Adaptive Ordering and Pricing for Perishable Products

Burnetas, Apostolos; Smith, Craig E.

doi:10.1287/opre.48.3.436.12437

Cited by 120 publications

(59 citation statements)

References 21 publications

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“…One such approach is based on a variant of a stochastic approximation algorithm that finds the critical fractile of the demand distribution using censored demand samples. Using this approach, Burnetas and Smith [5] develop an adaptive algorithm for ordering and pricing when inventory is perishable. They show that the average profit converges to the optimal, but they do not establish the rate of convergence.…”

Section: Literature Review and Our Contributions Classical Inventory mentioning

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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Section: Literature Review and Our Contributions Classical Inventory mentioning

confidence: 99%

A Nonparametric Asymptotic Analysis of Inventory Planning with Censored Demand

2009

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“…Burnetas and Smith [2] propose a stochastic approximation method for estimating the newsvendor quantile. Godfrey and Powell [5] and Powell et al [18] develop a method of iteratively approximating the convex objective function with piece-wise linear functions.…”

Section: Introductionmentioning

confidence: 99%

An Adaptive Algorithm for Finding the Optimal Base-Stock Policy in Lost Sales Inventory Systems with Censored Demand

et al. 2009

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We consider a periodic-review single-location single-product inventory system with lost sales and positive replenishment lead times. It is well known that the optimal policy does not possess a simple structure. Motivated by recent results showing that base-stock policies perform well in these systems, we study the problem of finding the best base-stock policy in such a system. In contrast to the classical inventory literature, we assume that the manager does not know the demand distribution a priori, but must make the replenishment decision in each period based only on the past sales (censored demand) data. We develop a nonparametric adaptive algorithm that generates a sequence of order-up-to levels whose T -period running average of the inventory holding and lost sales penalty cost converges to the cost of the optimal base-stock policy at the rate of O(1/T 1/3 ). Our analysis is based on recent advances in stochastic online convex optimization and on the uniform ergodicity of Markov chains associated with bases-stock policies.

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“…The basic focus is similar to that of van Ryzin and McGill (2000) insomuch as techniques are proposed to solve classes of problems, but the consequences of incorrect modeling assumptions are not investigated. For examples and references, see Burnetas and Smith (2000) and Carvalho and Puterman (2003).…”

Section: Introductionmentioning

confidence: 99%

Models of the Spiral-Down Effect in Revenue Management

Cooper

Homem-de-Mello

Kleywegt

2006

Operations Research

159

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The spiral-down effect occurs when incorrect assumptions about customer behavior cause high-fare ticket sales, protection levels, and revenues to systematically decrease over time. If an airline decides how many seats to protect for sale at a high fare based on past high-fare sales, while neglecting to account for the fact that availability of low-fare tickets will reduce high-fare sales, then high-fare sales will decrease, resulting in lower future estimates of high-fare demand. This subsequently yields lower protection levels for high-fare tickets, greater availability of low-fare tickets, and even lower high-fare ticket sales. The pattern continues, resulting in a so-called spiral down. We develop a mathematical framework to analyze the process by which airlines forecast demand and optimize booking controls over a sequence of flights. Within the framework, we give conditions under which spiral down occurs.

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Adaptive Ordering and Pricing for Perishable Products

Cited by 120 publications

References 21 publications

A Nonparametric Asymptotic Analysis of Inventory Planning with Censored Demand

A Nonparametric Asymptotic Analysis of Inventory Planning with Censored Demand

An Adaptive Algorithm for Finding the Optimal Base-Stock Policy in Lost Sales Inventory Systems with Censored Demand

Models of the Spiral-Down Effect in Revenue Management

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