Method for Portfolio Optimization with Transaction Costs
SSRN Electronic Journal, 2000
Inverse Optimization for the Recovery of Market Structure from Market Outcomes: An Application to the MISO Electricity Market
SSRN Electronic Journal, 2000
Adaptive Designs for Clinical Trials: Learning while Treating
On Some Dominance Results In Acheduling
Special Issue: Operational Research in Risk Management