Regret in the Newsvendor Model with Partial Information

Perakis, Georgia; Roels, Guillaume

doi:10.1287/opre.1070.0486

Cited by 303 publications

(198 citation statements)

References 43 publications

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“…Another robust approach attempts to minimize the worst-case regret over the distribution family. Some recent works using a minimax regret criterion include Ball and Queyranne (2009), Eren and Maglaras (2006), Perakis and Roels (2008), Levi et al (2011).…”

Section: Literature Reviewmentioning

confidence: 99%

The Data-Driven Newsvendor Problem: New Bounds and Insights

Levi

Perakis

Uichanco

2015

Operations Research

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180

104

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Consider the newsvendor model, but under the assumption that the underlying demand distribution is not known as part of the input. Instead, the only information available is a random, independent sample drawn from the demand distribution. This paper analyzes the sample average approximation (SAA) approach for the data-driven newsvendor problem. We obtain a new analytical bound on the probability that the relative regret of the SAA solution exceeds a threshold. This bound is significantly tighter than existing bounds, and it matches the empirical accuracy of the SAA solution observed in extensive computational experiments.This bound reveals that the demand distribution's weighted mean spread (WMS) affects the accuracy of the SAA heuristic.

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Section: Literature Reviewmentioning

confidence: 99%

The Data-Driven Newsvendor Problem: New Bounds and Insights

Levi

Perakis

Uichanco

2015

Operations Research

Self Cite

180

104

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“…See Scarf [34], Jagannathan [18], and Gallego and Moon [12]. Perakis and Roels [32] present an algorithm for minimizing regrets from not ordering the optimal quantity.…”

Section: Literature Review and Our Contributions Classical Inventorymentioning

confidence: 99%

A Nonparametric Asymptotic Analysis of Inventory Planning with Censored Demand

2009

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We study stochastic inventory planning with lost sales and instantaneous replenishment, where contrary to the classical inventory theory, the knowledge of the demand distribution is not available. Furthermore, we observe only the sales quantity in each period, and lost sales are unobservable, that is, demand data are censored. The manager must make an ordering decision in each period based only on historical sales data. Excess inventory is either perishable or carried over to the next period. In this setting, we propose non-parametric adaptive policies that generate ordering decisions over time. We show that the T -period 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 ). IntroductionThe problem of inventory control and planning has received much interest from practitioners and academics from the early years of operations research. The early literature in this area modeled demand as deterministic and having known quantities, but it soon became apparent that deterministic modeling was often inadequate, and uncertainty needed to be incorporated in modeling future demand. As a result, a majority of the papers on inventory theory during the past fifty years employ stochastic demand models. In these models, future demand is given by a specific exogenous random variable, and the inventory decisions are made with full knowledge of the future demand distribution. In many applications, however, the demand distribution is not known a priori. Even when past data have been collected, the selection of the most appropriate distribution and its parameters remains ambiguous. In the case when excess demand is lost, the information available to the inventory manager is further limited since she does not observe the realized demand but only observes the sales quantity (often referred to as censored demand), which is the smaller of the stocking level and the realized demand. Motivated by these realistic constraints, we develop a non-parametric approach to stochastic inventory planning in the presence of lost sales and censored demand.

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“…However, one major criticism against the maximin approach is that the resulting policies can be too conservative. A less conservative approach, called minimax regret, minimizes the maximum opportunity cost from not making the optimal decision instead (Savage [32]; Perakis and Roels [31]). Due to their second-order nature, closed-form expressions for the optimal bounds have been found for most of these robust models with known mean and variance.…”

Section: Introductionmentioning

confidence: 99%

Asymmetry and Ambiguity in Newsvendor Models

2018

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The traditional decision-making framework for newsvendor models is to assume a distribution of the underlying demand. However, the resulting optimal policy is typically sensitive to the choice of the distribution. A more conservative approach is to assume that the distribution belongs to a set parameterized by a few known moments. An ambiguity-averse newsvendor would choose to maximize the worst-case profit. Most models of this type assume that only the mean and the variance are known, but do not attempt to include asymmetry properties of the distribution. Other recent models address asymmetry by including skewness and kurtosis. However, closed-form expressions on the optimal bounds are difficult to find for such models. In this paper, we propose a framework under which the expectation of a piecewise linear objective function is optimized over a set of distributions with known asymmetry properties. This asymmetry is represented by the first two moments of multiple random variables that result from partitioning the original distribution. In the simplest case, this reduces to semivariance. The optimal bounds can be solved through a second-order cone programming (SOCP) problem. This framework can be applied to the risk-averse and risk-neutral newsvendor problems and option pricing. We provide a closed-form expression for the worst-case newsvendor profit with only mean, variance and semivariance information.

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Regret in the Newsvendor Model with Partial Information

Cited by 303 publications

References 43 publications

The Data-Driven Newsvendor Problem: New Bounds and Insights

The Data-Driven Newsvendor Problem: New Bounds and Insights

A Nonparametric Asymptotic Analysis of Inventory Planning with Censored Demand

Asymmetry and Ambiguity in Newsvendor Models

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