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33
Learning algorithms for separable approximations of discrete stochastic optimization problems
 Mathematics of Operations Research
, 2004
"... doi 10.1287/moor.1040.0107 ..."
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The impact of duplicate orders on demand estimation and capacity investment. Management Sci
, 2005
"... Motivated by a $2.2 billion inventory writeoff by Cisco Systems, we investigate how duplicate orders can lead a manufacturer to err in estimating the demand rate and customers ’ sensitivity to delay, and to make faulty decisions about capacity investment. We consider a manufacturer that sells throu ..."
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Cited by 14 (5 self)
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Motivated by a $2.2 billion inventory writeoff by Cisco Systems, we investigate how duplicate orders can lead a manufacturer to err in estimating the demand rate and customers ’ sensitivity to delay, and to make faulty decisions about capacity investment. We consider a manufacturer that sells through two distributors. If a customer finds that his distributor is out of stock, then he will sometimes seek to make a purchase from the other distributor; if the latter is also out of stock, the customer will order from both distributors. When his order is filled by one of the distributors, the customer cancels any duplicate orders. Furthermore, the customer cancels all of his outstanding orders after a random period of time. Assuming that the manufacturer is unaware of duplicate orders, we prove that she will overestimate both the demand rate and the cancellation rate. Surprisingly, failure to account for duplicate orders can cause shortterm underinvestment in capacity. However, in longterm equilibrium under stable demand conditions the manufacturer overinvests in capacity. Our results suggest that Cisco’s writeoff was caused by estimation errors and cannot be blamed entirely on the economic downturn. Finally, we provide some guidance on estimation in the presence of double orders. Key words: maximumlikelihood estimation; duplicate ordering; distribution channels; queueing systems; reneging History: Accepted by William S. Lovejoy, operations and supply chain management; received April 19, 2002. This paper was with the authors 3 1 months for 2 revisions. 2 1.
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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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.
Dynamic Inventory Management with Learning About the Demand Distribution and Substitution Probability
, 2008
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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
Sequential bayesoptimal policies for multiple comparions with a control
, 2012
"... We consider the problem of efficiently allocating simulation effort to determine which of several simulated systems have mean performance exceeding a known threshold. This determination is known as multiple comparisons with a control. Within a Bayesian formulation, the optimal fully sequential polic ..."
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Cited by 8 (5 self)
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We consider the problem of efficiently allocating simulation effort to determine which of several simulated systems have mean performance exceeding a known threshold. This determination is known as multiple comparisons with a control. Within a Bayesian formulation, the optimal fully sequential policy for allocating simulation effort is the solution to a dynamic program. We show that this dynamic program can be solved efficiently, providing a tractable way to compute the Bayesoptimal policy. The solution uses techniques from optimal stopping and multiarmed bandits. We then present further theoretical results characterizing this Bayesoptimal policy, compare it numerically to several approximate policies, and apply it to an application in ambulance positioning. Key words: multiple comparisons with a control; sequential experimental design; dynamic programming; Bayesian statistics; value of information. 1.
Bounds and heuristics for optimal Bayesian inventory control with unobserved lost sales
, 2009
"... In most retail environments, when inventory runs out, the unmet demand is lost and not observed. The sales data are effectively censored by the inventory level. Factoring this censored data effect into demand estimation and inventory control decision makes the problem difficult to solve. In this pap ..."
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Cited by 7 (2 self)
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In most retail environments, when inventory runs out, the unmet demand is lost and not observed. The sales data are effectively censored by the inventory level. Factoring this censored data effect into demand estimation and inventory control decision makes the problem difficult to solve. In this paper, we focus on developing bounds and heuristics for this problem. Specifically, we consider a finitehorizon inventory control problem for a nonperishable product with unobserved lost sales and a demand distribution having an unknown parameter. The parameter is estimated sequentially by the Bayesian updating method. We first derive a set of solution upper bounds that work for all prior and demand distributions. For a fairly general monotone likelihoodratio distribution family, we derive relaxed but easily computable lower and upper bounds along an arbitrary sample path. We then propose two heuristics. The first heuristic is derived from the solution bound results. Computing this heuristic solution only requires the evaluation of the objective function in the observed lostsales case. The second heuristic is based on the approximation of the firstorder condition. We combine the firstorder derivatives of the simpler observed lostsales and perishableinventory models to obtain the approximation. For the latter case, we obtain a recursive formula that simplifies the computation. Finally, we conduct an extensive numerical study to evaluate and compare the bounds and heuristics. The numerical results indicate that both heuristics perform very well. They outperform the myopicpolicies by a wide margin.
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.