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17
A robust optimization approach to supply chain management
 Operations Research
, 2003
"... Abstract. We propose a general methodology based on robust optimization to address the problem of optimally controlling a supply chain subject to stochastic demand in discrete time. The attractive features of the proposed approach are: (a) It incorporates a wide variety of phenomena, including deman ..."
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Cited by 38 (3 self)
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Abstract. We propose a general methodology based on robust optimization to address the problem of optimally controlling a supply chain subject to stochastic demand in discrete time. The attractive features of the proposed approach are: (a) It incorporates a wide variety of phenomena, including demands that are not identically distributed over time and capacity on the echelons and links; (b) it uses very little information on the demand distributions; (c) it leads to qualitatively similar optimal policies (basestock policies) as in dynamic programming; (d) it is numerically tractable for large scale supply chain problems even in networks, where dynamic programming methods face serious dimensionality problems; (e) in preliminary computational experiments, it often outperforms dynamic programming based solutions for a wide range of parameters. 1
Bias and variance approximation in value function estimates
 Management Science
, 2007
"... We consider a finite state, finite action, infinite horizon, discounted reward Markov Decision Process and study the bias and variance in the value function estimates that result from empirical estimates of the model parameters. We provide closedform approximations for the bias and variance, which ..."
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Cited by 28 (10 self)
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We consider a finite state, finite action, infinite horizon, discounted reward Markov Decision Process and study the bias and variance in the value function estimates that result from empirical estimates of the model parameters. We provide closedform approximations for the bias and variance, which can then be used to derive confidence intervals around the value function estimates. We illustrate and validate our findings using a large database describing the transaction and mailing histories for customers of a mailorder catalog firm.
Adaptive datadriven inventory control policies based on KaplanMeier estimator
, 2009
"... Using the wellknown productlimit form of the KaplanMeier estimator from statistics, we propose a new class of nonparametric adaptive datadriven policies for stochastic inventory control problems. We focus on the distributionfree newsvendor model with censored demands. The assumption is that the ..."
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Cited by 12 (1 self)
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Using the wellknown productlimit form of the KaplanMeier estimator from statistics, we propose a new class of nonparametric adaptive datadriven policies for stochastic inventory control problems. We focus on the distributionfree newsvendor model with censored demands. The assumption is that the demand distribution is not known and there is only sales data available. We study the theoretical performance of the new policies and show that for discrete demand distributions they converge almost surely to the set of optimal solutions. Computational experiments suggest that the new policies converge for general demand distributions, not necessarily discreet, and demonstrate that they are significantly more robust than previously known policies. As a byproduct of the theoretical analysis, we obtain new results on the asymptotic consistency of the KaplanMeier estimator for discrete random variables that extend existing work in statistics. To the best of our knowledge, this is the first application of the KaplanMeier estimator within an adaptive optimization algorithm, in particular, the first application to stochastic inventory control models. We believe that this work will lead to additional applications in other domains.
Integrated MultiEchelon Supply Chain Design with Inventories under Uncertainty
 MINLP Models, Computational Strategies. AIChE Journal
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Infinitehorizon models for inventory control under yield uncertainty and disruptions. Working paper
, 2006
"... We demonstrate the importance of using a sufficiently long time horizon analysis when modeling inventory systems subject to supply disruptions. Several publications use singleperiod newsboy models to study supply disruptions, and we show that such models underestimate the risk of supply disruptions ..."
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Cited by 10 (5 self)
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We demonstrate the importance of using a sufficiently long time horizon analysis when modeling inventory systems subject to supply disruptions. Several publications use singleperiod newsboy models to study supply disruptions, and we show that such models underestimate the risk of supply disruptions and generate suboptimal solutions. We examine a firm with an unreliable supplier that is subject to supply yield uncertainty as well as complete supply disruptions. We consider one case where the unreliable supplier is the only supply option, and a second case where a second, reliable (but more expensive) supplier is available. We develop models for both cases to determine the optimal order and reserve quantities. We then compare these results to those found when a singleperiod approximation is used. We demonstrate that a singleperiod approximation causes increases in cost, underutilizes the unreliable supplier, and distorts the order quantities which should be placed with the reliable supplier in the twosupplier case. Moreover, using a singleperiod model can lead to selecting the wrong strategy for mitigating supply risk. Key Words: supply chain disruptions, yield uncertainty, dualsourcing, inventory management 1
Lectures on Stochastic . . .
, 2009
"... The main topic of this book are optimization problems involving uncertain parameters, for which stochastic models are available. Although many ways have been proposed to model uncertain quantities, stochastic models have proved their flexibility and usefulness in diverse areas of science. This is ..."
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Cited by 2 (0 self)
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The main topic of this book are optimization problems involving uncertain parameters, for which stochastic models are available. Although many ways have been proposed to model uncertain quantities, stochastic models have proved their flexibility and usefulness in diverse areas of science. This is mainly due to solid mathematical foundations and theoretical richness of the theory of probability and stochastic processes, and to sound statistical techniques of using real data. Optimization problems involving stochastic models occur in almost all areas of science and engineering, so diverse as telecommunication, medicine, or finance, to name just a few. This stimulates interest in rigorous ways of formulating, analyzing, and solving such problems. Due to the presence of random parameters in the model, the theory combines concepts of the optimization theory, the theory of probability and statistics, and functional analysis. Moreover, in recent years the theory and methods of stochastic programming have undergone major advances. All these factors motivated us to present in an accessible and rigorous form contemporary models and ideas of stochastic programming. We hope that
DYNAMIC PRICING AND REPLENISHMENT IN A PRODUCTIONINVENTORY SYSTEM WITH MARKOVMODULATED DEMAND
, 2004
"... System with MarkovModulated Demand ..."
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Models and Algorithms for Integrated MultiStage Production/Distribution Problems
, 2005
"... We summarize a series of models and results related to the effective integration of production and transportation decision making in a multistage environment. For a deterministic two stage supply chain, we develop and analyze effective optimal algorithms. For continuous time stochastic version of ..."
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We summarize a series of models and results related to the effective integration of production and transportation decision making in a multistage environment. For a deterministic two stage supply chain, we develop and analyze effective optimal algorithms. For continuous time stochastic version of this model, we partially characterize the optimal policy structure, and develop heuristics. For a discrete time stochastic version of this model, we partially characterize the optimal policy structure. Finally, we introduce a model integrating production and transportation outsourcing that we are currently analyzing.
Optimal Pricing and Production Policies of a MaketoStock
, 2007
"... We study the effects of different pricing strategies available to a productioninventory system with capacitated supply, which operates in a fluctuating demand environment. The demand depends on the environment and on the offered price. For such systems, three plausible pricing strategies are invest ..."
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We study the effects of different pricing strategies available to a productioninventory system with capacitated supply, which operates in a fluctuating demand environment. The demand depends on the environment and on the offered price. For such systems, three plausible pricing strategies are investigated: Static pricing, where only one price is used at all times, environmentdependent pricing, where price changes with the environment, and dynamic pricing, where price depends on both the current environment and the stock level. The objective is to find an optimal replenishment and pricing policy under each of these strategies. This paper presents some structural properties of optimal replenishment policies, and a numerical study which compares the performances of these three pricing strategies. 1