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28
A singleitem inventory model for a nonstationary demand process
 Manufacturing & Service Operations Management
, 1999
"... In this paper, we consider an adaptive basestock policy for a singleitem inventory system, where the demand process is nonstationary. In particular, the demand process is an integrated moving average process of order (0, 1, 1), for which an exponentialweighted moving average provides the optimal ..."
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Cited by 59 (2 self)
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In this paper, we consider an adaptive basestock policy for a singleitem inventory system, where the demand process is nonstationary. In particular, the demand process is an integrated moving average process of order (0, 1, 1), for which an exponentialweighted moving average provides the optimal forecast. For the assumed control policy we characterize the inventory random variable and use this to find the safety stock requirements for the system. From this characterization, we see that the required inventory, both in absolute terms and as it depends on the replenishment leadtime, behaves much differently for this case of nonstationary demand compared with stationary demand. We then show how the singleitem model extends to a multistage, or supplychain context; in particular we see that the demand process for the upstream stage is not only nonstationary but also more variable than that for the downstream stage. We also show that for this model there is no value from letting the upstream stages see the exogenous demand. The paper concludes with some observations about the practical implications of this work.
The Censored Newsvendor and the Optimal Acquisition of Information
 Operations Research
, 1998
"... This paper investigates the effect of demand censoring on the optimal policy in newsvendor inventory models with general parametric demand distributions and unknown parameter values. We show that the newsvendor problem with observable lost sales reduces to a sequence of singleperiod problems while ..."
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Cited by 33 (3 self)
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This paper investigates the effect of demand censoring on the optimal policy in newsvendor inventory models with general parametric demand distributions and unknown parameter values. We show that the newsvendor problem with observable lost sales reduces to a sequence of singleperiod problems while the newsvendor problem with unobservable lost sales requires a dynamic analysis. Using a Bayesian Markov decision process approach we show that the optimal inventory level in the presence of partially observable demand is higher than when demand is completely observed. We explore the economic rationality for this observation and illustrate it with numerical examples. Key words: Inventory, Bayesian Markov decision processes, lost sales, demand estimation, censoring Inspite of the extensive research on inventory models, there still remain some practical issues that have not received due consideration. One of them is demand estimation and its effect on optimal policies. Most results in stocha...
Provably nearoptimal samplingbased policies for stochastic inventory control models
 Proceedings, 38th Annual ACM Symposium on Theory of Computing
, 2006
"... In this paper, we consider two fundamental inventory models, the singleperiod newsvendor problem and its multiperiod extension, but under the assumption that the explicit demand distributions are not known and that the only information available is a set of independent samples drawn from the true ..."
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Cited by 14 (2 self)
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In this paper, we consider two fundamental inventory models, the singleperiod newsvendor problem and its multiperiod extension, but under the assumption that the explicit demand distributions are not known and that the only information available is a set of independent samples drawn from the true distributions. Under the assumption that the demand distributions are given explicitly, these models are wellstudied and relatively straightforward to solve. However, in most reallife scenarios, the true demand distributions are not available or they are too complex to work with. Thus, a samplingdriven algorithmic framework is very attractive, both in practice and in theory. We shall describe how to compute samplingbased policies, that is, policies that are computed based only on observed samples of the demands without any access to, or assumptions on, the true demand distributions. Moreover, we establish bounds on the number of samples required to guarantee that with high probability, the expected cost of the samplingbased policies is arbitrarily close (i.e., with arbitrarily small relative error) compared to the expected cost of the optimal policies which have full access to the demand distributions. The bounds that we develop are general, easy to compute and do not depend at all on the specific demand distributions.
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.
Inventory Control with Unobservable Lost Sales and Bayesian Updates. Working Paper
, 2005
"... We study a finitehorizon lostsales inventory model. The demand distribution is unknown and is dynamically updated based on the previous sales data in a Bayesian fashion. We derive a samplepath representation of the first order optimality condition, which characterizes the key tradeoff of the prob ..."
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Cited by 10 (0 self)
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We study a finitehorizon lostsales inventory model. The demand distribution is unknown and is dynamically updated based on the previous sales data in a Bayesian fashion. We derive a samplepath representation of the first order optimality condition, which characterizes the key tradeoff of the problem. The expression allows us to see why the computation of the optimal policy is difficult and why the myopic solution is not a bound on the optimal solution. It enables us to develop simpler solution bounds and approximations. It also helps us to develop cost bounds as well as cost error bounds of the approximations. Numerical examples indicate that our approximations are most effective for products with short lifecycle. Otherwise, the myopic policy may be a reasonable choice. 1
Tactical Planning Models for Supply Chain Management
 Elvesier Publishers, 2003. OR/MS Handbook on Supply Chain Management: Design, Coordination and Operation
, 2004
"... ..."
Optimization and the price of anarchy in a dynamic newsboy model
 Stochastic Networks, invited session at the INFORMS Annual Meeting
, 2005
"... This paper examines a dynamic version of the newsboy problem in which a decision maker must maintain service capacity from several sources to attempt to meet uncertain demand for a perishable good, subject to the cost of providing sufficient capacity, and penalties for not meeting demand. A complete ..."
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Cited by 7 (3 self)
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This paper examines a dynamic version of the newsboy problem in which a decision maker must maintain service capacity from several sources to attempt to meet uncertain demand for a perishable good, subject to the cost of providing sufficient capacity, and penalties for not meeting demand. A complete characterization of the optimal outcome is obtained when normalized demand is modeled as Brownian motion. The centralized optimal solution is a function of variability in demand, production variables, and the cost of insufficient capacity. A closed form expression is obtained for the unique (state dependent) market clearing prices that allows the decentralized market to sustain the centralized optimal solution. The prices are a nonsmooth function of normalized demand and reserves. Consequently, prices show extreme volatility in the efficient decentralized market outcome. Standard policy designs are examined to improve the behavior of the decentralized market, including price caps and partial decentralization where the buyer owns a portion of the total service capacity. It is shown that these remedies fail: The market outcome in a partially decentralized model is shown to be inefficient even if the buyer owns a substantial portion of the service capacity. Under the presence of a price cap, a market equilibrium, efficient or not, fails to exist under very general conditions.
A dynamic newsboy model for optimal reserve management in electricity markets, Submitted for publication
 SIAM J. Control and Optimization
"... Abstract. This paper examines a dynamic version of the newsboy problem in which a decision maker must maintain service capacity from several sources to meet demand for a perishable good, subject to the cost of providing sufficient capacity, and penalties for not meeting demand. The focus application ..."
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Cited by 7 (4 self)
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Abstract. This paper examines a dynamic version of the newsboy problem in which a decision maker must maintain service capacity from several sources to meet demand for a perishable good, subject to the cost of providing sufficient capacity, and penalties for not meeting demand. The focus application is the realtime operation of an electric power network in which there are multiple sources of power that are distinguished by their cost, as well as their responsiveness in terms of ‘ramp rate’. A complete characterization of the optimal outcome is obtained when normalized demand is modeled as Brownian motion. The optimal policy is affine: It is characterized by affine switching curves in the multidimensional state space. The optimal affine parameters are functions of variability in demand, production variables, and the cost of insufficient capacity.
An Asymptotic Analysis of Inventory Planning with Censored Demand
, 2006
"... We study stochastic inventory planning with lost sales, where contrary to classical inventory theory, the knowledge of the demand distribution is not available a priori. While the manager observes the sales quantities in each period, lost sales are unobservable, i.e., demand data is censored. The de ..."
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Cited by 6 (1 self)
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We study stochastic inventory planning with lost sales, where contrary to classical inventory theory, the knowledge of the demand distribution is not available a priori. While the manager observes the sales quantities in each period, lost sales are unobservable, i.e., demand data is censored. The decision in each period depends only on historical sales data. Excess inventory is either perishable or carried over to the next period. In this setting, we propose nonparametric adaptive policies that generate ordering decisions over time. We show that the Tperiod average expected cost of our policy differs from the benchmark newsvendor cost – the minimum expected cost that would have incurred if the manager had known the underlying demand distribution) – by at most O(1/ T). Computational results show that our policies perform well.